Modelling and Analysing Moving Objects and Travelling Subjects

Modelling and Analysing

Moving Objects and Travelling Subjects

Bridging theory and practice

Matthias Delafontaine

To the memory of my grandfather Paul

Copyright © Matthias Delafontaine, Department of Geography, Faculty of Sciences, Ghent

University, 2011. All rights reserved. No part of this publication may be reproduced, stored

in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical,

photocopying, recording, or otherwise, without permission in writing from the proprietor(s).

ISBN: 978-94-90695620

Legal deposit: D/2011/12.134/12

NUR: 755/905/983/984

The research reported in this dissertation was conducted at the CartoGIS research unit,

Department of Geography, Faculty of Sciences, Ghent University, and funded by the

Research Foundation – Flanders.

Faculty of Sciences

Department of Geography

Modelling and Analysing

Moving Objects and Travelling Subjects

Bridging theory and practice

Dissertation submitted in accordance with the requirements for the degree of

Doctor of Sciences : Geography

Modelleren en Analyseren

van Bewegende Objecten en Personen die Zich Verplaatsen

Een brug tussen theorie en praktijk

Proefschrift aangeboden tot het behalen van de graad van

Doctor in de Wetenschappen : Geografie

by / door

Matthias Delafontaine

Supervisors

Prof. Dr. Nico Van de Weghe

Ghent University

Dr. Tijs Neutens

Ghent University

Members of the Reading Committee

Prof. Dr. Robert Weibel

University of Zurich

Prof. Dr. Roland Billen

University of Liege

Prof. Dr. Frank Witlox

Ghent University

Remaining members of the Examination Committee

Prof. Dr. Anthony G. Cohn

University of Leeds

Prof. Dr. Christophe Claramunt

Naval Academy Research Institute

Prof. Dr. Ben Derudder

Ghent University

Prof. Dr. Philippe De Maeyer

Ghent University

“And crawling on this planet's face, some insects called the human race.

Lost in time. And lost in space.” (The Rocky Horror Picture Show)

Table of contents I

Table of contents

Preface ................................................................................................................. VII

List of figures ......................................................................................................... IX

List of tables ......................................................................................................... XIII

List of algorithms .................................................................................................. XV

1 Introduction ..................................................................................................... 1

1.1 Background and motivation ....................................................................................... 1

1.2 Rationale and synopsis ............................................................................................... 4

References ............................................................................................................................ 10

Part I – Moving Objects ................................................................................. 19

2 A Qualitative Trajectory Calculus to reason about moving point objects ......... 21

2.1 Introduction .............................................................................................................. 21

2.2 Background ............................................................................................................... 22

2.3 The Qualitative Trajectory Calculus ......................................................................... 22

2.3.1 Simplifications ...................................................................................................... 22

2.3.2 Continuity, conceptual neighbours, and transitions ............................................ 23

2.3.3 Types of QTC ......................................................................................................... 24

2.4 QTC – Basic (QTCB) ................................................................................................... 25

2.5 QTC – Double Cross (QTCC) ...................................................................................... 27

2.6 Representing and reasoning with QTC ..................................................................... 31

2.6.1 Conceptual neighbourhood diagrams .................................................................. 31

2.6.2 Composition tables ............................................................................................... 33

2.6.3 Incomplete knowledge ......................................................................................... 36

2.7 Extending QTC .......................................................................................................... 37

2.7.1 Multiple MPOs ...................................................................................................... 38

2.7.2 Multiple time points and intervals ....................................................................... 38

2.7.3 Multiple topological relations .............................................................................. 38

2.8 Example case ............................................................................................................ 39

2.9 Future research directions ....................................................................................... 41

2.10 Conclusion ................................................................................................................ 41

References ............................................................................................................................ 42

3 Inferring additional knowledge from QTCN relations ....................................... 45

3.1 Introduction .............................................................................................................. 45

3.2 Qualitative versus quantitative questions ............................................................... 46


II

3.4 The Qualitative Trajectory Calculus on Networks .................................................... 49

3.4.1 Definitions and restrictions concerning networks and moving objects ............... 49

3.4.2 Definition of QTCN relations ................................................................................. 53

3.5 Composition ............................................................................................................. 56

3.5.1 Composition of QTCN relations ............................................................................. 57

3.5.2 Temporal Constraints ........................................................................................... 57

3.5.3 Spatial Constraints ............................................................................................... 58

3.6 Transforming QTCN into the Relative Trajectory Calculus on Networks .................. 60

3.7 Discussion ................................................................................................................. 65

3.7.1 A Police/Gangster Example .................................................................................. 65

3.7.2 A Collision Avoidance Application ........................................................................ 67

3.8 Conclusions and future work ................................................................................... 68

References ............................................................................................................................ 69

4 Qualitative relations between moving objects in a network changing its

topological relations ............................................................................................. 73

4.1 Introduction .............................................................................................................. 73


4.3 The Qualitative Trajectory Calculus on Networks .................................................... 74

4.3.1 Definition .............................................................................................................. 74

4.3.2 Relations in QTCN .................................................................................................. 76

4.3.3 Transitions in QTCN ............................................................................................... 77

4.3.4 Theory of Dominance ........................................................................................... 79

4.4 Topological changes in networks: QTCDN’ ................................................................ 80

4.4.1 Topological Change and Dynamic Networks ........................................................ 80

4.4.2 Relations in QTCDN’ ............................................................................................... 81

4.4.3 Transitions in QTCDN’ ............................................................................................. 81

4.5 Conclusions and Future work ................................................................................... 82

References ............................................................................................................................ 85

5 Implementing a qualitative calculus to analyse moving point objects ............. 87

5.1 Introduction .............................................................................................................. 87

5.2 The Qualitative Trajectory Calculus (QTC) ............................................................... 89

5.2.1 Types of QTC ......................................................................................................... 89

5.2.2 Unconstrained movement .................................................................................... 90

5.3 A QTC-based information system ............................................................................ 92

5.3.1 Trajectory representations ................................................................................... 92

5.3.2 Conceptual model ................................................................................................. 92

5.3.3 Implementation prototype ................................................................................... 94

5.4 Case studies .............................................................................................................. 97

Table of contents III

5.4.1 Cars on a street .................................................................................................... 97

5.4.2 Squash rally ........................................................................................................ 100

5.5 Discussion ............................................................................................................... 101

5.6 Conclusions and outlook ........................................................................................ 104

References .......................................................................................................................... 105

Appendix A ......................................................................................................................... 109

Appendix B ......................................................................................................................... 110

6 Modelling moving objects in geospatial sketch maps ................................... 113

6.1 Introduction ............................................................................................................ 113

6.2 Extended Sketch Maps ........................................................................................... 114

6.3 Moving objects in geospatial sketch maps ............................................................ 116

6.3.1 Moving point objects and geospatial lifelines .................................................... 116

6.3.2 Lifeline glyphs ..................................................................................................... 118

6.3.3 Typology of lifeline representations ................................................................... 121

6.3.4 Multiple lifelines ................................................................................................. 121

6.4 Conclusions and outlooks ....................................................................................... 122

References .......................................................................................................................... 123

Part II – Travelling subjects .......................................................................... 125

7 Analysing spatiotemporal sequences in Bluetooth tracking data .................. 127

7.1 Introduction ............................................................................................................ 127

7.2 Sequence Alignment Methods ............................................................................... 129

7.2.1 Background......................................................................................................... 129

7.2.2 Methodology ...................................................................................................... 129

7.3 Case study .............................................................................................................. 131

7.3.1 Data collection .................................................................................................... 131

7.3.2 Data preparation ................................................................................................ 133

7.3.3 Sequence alignment ........................................................................................... 135

7.3.4 Results ................................................................................................................ 136

7.4 Conclusions ............................................................................................................. 140

References .......................................................................................................................... 141

8 Modelling potential movement in constrained travel environments using rough

space–time prisms .............................................................................................. 145

8.1 Introduction ............................................................................................................ 145

8.2 Background ............................................................................................................. 147

8.3 A space-time prism in an unconstrained travel environment ............................... 149

8.4 A rough space-time prism in an unconstrained travel environment ..................... 151

8.5 A space-time prism in an obstacle-constrained travel environment ..................... 153

IV

8.6 A rough space-time prism in an obstacle-constrained travel environment .......... 159

8.6.1 Combination of approaches ............................................................................... 159

8.6.2 Algorithm ............................................................................................................ 161

8.6.3 Example .............................................................................................................. 163

8.7 Conclusions ............................................................................................................. 166

References .......................................................................................................................... 168

9 Reconciling place-based and person-based accessibility: a GIS toolkit .......... 171

9.1 Introduction ............................................................................................................ 171

9.2 Related tools........................................................................................................... 173

9.3 PrismMapper .......................................................................................................... 175

9.3.1 Accessibility measures ........................................................................................ 175

9.3.2 System ................................................................................................................ 179

9.4 Example case .......................................................................................................... 183

9.5 Conclusion .............................................................................................................. 190

References .......................................................................................................................... 191

10 The relationship between opening hours and accessibility of public service

delivery ............................................................................................................... 195

10.1 Introduction ............................................................................................................ 195

10.2 Space-time demands, opening hours and accessibility ......................................... 197

10.3 Method ................................................................................................................... 199

10.3.1 Measuring accessibility .................................................................................. 199

10.3.2 Optimising opening hours in terms of accessibility ........................................ 202

10.4 Case study .............................................................................................................. 206

10.4.1 Data ................................................................................................................ 206

10.4.2 Data preparation ............................................................................................ 211

10.4.3 Results ............................................................................................................ 212

10.5 Conclusion and avenues for future work ............................................................... 217

References .......................................................................................................................... 219

11 The impact of opening hours on the equity of individual space-time

accessibility ......................................................................................................... 225

11.1 Introduction ............................................................................................................ 225

11.2 Method ................................................................................................................... 227

11.2.1 Scheduling procedure ..................................................................................... 227

11.2.2 Equity approaches .......................................................................................... 228

11.3 Case study .............................................................................................................. 229

11.3.1 Input data ....................................................................................................... 230

11.3.2 Evaluation functions and computation .......................................................... 236

Table of contents V

11.3.3 Results ............................................................................................................ 238

11.4 Conclusion .............................................................................................................. 249

References .......................................................................................................................... 250

12 Discussion and conclusions ....................................................................... 253

References .......................................................................................................................... 263

Samenvatting (Dutch summary) .......................................................................... 268

References .......................................................................................................................... 271

Biographical sketch ............................................................................................. 273

Preface VII

Preface

Writing a doctoral dissertation has been a long journey, and it is true: you can never finish a

PhD, you just quit working on it. Nevertheless, the compilation of four years of intense

endeavour and engagement somehow releases me and offers me the opportunity to look

back. Rather than as a static collection of scientific achievements, my dissertation appears to

me as a chronology reflecting in many respects the evolution that my research and the way I

dealt with it have gone through. In that sense, I am elated by the impression of having

acquired and developed certain skills that are much more universal than the sheer context

of research.

Beyond my personal movement, much has happened and changed in my environment over

the course of this study. Of these events, probably the most drastic one has been the loss of

my dear grandfather Paul Hubert, to whom I owe great respect. To heartily acknowledge

him, I have dedicated this work to his fond memory.

Pursuing a PhD is often regarded as a lonesome and isolating experience. I do recognize this

perception and I must admit that numerous solitary activities may have enabled me to find

the necessary reflection. Yet, I could by no means have carried out this research without the

support of many others. Whereas it would lead me too far to mention each name

exhaustively, I would like to express my sincere appreciation to all the people that have

thereby assisted me in any respect. Let me explicitly address some of them.

To begin with, I wish to thank my supervisors Nico Van de Weghe and Tijs Neutens for their

admirable academic guidance and for their willingness to be always available for me. Nico

Van de Weghe was the person who picked me up after graduating in geography and

convinced me to apply for a doctoral grant. I have come to know him as a reliable, pure and

devoted scientist. I am grateful to him for giving me the opportunity to conduct doctoral

research and to offer me the necessary academic freedom. I greatly appreciate his openness

to discuss and explore fresh ideas and his courage to face novel research challenges.

I also owe much gratitude to my other supervisor, Tijs Neutens. He has been the person with

the unparalleled ability to constantly motivate and inspire me, even in the more awkward

circumstances. I highly commend his great enthusiasm, solidity and diligence, but also his

fine research skills and abundant sense of humour which have made working with him a

great pleasure.

Furthermore, I am indebted to Anthony Cohn for his genuine interest in and contribution to

this research. Our fruitful collaboration has benefited from his kind and honest attitude, his

constructive and discerning comments, and his excellent academic advice.

VIII

In addition, I would like to thank my former academic guide and colleague Peter Bogaert for

his obligingness, open-hearted support and contribution to this work. My grateful

acknowledgment goes to five other contributors as well: thank you Tim Schwanen, Philippe

De Maeyer, Frank Witlox, Mathias Versichele, and Hossein Chavoshi.

Besides the already named, my deep appreciation further extends to other colleagues at the

Department of Geography at Ghent University – especially to our matchless secretary Helga

Vermeulen and to my colleague assistants. Moreover, I gratefully recognize the Research

Foundation – Flanders for funding this research.

Beyond the academic context, I have been strongly supported by my friends and family.

Special thanks to my friends for the many gorgeous and memorable moments of distraction

that gave me precious time to breath and kept my mind and – to a lesser extent also my

body – in good shape.

The most unconditional and all-embracing help and assistance come from my family. Thanks

ever so much to my grandmother Germaine, my parents Ann and Joris, Martine and Hendrik,

my sisters and brothers Ruth and Bram, Pieter and Kimberly.

Last but not least, I must acknowledge my fiancée and best friend. Lien, thanks awfully for

taking care of me and offering me your unqualified love, encouragement and understanding.

I’ll cherish our wonderful years in Ghent as a dear memory and I look forward to marrying

you and continuing our life in Torhout.

Ghent, March 15, 2011.

List of figures IX

List of figures

Figure 2.1 – Simplification in QTC of a real-life situation (a) by taking cumulatively account of

the relational simplification (b), the object simplification (c), and the temporal

simplification (d) (simple arrows for trajectories, double arrows for instantaneous

velocity vectors). .......................................................................................................... 23

Figure 2.2 – Two MPOs represented in a typical two-dimensional QTCB (a), QTCC (b), and

QTCN (c) setting. The frame of spatial reference is represented by the dashed line... 25

Figure 2.3 – QTCB1 (a), and QTCB2 (b) relation icons. ............................................................... 27

Figure 2.4 – Different use of the double cross in the Double Cross Calculus (Galton 2001) (a),

and the QTCC calculus (b). ............................................................................................ 28

Figure 2.5 – QTCC1 relation icons. ............................................................................................. 29

Figure 2.6 – QTCC2 relations and the minimal number of spatial dimensions supporting them:

respectively the dotted, dashed, and straight boundaries for one, two, and three

dimensions.................................................................................................................... 30

Figure 2.7 – CNDs for QTCB1 in n-dimensional space (a), for QTCB2 in a one-dimensional space

(b), and for QTCB2 in a two- or higher-dimensional space (c). The straight, dashed and

dotted lines respectively represent the conceptual distances one, two and three. ... 31

Figure 2.8 – CND for QTCC1 in a two-or higher-dimensional space. Links have been gray-

shaded according to the conceptual distance between the adjacent relations. ......... 32

Figure 2.9 – Configuration of two cars k and l at sample time stamps during an overtake

event. ............................................................................................................................ 40

Figure 3.1 – Bifurcating (a) and non-bifurcating (b) shortest paths. ....................................... 52

Figure 3.2 – A shortest path omitting node pass event. ......................................................... 52

Figure 3.3 – 57 Canonical cases for QTCN at level 2. ................................................................ 55

Figure 3.4 – Animations for the composition of (+ −) and (− 0); a movement arrow next to

an object indicates that the object is passing a node. ................................................. 57

Figure 3.5 – Possible relative movement configurations in QTCN for R1(k, l) R2(l, m) where

m lies on the simple shortest path between k and l and none of the objects is located

at a node. ...................................................................................................................... 59

Figure 3.6 – Possible relative movement configurations in QTCN for R1(k, l) R2(l, m) where k

lies on the simple shortest path between m and l and none of the objects is located at

a node. .......................................................................................................................... 60

Figure 3.7 – A transition in QTCN from (− 0 +) via (0 0 +) to (+ 0 +). ............................ 64

Figure 3.8 – Examples of transformations from QTCB to RTC. ................................................. 65

Figure 3.9 – Simplified animation of three policemen chasing a gangster. ............................. 66

Figure 3.10 – Two scenes without collision danger for two moving objects. .......................... 67

Figure 4.1 – Speed Change Event. ............................................................................................ 78

Figure 4.2 – Node Pass Event. .................................................................................................. 78

X

Figure 4.3 – Continuous Shortest Path Change Event. ............................................................ 78

Figure 4.4 – The CND of QTCN. ................................................................................................. 79

Figure 4.5 – Discontinuous Shortest Path Change Event. ........................................................ 82

Figure 4.6 – Transition in QTCDN’ due to a combination of a Discontinuous Shortest Path

Change Event with a Node Pass Event. ........................................................................ 82

Figure 4.7 – Possible QTCDN’ transitions due to a Discontinuous Shortest Path Change Event

(combined and/or otherwise) (a) and due to the combination of a Discontinuous

Shortest Path Change Event with a Speed Change Event (b)....................................... 83

Figure 4.8 – Possible QTCDN’ transitions due to a combination of a Discontinuous Shortest

Path Change Event with a Node Pass Event or (exclusive) with a Continuous Shortest

Path Change Event........................................................................................................ 83

Figure 4.9 – Possible QTCDN’ transitions due to the combination of a Speed Change Event

with a combined Discontinuous Shortest Path Change Event (a) and due to the

combination of a Speed Change Event with the combination of a Discontinuous

Shortest Path Change Event and a Node Pass Event or (exclusive) a Continuous

Shortest Path Change Event (b). .................................................................................. 84

Figure 5.1 – Two MPOs represented in a typical QTCB (a), QTCC (b), and QTCN (c) setting. The

frame of spatial reference is represented by the dashed line. .................................... 89

Figure 5.2 – Properties of two MPOs k and l at a time instant t. ............................................. 90

Figure 5.3 – UML class diagram for a QTC-based information system .................................... 93

Figure 5.4 – A continuous MPO trajectory (a) and a representation of it according to

Assumption 5.1 with fixes (crosses) per second (b). .................................................... 95

Figure 5.5 – Schematic sketch of the study area. .................................................................... 97

Figure 5.6 – Duration (gray bars) and frequency (black bars) for 24 fourth order simple

permutable patterns in QTC-C22. .............................................................................. 101

Figure 5.7 – Trajectories of two objects k and l during a time interval for two situations (A

and B) according to two representations: realistic representation (a), (c);

representation satisfying Assumptions 5.1-5.3 (b), (d). Crosses represent fixes. ..... 103

Figure 6.1 – ER diagram of the extended sketch map ontology. ........................................... 116

Figure 6.3 – Map of a geospatial lifeline of a butterfly moving from A to B, passing flowers on

its way (own illustration after (Laube 2005)). ............................................................ 117

Figure 6.2 – Single-stroke glyph drawn in CogSketch (Forbus et al. 2008). ........................... 117

Figure 6.4 – A Shrewd Sketch Interpretation and Simulation Tool (ASSIST) (Davis 2002). ... 118

Figure 6.5 – Sketch map representations of the butterfly lifeline in Figure 6.3: explicit single-

stroke lifeline glyph (a), explicit multi-stroke lifeline glyph (b), explicit multi-stroke

lifeline glyph (c), implicit representation by means of six flower glyphs and four arrow

glyphs. ......................................................................................................................... 119

Figure 6.6 – Typology of lifeline representations in geospatial sketch maps. ....................... 121

Figure 7.1 – Pairwise alignment. ............................................................................................ 130

List of figures XI

Figure 7.2 – Schematic map of Flanders Expo with indication of entrances and exits for

visitors (arrows), exhibition halls (H1-H8, black rectangles), and Bluetooth nodes (A-T,

x-marks) with 20m radio range (black circles). .......................................................... 132

Figure 7.3 – Distribution of Bluetooth device classes across observed devices .................... 133

Figure 7.4 – Histogram of observed days per device ............................................................. 133

Figure 7.5 – Histogram of device-day duration. ..................................................................... 133

Figure 7.6 – Extract of transcoded Bluetooth sequences. ..................................................... 135

Figure 7.7 – Sequence alignment scoring matrix. .................................................................. 136

Figure 7.8 – Multiple alignment guide tree with clusters and subclusters labeled at their root

node. ........................................................................................................................... 137

Figure 7.9 – Extract of the sorted and colour coded multiple alignment. ............................. 138

Figure 8.1 – Space-time prism obtained from the intersection of a forward cone and a

backward cone. .......................................................................................................... 150

Figure 8.2 – An uncertain space-time prism modelled by its lower (grey), and upper (black

outlines) approximation. ............................................................................................ 153

Figure 8.3 – Travel environment constrained by university buildings A, B, and C. ............... 154

Figure 8.4 – Shortest paths (black lines) from the origin (big dot) to all obstacle vertices

(small dots). ................................................................................................................ 156

Figure 8.5 – Shortest paths (black lines) from the destination (big dot) to all obstacle vertices

(small dots). ................................................................................................................ 156

Figure 8.6 – Parent forward reachability body (grey) with indication of the parent vertex

(black dot) and the spatial extrusion zones (black outlines). ..................................... 158

Figure 8.7 – Parent backward reachability body (grey) with indication of the parent vertex

(black dot) and the spatial extrusion zones (black outlines). ..................................... 159

Figure 8.8 – Obstacle-constrained space-time prism (grey) with indication of obstacles

(black). ........................................................................................................................ 160

Figure 8.9 – Obstacle-constrained lower space-time prism (grey) with indication of obstacles

(black). ........................................................................................................................ 165

Figure 8.10 – Obstacle-constrained upper space-time prism (grey) with indication of

obstacles (black). ........................................................................................................ 165

Figure 8.11 – Cross section through time of lower (dark grey) and upper (light grey) prisms

along the axis origin (o) – destination (d), with indication of vertical obstacle

extrusions (white rectangles). .................................................................................... 166

Figure 9.1 – Space-time prism and related concepts. ............................................................ 176

Figure 9.2 – Cross section through space-time of a STP (left) and a RSTP (right). ................ 177

Figure 9.3 – PrismMapper system architecture. .................................................................... 179

Figure 9.4 – PrismMapper workflow. ..................................................................................... 182

Figure 9.5 – PrismMapper main application window. ........................................................... 183

Figure 9.6 – Public libraries in Ghent (Belgium). .................................................................... 184

Figure 9.7 – Map of ACCESS on Monday. ............................................................................... 185

XII

Figure 9.8 – Map of ACCESS on Tuesday. ............................................................................... 185

Figure 9.9 – Map of CUMF on Monday. ................................................................................. 186

Figure 9.10 – Map of CUMF on Tuesday. ............................................................................... 186

Figure 9.11 – Map of MINT on Monday. ................................................................................ 187

Figure 9.12 – Map of MINT on Tuesday. ................................................................................ 187

Figure 9.13 – Map of MINTF on Monday. .............................................................................. 188

Figure 9.14 – Map of MINTF on Tuesday. .............................................................................. 188

Figure 9.15 – Map of MAXD on Monday. ............................................................................... 189

Figure 9.16 – Map of MAXD on Tuesday. ............................................................................... 189

Figure 10.1 – Cross section through space (horizontal axis) and time (vertical axis) of the

space-time prism (grey) between fixed activities xj and xj+1 of an individual i, with the

indication of the PAW with respect to the opening hour interval hk of service facility f.

.................................................................................................................................... 200

Figure 10.2 – Study area and sampled households. .............................................................. 207

Figure 10.3 – Spatial distribution of government offices. ..................................................... 207

Figure 10.4 – Estimation of distance decay parameters. ....................................................... 211

Figure 10.5 – Total accessibility for all 900 optimal regimes with indication of the current

regime. ........................................................................................................................ 213

Figure 11.1 – Public libraries in Ghent. .................................................................................. 230

Figure 11.2 – Sampled households and population density in Ghent. .................................. 234

Figure 11.3 – Composition of the lower and upper halves in terms of employment status. 238

Figure 11.4 – Box-and-Whisker diagrams of the accessibility level per regime. ................... 247

Figure 11.5 – Theil index of the accessibility level per regime. ............................................. 248

Figure 11.6 – Box-and-Whisker diagrams per regime for the lower (left) and upper (right)

halves of the population. ............................................................................................ 248

List of tables XIII

List of tables

Table 1.1 – Manuscripts included in the dissertation. ............................................................... 5

Table 2.1 – The number of base relations, transitions, theoretical combinations of base

relations, and the ratio transitions / theoretical combinations for the Basic and

Double Cross QTC calculi. ............................................................................................. 33

Table 2.2 – CT for QTCB1 in a one-dimensional space. ............................................................. 34

Table 2.3 – CT for the speed constraint. .................................................................................. 35

Table 2.4 – CRT for QTCC1 in a two-dimensional space. ........................................................... 36

Table 2.5 – Intersection of coarse solutions to obtain fine knowledge, with U0 = U \{0}. ...... 37

Table 2.6 - QTCB1 matrix for four MPOs k, l, m, and n at time t. .............................................. 38

Table 2.7 – Trajectory sample points of two cars k and l during an overtake event. .............. 39

Table 3.1 – Composition table for QTCN at level 1 restricted to relations lasting over time

intervals; A0 and B0 stand for the set {−, +}. ................................................................. 58

Table 3.2 – Composition table for relative movement in QTCN, for R1(k, l) R2(l, m) where m

lies on the simple shortest path between k and l and none of the objects is located at

a node. .......................................................................................................................... 59

Table 3.3 – Composition table for relative movement in QTCN, for R1(k, l) R2(l, m) where k

lies on the simple shortest path between m and l and none of the objects is located at

a node. .......................................................................................................................... 60

Table 3.4 – Transformations from all QTCN canonical cases to RTCN relations. ...................... 64

Table 3.5 – Transformations from QTCN into RTCN relations. .................................................. 65

Table 3.6 – Composition results inferred over [t1, t3] due to spatial and temporal constraints.

...................................................................................................................................... 66

Table 5.1 – Relation syntax for QTCB and QTCC subtypes. ....................................................... 92

Table 5.2 – Transition table for QTC relation symbols at transition instant t ......................... 96

Table 5.3 – Summary of QTC-B21 relations with their cumulative instant, interval, and total

frequencies, and duration for 503 car pairs. ................................................................ 98


frequencies, and duration for 503 car pairs. ................................................................ 99

Table 5.5 – Complete sequence, transition time and duration of QTC-C21 relations between

two squash opponents during a rally lasting 37 s. ..................................................... 112

Table 6.1. – Export of spatial and temporal ink of the stroke in Fig. 2 as a set of timestamped

polyline vertices. ......................................................................................................... 117

Table 7.1 – Number of members and common patterns per cluster. Pattern episodes are

colour coded to hall location and annotated with hall numbers or node characters.

Hollow episode symbols represent episodes at one of the eight exhibition halls. ... 139

Table 7.2 – Median (top) and average (bottom) sequence per cluster. ................................ 140

Table 8.1 – Space-time prism volumes in m².s according to four different scenarios. ......... 164

XIV

Table 10.1 – Locational benefit calculation example ............................................................. 202

Table 10.2 – Current regime of opening hours for the government offices in Ghent (1-15). 208

Table 10.3 – Congestion factor according to day type, day time and road class. ................. 210

Table 10.4 – Optimal 405-hour regime. ................................................................................. 214

Table 10.5 – Contiguous sub-optimal 405-hour regime. ....................................................... 216

Table 11.1 – Library collection size (2010) and attractiveness estimate. .............................. 231

Table 11.2 – Opening hours of public libraries in Ghent ....................................................... 231

Table 11.3 – Utilitarian regime of 209 opening hours, with indication of the allocation order

of each hour in the scheduling procedure. Allocated hours are gray-scaled according

to an equal interval classification into five classes of the allocation order. .............. 240

Table 11.4 – Egalitarian regime of 209 opening hours, with indication of the allocation order



Table 11.5 – Distributive regime of 209 opening hours, with indication of the allocation order



Table 12.1 – Main and application-oriented contributions. .................................................. 254

List of algorithms XV

List of algorithms

Algorithm 8.1 – Main algorithm for computation of rough obstacle-constrained space-time

prisms. ........................................................................................................................ 162

Algorithm 10.1 – Computational procedure to determine the optimal n-MOI regime. ....... 203

Algorithm 10.2 – Computational procedure to determine the (sub)optimal connected n-MOI

regime. ........................................................................................................................ 205

Algorithm 11.1 – Iterative scheduling procedure. ................................................................. 227

Introduction 1

1 Introduction

1.1 Background and motivation

The act of moving through geographical space takes an essential and inherent part in the

daily life of human beings, animals, goods, and data. The rationale that motion is a

fundamental and omnipresent phenomenon which by definition relates space to time –

which in turn equals capital – feeds a general and everlasting scientific interest in modelling

and analysing moving entities. Moving objects and travelling subjects therefore constitute a

principal unit of analysis in many major domains of both theoretical and applied scientific

research, including artificial intelligence, behavioural sciences and ethology, geographical

information science (GIScience), knowledge representation, robotics, sports science, and

transportation and operations research. This scientific versatility has produced a broad

variety of theories, methodologies, applications, and technologies to collect, explore,

represent, reason about, analyse and extract information from data about moving objects.

This dissertation intends to contribute to these scientific developments – those in GIScience

in particular – with the implicit aim to close the gap between theory and practice by

implementing fundamental theoretical knowledge into practicable applications.

Over the past decades, technological evolutions have importantly re-established the topic of

moving objects as an active and even cutting-edge research issue. First of all, the

development of increasingly advanced means of transport has triggered the movement of

increasing volumes at increasing speeds over increasing distances. Second, major advances

have been made in technologies for positioning and tracking moving objects. The

establishment of satellite navigation systems in the 1970s, or rather the public disclosure of

the use of the Global Positioning System (GPS) in 1983, have been milestones in the

evolution of tracking systems enabling the collection of detailed trajectory data. They

heralded a worldwide production and distribution of mobile position-aware devices able to

determine and store their trajectories over time. GPS units are nowadays commonly

integrated in navigation systems of motorised vehicles as well as in portable appliances such

as smart phones. Apart from satellite navigation systems, other tracking technologies have

recently arisen, some of which complement the capabilities of GPS tracking. These include,

among others, video surveillance systems, mobile positioning systems, wireless tracking

systems, and radio-frequency identification (RFID). Third, along with the progress in tracking

and positioning systems, rapid advances have been made in information and communication

technology (ICT) in general, which support information systems to store, manipulate,

process, query and communicate increasingly larger data volumes. In particular, the

emergence and democratisation of geographical information systems (GIS) capable of

handling spatiotemporal information has been significant in this respect.

2 Chapter 1

This dissertation fits in the broad scope of GIScience. As for geography, geographical

information and GIS1, GIScience has been defined in many different ways. According to

Goodchild (2010), who initiated the term (Goodchild 1992), perhaps the most

comprehensive and meanwhile fairly succinct definition was published by Mark (2003, p. 1-

2) and adopted by the University Consortium for Geographic Information Science (UCGIS):

“The development and use of theories, methods, technology, and data for understanding

geographic processes, relationships, and patterns.” GIScience is generally recognised as the

science behind GISs, which can be described as information systems that integrate

hardware, software, and data for capturing, managing, analysing and displaying geographical

information (i.e. information with a geographical reference). Research in GIScience

concerning moving objects has, given the spatiotemporal nature of motion, followed a more

general and long-lasting research trend addressing the incorporation and exploration of the

temporal component of geospatial information, in order to support time-integrative or

genuine spatio-temporal GISs (Langran 1993, Peuquet 1994, Raper 2000, Ott & Swiaczny

2001). This evolution has been characterised by a major shift in the perception of

geoinformation as dynamic information – sometimes referred to as geo-temporal

information (O'Connor, Zerger & Itami 2005) – rather than a collection of static facts with a

fixed geospatial extent as represented through traditional maps. It has been generally

acknowledged that the modelling of time-dependent geographical information is unique to

GIS and therefore takes an integral part in GIScience which cuts across most of its other

topics (Goodchild 1992, Goodchild 2004, Mark 2003). In spite of the community’s consensus

on the important role of time for geographic information handling, the development of true

spatiotemporal GISs has progressed slowly (Laube 2005) and even continues today.

Together with the growing capabilities to collect data about moving objects, the integration

of time has initiated another vital shift in GIScience from a place-based to a person-based

perspective (Miller 2003, Miller 2007). According to the place-based perspective, attributes

are in the first place related to locations, which are by consequence the principal unit of

analysis to start from. The place-based perspective is predominant in geography and

cartography, and in turn in traditional GIScience and GISs. While definitely viable and

valuable, a growing need existed for a complementary perspective which places individuals,

rather than places, at the centrepoint. Especially the critique that many place-based

approaches tend to reduce the individual and his/her space-time behaviour to a set of

attributes associated to a static location (e.g. the individual’s residence), has fostered the

need for a person-based perspective. According to Miller (2007, p. 527), the person-based

perspective “focuses on individuals in space and time and their allocation of activities in the

physical and virtual worlds”. The growing attention to person-based approaches has

1 Already in the early years of GIS, there has been considerable ambiguity about its definition (e.g. Maguire

1991, Raper & Livingstone 1995, Dangermond 1988, Chan & Williamson 1997). A further discussion thereof is considered out of this dissertation’s scope.

Introduction 3

provoked a renewed interest into Hägerstrand’s famous work What about people in

Regional Science? (Hägerstrand 1970) and a significant revival of the classical time

geography building on his milestone oeuvre (Timmermans, Arentze & Joh 2002, Kwan 2002,

Kwan 2004, Levinson & Krizek 2005, Miller 2007, Couclelis 2009, Neutens, Schwanen &

Witlox 2011).

Both the above mentioned trends have, until present, importantly coloured GIScience in

general and the research on moving objects in particular. More than that, they are especially

reflected within this dissertation and intertwine its contributions in various ways (see section

1.2). Above all, they propelled the modelling and analysis of moving objects and travelling

subjects to the forefront of the GIScience research agenda. Perhaps this development is best

illustrated by the multitude of international research initiatives and publications dedicated

to the topic. First of all, numerous recent international meetings have brought together

leading world-class scientists in the field to exchange their knowledge and ideas. These

include seminars such as those at Dagstuhl (Bitterlich et al. 2008, Sack et al. 2010),

workshops (e.g. Van de Weghe et al. 2008, Gottfried et al. 2009, Billen et al. 2010), and

summer schools (e.g. http://mss2010.modap.org/). Second, a number of major international

projects, such as MOVE (http://www.move-cost.info), GeoPKDD (http://www.geopkdd.eu),

and MODAP (http://www.modap.org), support a more systematic research of the topic.

Third, an unlimited body of publications has explicitly addressed the topic of moving objects.

Without aiming for an exhaustive overview, some important themes within this very wealth

of contributions may be reported here. A first frequently researched issue concerns the

tracking of and collection of data about moving objects (e.g. Cohen & Medioni 1999, Aslam

et al. 2003, Tseng et al. 2003, Civilis, Jensen & Pakalnis 2005, O'Connor, Zerger & Itami 2005,

Yilmaz, Javed & Shah 2006, Shoval & Isaacson 2007b, Wang et al. 2007, Renso et al. 2008,

Shoval 2008, Ahas 2010). A second important theme is the modelling, storing, and querying

of moving objects in databases (i.e. moving objects databases or briefly MODs) (e.g. Hornsby

& Egenhofer 2002, Brakatsoulas, Pfoser & Tryfona 2004, Jensen, Lin & Ooi 2004, Wolfson &

Mena 2005, Rodríguez 2005, Güting & Schneider 2005, Güting, de Almeida & Ding 2006,

Saltenis et al. 2000, de Almeida & Güting 2005, Revesz 2010). Building on the development

of MODs, many research efforts have addressed knowledge discovery from and data mining

of moving objects data, including contributions on the extraction of clusters (e.g. Li, Han &

Yang 2004, Zhang & Lin 2004, Buzan, Sclaroff & Kollios 2004, Nanni & Pedreschi 2006,

Jensen, Lin & Ooi 2007, Rinzivillo et al. 2008), patterns (e.g. Du Mouza & Rigaux 2004, Laube,

Imfeld & Weibel 2005, Gudmundsson, van Kreveld & Speckmann 2007, Laube, Duckham &

Wolle 2008, Wilson 2008, Dodge, Weibel & Lautenschutz 2008, Demšar & Virrantaus 2010),

and similarity within moving objects data (e.g. Van Kreveld & Luo 2007, Pelekis et al. 2007,

Lin & Su 2008, Dodge, Weibel & Forootan 2009). In addition, visualisation techniques

supporting the analysis of moving objects have been extensively studied (e.g. Rinzivillo et al.

2008, Andrienko & Andrienko 2008, Andrienko et al. 2009, Willems et al. 2010, Andrienko et

4 Chapter 1

al. 2010). Finally, a significant share of publications is dedicated to the prediction and

simulation of moving objects and/or travelling agents (e.g. Elnagar & Gupta 1998, Bors &

Pitas 2000, Wahle & Schreckenberg 2001, Brinkhoff 2002, Ray & Claramunt 2003, Mostafavi

& Gold 2004, Chih-Yu & Yu-Chee 2004, Chen, Jin & Yue 2007, Shoshany, Even-Paz & Bekhor

2007, El-Geneidy, Krizek & Iacono 2007, Hoyoung et al. 2008).

1.2 Rationale and synopsis

This dissertation consists of a compilation of ten international peer-reviewed manuscripts

(Chapters 2-11) 2, each of which intends to fulfil two general objectives. The first objective

reads as follows:

Objective 1 To present an original contribution to GIScience and its potential for

modelling and analysing moving objects and travelling subjects in particular.

The first objective confirms the focus on GIScience and its research about modelling and

analysing moving objects. Furthermore, the objective implies a claim on the originality and

scientific contribution of each of the included manuscripts that has also been required by

their editors and/or publishers. One of the critiques on contributions in GIScience is that

they often negate the scientific responsibility of GIScience to underpin GISs and somehow let

GIScience exist as a science separated from its technologies, tools, practices, and users

(Pickles 1997, Aitken & Michel 1995, Elwood 2006, Leszczynski 2009). This discordance

between GIScience and GISs is, among others, reflected in the results of citation analyses

(e.g. Nelhans 2007) and the incompatibility of the vocabularies used in both domains

(Schuurman 2000). Therefore, on top of the first objective, a second objective is pursued:

Objective 2 To add to or enhance the practical usefulness of existing theoretical

contributions and thus facilitate closing gaps between science and

technology, and between theory and applications.

The second objective is particularly reflected through manuscripts that address the

implementation and/or empirical application of fundamental formalisms that have hitherto

remained largely theoretical.

An overview of the academic manuscripts included in this dissertation is provided in Table

1.1. The majority of these have been published or are forthcoming in an international peer

reviewed book or journal, while the others have been submitted for possible publication and

are under review at the time of writing. The content of the dissertation has been divided

into the chapters that deal with moving objects in general (Part I, Chapters 2-6), and the

2 The major part in the development of each manuscript is to be attributed to the first author, although for

chapter 10, it should be noted that the second author has addressed the entire implementation and experimental design.

Introduction 5

Cap Title Authors Outlet Status P

ar

t I

–

Mo

vin

g o

bj

ec

ts

2 A Qualitative Trajectory Calculus to reason about moving point objects

Delafontaine M. Chavoshi S. H. Cohn A. G. Van de Weghe N.

Qualitative Spatio-Temporal Representation and Reasoning: Trends and Future Directions (book chapter)

published 2011

3 Inferring additional knowledge from QTCN relations

Delafontaine M. Bogaert P. Cohn A. G. Witlox F. De Maeyer P. Van de Weghe N.

Information Sciences (journal article)

published 2011

4

Qualitative relations between moving objects in a network changing its topological relations

Delafontaine M. Van de Weghe N. Bogaert P. De Maeyer P.

Information Sciences (journal article)

published 2008

5

Implementing a qualitative calculus to analyse moving point objects

Delafontaine M. Cohn A. G. Van de Weghe N.

Expert Systems With Applications (journal article)

published 2011

6 Modelling moving objects in geospatial sketch maps

Delafontaine M. Van de Weghe N.

AGILE Workshop on Adaptation in Spatial Communication (conference paper)

published 2009

Pa

rt

II

– T

ra

ve

llin

g s

ub

je

ct

s 7

Analysing spatiotemporal sequences in Bluetooth tracking data

Delafontaine M. Versichele M. Neutens T. Van de Weghe N.

Environment and Planning B (journal article)

submitted

8

Modelling potential movement in constrained travel environments using rough space-time prisms

Delafontaine M. Neutens T. Van de Weghe N.

International Journal of Geographical Information Science (journal article)

in press

9 Reconciling place-based and person-based accessibility: a GIS toolkit

Delafontaine M. Neutens T. Van de Weghe N.

International Journal of Geographical Information Science (journal article)

submitted

10

The relationship between opening hours and accessibility of public service delivery

Neutens T. Delafontaine M. Schwanen T. Van de Weghe N.

Journal of Transport Geography (journal article)

in press

11

The impact of opening hours on the equity of individual space-time accessibility

Delafontaine M. Neutens T. Schwanen T. Van de Weghe N.

Computers, Environment and Urban Systems (journal article)

in press

Table 1.1 – Manuscripts included in the dissertation.

chapters that address travelling subjects, i.e. the travel behaviour of individuals (part II,

chapters 7-11).

6 Chapter 1

Part I – Moving objects

The first part of the dissertation considers moving objects in their most general form of

entities whose position or geometric attributes change over time. In this respect, moving

objects have often been modelled as moving points which are referred to as moving point

objects (MPOs). This representation is predominant in GIScience (Laube, Imfeld & Weibel

2005) and also underlies the research presented in Part I. MPOs are a purified

conceptualisation of moving objects that is appealing for two reasons. On the one hand, it

allows analysts to focus strictly on the movement of the entity at hand and abstract away

from other, often irrelevant, geometric properties that may otherwise obscure the analysis.

On the other hand, compared to any other geometry of a higher dimension, MPOs are much

more elegant and efficient to handle from a computational point of view.

The contributions in Part I are situated in qualitative reasoning (QR), a research field that has

remained principally theoretical, despite its considerable potential of applications. QR is a

major field of artificial intelligence, which has been adopted in GIScience, especially its

subfield of qualitative spatial reasoning (QSR) (Freksa 1992, Egenhofer & Mark 1995, Cohn &

Renz 2007). QR seeks to develop techniques to enable information systems to reason about

the behaviour of physical systems, without the kind of precise quantitative information

needed by conventional analysis techniques such as numerical simulators (Weld & de Kleer

1989, Iwasaki 1997). Key to QR are qualitative representations: symbolic representations of

discrete quantity spaces, such that “the distinctions made in these discretisations are

relevant to the behaviour being modelled” (Cohn 1996, p. 124). One common algebraic

framework in QR for representing and reasoning is a qualitative calculus3. In brief, and

although there is no precise definition, a qualitative calculus arises from a set of jointly

exhaustive and pairwise disjoint relations, together with a set of operations to reason about

these relations (Ligozat & Renz 2004).

The following interrelated research questions are addressed in Part I:

Question 1 How to formally describe the relations between MPOs adequately in a

qualitative manner such that a calculus is obtained to represent and reason

about these relations?

Question 2 How to implement this calculus in an information system?

Chapters 2-4 formulate an answer to the first question, whereas the second question is

tackled in Chapter 5. To this end, a dedicated qualitative calculus for handling qualitative

relations among MPOs, namely the Qualitative Trajectory Calculus (QTC), is considered. QTC

was introduced in 2004 in the doctoral dissertation of Van de Weghe (2004). His

3 Plural: calculi.

Introduction 7

fundamental work has been complemented by a number of later contributions. In this light,

Chapter 2 presents a theoretical overview of the fundamental types of QTC and

demonstrates how the calculus implements major reasoning concepts, how it can be

extended, and how it can be employed in order to represent raw moving object data. This

chapter has been published in Qualitative Spatio-Temporal Representation and Reasoning:

Trends and Future Directions (Delafontaine et al. 2011b). Chapter 3 and 4 add to Chapter 2 in

that they further elaborate a specific type of QTC: the Qualitative Trajectory Calculus on

Networks (QTCN). QTCN considers objects that are constrained in their movement by

networks, as is the case for most transportation means. Chapter 3 – published in Information

Sciences (Delafontaine et al. 2011a) – introduces a formal axiomatisation of QTCN, explores

its reasoning power and its ability to infer additional knowledge. In QTCN, the networks that

delineate the movements are assumed to be static, i.e. they remain topologically unaltered

over time. This assumption, however, does not always mirror the reality. In multi-modal

transportation networks, for instance, temporal connections or disconnections such as the

opening of a bridge over a waterway might be common. Therefore, Chapter 4, published in

Information Sciences (Delafontaine et al. 2008), extends QTCN to networks that may change

topologically by introducing the Qualitative Trajectory Calculus on Changing Networks

(QTCDN’).

Although in Chapters 2-4 applications of QTC are touched, the main focus is on the

theoretical framework. Chapter 5, published in Expert Systems With Applications

(Delafontaine, Cohn & Van de Weghe 2011), aims to provide a more systematic basis for

QTC-based applications by addressing the implementation of QTC in an information system.

A prototype QTC-based information system, named QTCAnalyst, is developed and

illustrated. Starting from raw trajectory data, QTCAnalyst is able to automatically generate

and export QTC representations that model relations among moving objects. Typically, the

input data will be obtained from tracking systems such as GPS devices, although alternative

data sources and input modalities are worthwhile exploring. Given that reasoning with

qualitative information particularly reflects human cognition, communication and decision

making, the incorporation of human-originated data merits particular attention, especially in

view of the growing capabilities for human-computer interaction. As Forbus et al. (2003)

argue that “qualitative spatial reasoning is essential for working with sketch maps” (Forbus,

Usher & Chapman 2003, p. 61), a promising extension of QTCAnalyst may be to support

input from freehand sketching. To this end – as a branch-line in this dissertation – Chapter 6

addresses the modelling of moving objects in geospatial sketch maps and how MPO

trajectories can be obtained from such sketch maps. The chapter has been presented at the

AGILE Workshop on Adaptation in Spatial Communication (Delafontaine & Van de Weghe

2009).

8 Chapter 1

Part II – Travelling subjects

In line with the trend towards a person-based GIScience (see section 1.1), the second part of

this dissertation addresses the movement behaviour of individuals, in lieu of unspecified

entities. Unlike other entities, individuals most often control to a large extent the actions

they undertake in space over time. This reasoning supports two research perspectives on

analysing travel behaviour. On the one hand, the examination of revealed behaviour may

offer insights on individuals’ decisions and rationale underlying their activities. Knowledge

extracted from the monitoring and analysis of revealed travel behaviour constitutes the

basis for location-based services and may importantly feed decisions about transport (e.g.

navigation, logistics, traffic management) and security issues (e.g. evacuation and rescue

policies, crowd control).

On the other hand, individuals are subject to a set of constraints on their space-time

behaviour which provides a foundation for analysing potential behaviour. Research on

potential behaviour may improve our assessment and understanding of the effects of

different space-time constraints on individual movement and on the feasibility for

individuals to participate in activities and to travel in between them. Important applications

related to potential behaviour lie in planning, development and prospection, especially

within the context of regional science and transport studies (e.g. urban planning,

transportation planning, traffic forecasting, agent-based modelling, accessibility assessment,

wayfinding).

Part II focuses on the following fundamental research question related to the revealed and

potential space-time behaviour of individuals:

Question 3 How to model and analyse revealed and potential behaviour of individuals

starting from raw tracking data?

Partial answers to this question are given in Chapters 7 and 8. Chapter 7 (Delafontaine et al.

2011d, submitted) scrutinises a key aspect of revealed behaviour, i.e. the chronological

sequence of observed activities. In particular, Chapter 7 examines behavioural sequences

within tracking data of visitors walking around at a big trade fair. The chapter is innovative in

using tracking data obtained from Bluetooth sensing, i.e. a burgeoning, yet largely

unexplored tracking approach, and in applying sequence alignment methods, which have a

long tradition in bioinformatics, but have only recently been adopted as a data mining

technique in GIScience (Shoval & Isaacson 2007a).

Chapter 8, forthcoming in the International Journal of Geographical Information Science

(Delafontaine, Neutens & Van de Weghe 2011a), concentrates on the modelling of potential

behaviour. Potential behaviour plays a central role in time geography (Hägerstrand 1970)

and is especially captured in its key concept of a space-time prism (STP). A STP embodies the

set of space-time points that an individual may reach given a set of spatial and temporal

Introduction 9

constraints. This delineated volume and its spatial projection are usually referred to as

potential path space and potential path area respectively. Given the renewed interest in

time geography (see section 1.1), many recent implementations of STPs have considered

network-constrained travel environments (cf. Chapters 3-4, e.g. Neutens et al. 2008, Miller &

Bridwell 2009, Kuijpers & Othman 2009, Kuijpers et al. 2010). Chapter 8, extends these

implementations in at least two ways by introducing rough obstacle-constrained STPs. First,

building on the tenets of rough set theory (Pawlak 1982), these space-time prisms account

for the uncertainty of space-time constraints, especially the uncertainty related to space-

time constraints stemming from tracking data (cf. question 3). Second, they represent

potential path spaces within travel environments that can be modelled as open spaces

constrained by discrete obstacles (i.e. obstacle-constrained environments), rather than

linear networks.

The remaining contributions of Part II also rely on the modelling of potential behaviour and

the related time-geographical framework. In line with the second objective, however, their

main focus is on the more application-centric issue of accessibility, which can be defined as

an individual’s ability to travel and participate in activities given the available transport and

land use system (Pirie 1979, Pooler 1987). Therefore, two additional research questions have

been investigated:

Question 4 How to measure the accessibility of opportunities to individuals through the

consideration of space-time constraints?

Question 5 How do time constraints of opportunities affect their accessibility and how

can these be manipulated in order to control individual accessibility?

The fourth question is addressed starting from the general concern that, until present,

despite the important efforts that have stressed the advantages and need for a person-

based assessment (Kwan 2009, Miller 2007, Neutens et al. 2010), there remains a strong

tradition to evaluate accessibility from a place-based perspective in empirical research. In

this dissertation it is argued that the place-based and people-based perspectives

complement each other in many respects. Therefore, Chapter 9 (Delafontaine, Neutens &

Van de Weghe 2011b, submitted) aims to combine both perspectives into a new kind of STP

denoted as a reverse STP. Reverse STPs implement some important space-time constraints

of conventional person-based STPs, while supporting the advantages of place-based

approaches such as the ability to generate area-covering maps. More than that, based on

reverse STPs, Chapter 9 introduces and illustrates a novel GIS toolkit, named PrismMapper,

for measuring and mapping an individual’s accessibility to services.

Beyond combining place-based and person-based approaches, the PrismMapper toolkit

contributes through the explicit consideration of service facility opening hours in its

assessment of accessibility. Opening hours have often been overlooked as temporal

10 Chapter 1

constraints that delimit the accessibility of services to individuals which should be taken into

account when measuring person-based accessibility. This observation has lead to the fifth

research question. Chapters 10 and 11 seek for an answer to this question through

examining how opening hours of services affect individual accessibility and how this

accessibility can be amended by adopting different opening hour schedules. Chapter 10,

forthcoming in Journal of Transport Geography (Neutens et al. 2011) presents a procedure

to determine a regime of opening hours of services which optimises the absolute level of

person-based accessibility to these services. The procedure is implemented in a case study

focussing on the accessibility of government offices to citizens in the city of Ghent (Belgium).

Finally, in Chapter 11, forthcoming in Computers, Environment and Urban Systems

(Delafontaine et al. 2011c), the approach of Chapter 10 is generalised, such that a regime

can be derived which maximises any arbitrary function of individual accessibility, rather than

only its absolute sum across the population. This generalised algorithm is then applied

according to evaluation functions that draw on different equity principles in order to assess

the effects of (re)scheduling opening hours on the equity of person-based accessibility

among individuals. This is illustrated in a case study considering the accessibility of public

libraries in Ghent.

To conclude this dissertation, Chapter 12 summarises its main achievements and results, and

evaluates the postulated objectives and research questions within the wider research

context.

References

Ahas, R. (2010) Special issue on mobile positioning and tracking in geography and planning. Journal of

Urban Technology, 17, 1.

Aitken, S. C. & Michel, S. M. (1995) Who contrives the real in GIS? Geographic information, planning

and critical theory. Cartography and Geographic Information Science, 22, 1, 17-29.

Andrienko, G. & Andrienko, N. (2008) Spatio-temporal aggregation for visual analysis of movements.

In IEEE Symposium on Visual Analytics Science and Technology 2008, 51-58.

Andrienko, G., Andrienko, N., Demsar, U., Dransch, D., Dykes, J., Fabrikant, S. I., Jern, M., Kraak, M. J.,

Schumann, H. & Tominski, C. (2010) Space, time and visual analytics. International Journal of

Geographical Information Science, 24, 10, 1577-1600.

Andrienko, G., Andrienko, N., Rinzivillo, S., Nanni, M. & Pedreschi, D. (2009) A visual analytics toolkit

for cluster-based classification of mobility data. In Proceedings of the 11th International

Symposium on Advances in Spatial and Temporal Databases, 5644, 432-435.

Aslam, J., Butler, Z., Constantin, F., Crespi, V., Cybenko, G. & Rus, D. (2003) Tracking a moving object

with a binary sensor network. In Proceedings of the 1st International Conference on

Embedded networked sensor systems. Los Angeles, California, USA: ACM.

Billen, R., Gottfried, B., Klippel, A., Laube, P. & Van de Weghe, N. (2010) Proceedings of the 1st

Workshop on Movement Pattern Analysis (MPA'10). In conjunction with GIScience 2010,

Zurich, Switzerland.

Introduction 11

Bitterlich, W., Sack, J. R., Sester, M. & Weibel, R. (2008) Abstracts collection - Representation,

analysis and visualization of moving objects. In Dagstuhl Seminar 08451. Dagstuhl, Germany:

Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Germany.

Bors, A. G. & Pitas, I. (2000) Prediction and tracking of moving objects in image sequences. IEEE

Transactions on Image Processing, 9, 8, 1441-1445.

Brakatsoulas, S., Pfoser, D. & Tryfona, N. (2004) Modeling, storing, and mining moving object

databases. In Proceedings of the International Database Engineering and Applications

Symposium, 68-77. IEEE Computer Society.

Brinkhoff, T. (2002) A framework for generating network-based moving objects. Geoinformatica, 6, 2,

153-180.

Buzan, D., Sclaroff, S. & Kollios, G. (2004) Extraction and clustering of motion trajectories in video. In

Proceedings of the 17th International Conference on Pattern Recognition (ICPR'04) Volume 2,

IEEE Computer Society, 521-524.

Chan, T. O. & Williamson, I. P. (1997) Definition of GIS: the manager's perspective. In Proceedings of

the International Workshop on Dynamic and Multi-Dimensional GIS. Hong Kong.

Chen, H. R., Jin, P. Q. & Yue, L. H. (2007) Modeling and predicting the extents of moving spatial

objects - art. no. 679524. In Proceedings of the 2nd International Conference on Space

Information Technology, eds. C. Wang, S. Zhong & J. L. Wei, Wuhan, China, 79524-79524.

Chih-Yu, L. & Yu-Chee, T. (2004) Structures for in-network moving object tracking in wireless sensor

networks. In BroadNets 2004, Proceedings of the First International Conference on

Broadband Networks, 718-727.

Civilis, A., Jensen, C. S. & Pakalnis, S. (2005) Techniques for efficient road-network-based tracking of

moving objects. IEEE Transactions on Knowledge and Data Engineering, 17, 5, 698-712.

Cohen, I. & Medioni, G. (1999) Detecting and tracking moving objects for video surveillance. In IEEE

Computer Society Conference on Computer Vision and Pattern Recognition, 1999, 325 Vol. 2.

Cohn, A. (1996) Calculi for qualitative spatial reasoning. In Artificial Intelligence and Symbolic

Mathematical Computation, eds. J. Calmet, J. Campbell & J. Pfalzgraf, Springer Berlin /

Heidelberg, 124-143.

Cohn, A. G. & Renz, J. (2007) Qualitative spatial reasoning. In Handbook of Knowledge

Representation, eds. F. van Harmelen, V. Lifschitz & B. Porter. Elsevier Science.

Couclelis, H. (2009) Rethinking time geography in the information age. Environment and Planning A,

41, 7, 1556-1575.

Dangermond, J. (1988) Introduction and overview of GIS. In Geographic Information Systems

Seminar, Data Sharing - Myth or Reality. Ontario, Canada: Ministry of Natural Resources.

de Almeida, V. & Güting, R. H. (2005) Indexing the trajectories of moving objects in networks.

Geoinformatica, 9, 1, 33-60.

Delafontaine, M., Bogaert, P., Cohn, A. G., Witlox, F., De Maeyer, P. & Van de Weghe, N. (2011a)

Inferring additional knowledge from QTCN relations. Information Sciences, 181, 9, 1573-1590.

Delafontaine, M., Chavoshi, S. H., Cohn, A. G. & Van de Weghe, N. (2011b) A Qualitative Trajectory

Calculus to reason about moving point objects. In Qualitative Spatio-Temporal

Representation and Reasoning: Trends and Future Directions, ed. S. M. Hazarika. Hershey, PA,

USA: IGI Global.

12 Chapter 1

Delafontaine, M., Cohn, A. G. & Van de Weghe, N. (2011) Implementing a qualitative calculus to

analyse moving point objects. Expert Systems with Applications, 38, 5, 5187-5196.

Delafontaine, M., Neutens, T., Schwanen, T. & Van de Weghe, N. (2011c) The impact of opening

hours on the equity of individual space-time accessibility. Computers, Environment and

Urban Systems, forthcoming.

Delafontaine, M., Neutens, T. & Van de Weghe, N. (2011a) Modelling potential movement in

constrained travel environments using rough space–time prisms. International Journal of

Geographical Information Science, forthcoming.

Delafontaine, M., Neutens, T. & Van de Weghe, N. (2011b) Reconciling place-based and person-based

accessibility: a GIS toolkit. International Journal of Geographical Information Science,

submitted for publication.

Delafontaine, M. & Van de Weghe, N. (2009) Modelling moving objects in geospatial sketch maps. In

Proceedings of the AGILE Workshop on Adaptation in Spatial Communication, eds. M. Tomko

& K.-F. Richter, Hannover, Germany, 7-17.

Delafontaine, M., Van de Weghe, N., Bogaert, P. & De Maeyer, P. (2008) Qualitative relations

between moving objects in a network changing its topological relations. Information

Sciences, 178, 8, 1997-2006.

Delafontaine, M., Versichele, M., Neutens, T. & Van de Weghe, N. (2011d) Analysing spatiotemporal

sequences in Bluetooth tracking data, Environment and Planning B: Planning and Design,

submitted for publication.

Demšar, U. & Virrantaus, K. (2010) Space–time density of trajectories: exploring spatio-temporal

patterns in movement data. International Journal of Geographical Information Science, 24,

10, 1527-1542.

Dodge, S., Weibel, R. & Forootan, E. (2009) Revealing the physics of movement: Comparing the

similarity of movement characteristics of different types of moving objects. Computers,

Environment and Urban Systems, 33, 6, 419-434.

Dodge, S., Weibel, R. & Lautenschutz, A. (2008) Towards a taxonomy of movement patterns.

Information Visualization, 7, 3-4, 240-252.

Du Mouza, C. & Rigaux, P. (2004) Mobility patterns. In Proceedings of the 2nd Workshop on Spatio-

Temporal Database Management (STDBM 04), Toronto, Canada, 297-319.

Egenhofer, M. J. & Mark, D. (1995) Naive Geography. In Spatial Information Theory: A Theoretical

Basis for GIS, eds. A. U. Frank & W. Kuhn, Berlin / Heidelberg: Springer-Verlag, 1-15.

El-Geneidy, A. M., Krizek, K. J. & Iacono, M. J. (2007) Predicting bicycle travel speeds along different

facilities using GPS data: a proof of concept model. In Proceedings of the 86th Annual

Meeting of the Transportation Research Board (TRB), Compendium of Papers. Washington,

DC, USA.

Elnagar, A. & Gupta, K. (1998) Motion prediction of moving objects based on autoregressive model.

IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, 28, 6, 803-

810.

Elwood, S. (2006) Critical issues in participatory GIS: Deconstructions, reconstructions, and new

research directions. Transactions in GIS, 10, 5, 693-708.

Introduction 13

Forbus, K. D., Usher, J. E. & Chapman, V. (2003) Qualitative spatial reasoning about sketch maps. In

Proceedings of the 15th Innovative Applications of Artificial Intelligence Conference (IAAI-03),

Acapulco, Mexico: American Assocation for Artificial Intelligence, 61-72.

Freksa, C. (1992) Using orientation information for qualitative spatial reasoning. In Theories and

Methods of Spatio-Temporal Reasoning in Geographic Space, eds. A. U. Frank, I. Campari & U.

Formentini, Pisa, Italy: Springer-Verlag, 162-178.

Goodchild, M. F. (1992) Geographical information science. International Journal of Geographical

Information Systems, 6, 1, 31-45.

Goodchild, M. F. (2004) GIScience, geography, form, and process. Annals of the Association of

American Geographers, 94, 4, 709-714.

Goodchild, M. F. (2010) Twenty years of progress: GIScience in 2010. Journal of Spatial Information

Science, 1, 3-20.

Gottfried, B., Van de Weghe, N., Billen, R. & De Maeyer, P. (2009) Proceedings of the 4th Workshop

on Behaviour Monitoring and Interpretation – Studying Moving Objects in a Three-

Dimensional World, in conjunction with 3D-GeoInfo 2009, Ghent, Belgium, CEUR Workshop

Proceedings.

Gudmundsson, J., van Kreveld, M. & Speckmann, B. (2007) Efficient detection of patterns in 2D

trajectories of moving points. Geoinformatica, 11, 195-215.

Güting, R., Hartmut, de Almeida, V., Teixeira & Ding, Z. (2006) Modeling and querying moving objects

in networks. The International Journal on Very Large Data Bases, 15, 2, 165-190.

Güting, R. H. & Schneider, M. (2005) Moving objects databases. San Fransisco, CA, USA: Morgan

Kaufmann, 389.

Hägerstrand, T. (1970) What about people in regional science? Papers in Regional Science, 24, 1, 6-

21.

Hornsby, K. & Egenhofer, M. J. (2002) Modeling moving objects over multiple granularities. Annals of

Mathematics and Artificial Intelligence, 36, 1-2, 177-194.

Hoyoung, J., Qing, L., Heng Tao, S. & Xiaofang, Z. (2008) A hybrid prediction model for moving

objects. In IEEE 24th International Conference on Data Engineering, ICDE 2008., 70-79.

Iwasaki, Y. (1997) Qualitative reasoning and the science of design. IEEE Expert: Intelligent Systems

and Their Applications, 12, 3, 2-4.

Jensen, C., S., Lin, D. & Ooi, B., Chin (2007) Continuous clustering of moving objects. IEEE

Transactions on Knowledge and Data Engineering, 19, 9, 1161-1174.

Jensen, C. S., Lin, D. & Ooi, B. C. (2004) Query and update efficient B+-tree based indexing of moving

objects. In Proceedings of the 30th International Conference on Very Large Data Bases -

Volume 30, 768-779. Toronto, Canada: VLDB Endowment.

Kuijpers, B., Miller, H. J., Neutens, T. & Othman, W. (2010) Anchor uncertainty and space-time prisms

on road networks. International Journal of Geographical Information Science, 24, 8, 1223 -

1248.

Kuijpers, B. & Othman, W. (2009) Modeling uncertainty of moving objects on road networks via

space–time prisms. International Journal of Geographical Information Science, 23, 9, 1095 -

1117.

Kwan, M.-P. (2004) GIS methods in time-geographic research: Geocomputation and geovisualization

of human activity patterns. Geografiska Annaler: Series B, Human Geography, 86, 4, 267-280.

14 Chapter 1

Kwan, M. P. (2002) Time, information technologies, and the geographies of everyday life. Urban

Geography, 23, 5, 471-482.

Kwan, M. P. (2009) From place-based to people-based exposure measures. Social Science &

Medicine, 69, 9, 1311-1313.

Langran, G. E. (1993) Time in Geographic Information Systems. Bristol, PA: Taylor & Francis.

Laube, P. (2005) Analysing Point Motion - Spatio-Temporal Data Mining of Geospatial Lifelines,

Doctoral Dissertation, Zürich: Universität Zürich, 135.

Laube, P., Duckham, M. & Wolle, T. (2008) Decentralized movement pattern detection amongst

mobile geosensor nodes. In Proceedings of the 5th International Conference on Geographic

Information Science, eds. T. Cova, H. Miller, K. Beard, A. Frank & M. Goodchild, Springer

Berlin / Heidelberg, 199-216.

Laube, P., Imfeld, S. & Weibel, R. (2005) Discovering relative motion patterns in groups of moving

point objects. International Journal of Geographical Information Science, 19, 6, 639-668.

Leszczynski, A. (2009) Rematerializing GIScience. Environment and Planning D: Society and Space, 27,

4, 609-615.

Levinson, D. M. & Krizek, K. J. (2005) Access to Destinations. Elsevier, 422.

Li, Y., Han, J. & Yang, J. (2004) Clustering moving objects. In Proceedings of the 10th ACM SIGKDD

International Conference on Knowledge Discovery and Data Mining, Seattle, WA, USA: ACM,

617-622.

Ligozat, G. & Renz, J. (2004) What is a qualitative calculus? A general framework. In Proceddings of

the 8th Pacific Rim International Conference on Artificial Intelligence (PRICAI'04), Auckland,

New Zealand, 53-64.

Lin, B. & Su, J. (2008) One way distance: For shape based similarity search of moving object

trajectories. Geoinformatica, 12, 2, 117-142.

Maguire, D. J. (1991) An overview and definition of GIS. In Geographical Information Systems

Principles and Applications, eds. D. J. Maguire, M. F. Goodchild & D. W. Rhind, New York:

Longman Scientific and Technical; John Wiley and Sons, 9-20.

Mark, D. M. (2003) Geographic information science: Defining the field. In Foundations of Geographic

Information Science, eds. M. Duckham, M. F. Goodchild & M. F. Worboys, New York: Taylor

and Francis, 1-18.

Miller, H. (2007) Place-based versus people-based geographic information science. Geography

Compass, 1, 3, 503-535.

Miller, H. J. (2003) What about people in geographic information science? Computers, Environment

and Urban Systems, 27, 5, 447.

Miller, H. J. & Bridwell, S. A. (2009) A field-based theory for time geography. Annals of the Association

of American Geographers, 99, 1, 49-75.

Mostafavi, M. A. & Gold, C. (2004) A global kinetic spatial data structure for a marine simulation.

International Journal of Geographical Information Science, 18, 3, 211-227.

Nanni, M. & Pedreschi, D. (2006) Time-focused clustering of trajectories of moving objects. Journal of

Intelligent Information Systems, 27, 3, 267-289.

Nelhans, G. (2007) Citations within the GI literature – Theoretical works or good examples? In The

European Information Society: Leading the way with geo-information, Proceedings of the

Introduction 15

10th AGILE International Conference on Geographic Information Science, Aalborg University,

Denmark.

Neutens, T., Delafontaine, M., Schwanen, T. & Van de Weghe, N. (2011) The relationship between

opening hours and accessibility of public service delivery, Journal of Transport Geography,

forthcoming.

Neutens, T., Schwanen, T. & Witlox, F. (2011) The prism of everyday life: Towards a new research

agenda for time geography. Transport Reviews: A Transnational Transdisciplinary Journal, 31,

1, 25-47.

Neutens, T., Schwanen, T., Witlox, F. & De Maeyer, P. (2010) Equity of urban service delivery: A

comparison of different accessibility measures. Environment and Planning A, 42, 7, 1613-

1635.

Neutens, T., Van de Weghe, N., Witlox, F. & De Maeyer, P. (2008) A three-dimensional network-

based space–time prism. Journal of Geographical Systems, 10, 1, 89-107.

O'Connor, A., Zerger, A. & Itami, B. (2005) Geo-temporal tracking and analysis of tourist movement.

Mathematics and Computers in Simulation, 69, 1-2, 135-150.

Ott, T. & Swiaczny, F. (2001) Time-integrative Geographic Information Systems - Management and

Analysis of Spatio-Temporal Data. Berlin: Springer.

Pawlak, Z. (1982) Rough sets. International Journal of Information and Computer Science, 11, 5, 341-

356.

Pelekis, N., Kopanakis, I., Marketos, G., Ntoutsi, I., Andrienko, G. & Theodoridis, Y. (2007) Similarity

search in trajectory databases. In Proceedings of the 14th International Symposium on

Temporal Representation and Reasoning (TIME 2007), 129-140.

Peuquet, D. J. (1994) It's about time: A conceptual framework for the representation of temporal

dynamics in geographic information systems. Annals of the Association of American

Geographers, 84, 3, 441-461.

Pickles, J. (1997) Tool or science? GIS, technoscience, and the theoretical turn. Annals of the

Association of American Geographers, 87, 2, 363-372.

Pirie, G. H. (1979) Measuring accessibility – Review and proposal. Environment and Planning A, 11, 3,

299-312.

Pooler J. (1987) Measuring geographical accessibility: A review of current approaches and problems

in the use of population potentials. Geoforum, 18, 3, 269-289.

Raper, J. (2000) Multidimensional Geographic Information Science. London, UK: CRC Press, 332.

Raper, J. & Livingstone, D. (1995) Development of a geomorphological spatial model using object-

oriented design. International Journal of Geographical Information Science, 9, 4, 359-383.

Ray, C. & Claramunt, C. (2003) A distributed system for the simulation of people flows in an airport

terminal. Knowledge-Based Systems, 16, 4, 191-203.

Renso, C., Puntoni, S., Frentzos, E., Mazzoni, A., Moelans, B., Pelekis, N. & Pini, F. (2008) Wireless

network data sources: Tracking and synthesizing trajectories. In Mobility, Data Mining and

Privacy, eds. F. Giannotti & D. Pedreschi, Springer, 73-100.

Revesz, P. (2010) Moving objects databases. In Introduction to Databases, Springer London, 111-135.

Rinzivillo, S., Pedreschi, D., Nanni, M., Giannotti, F., Andrienko, N. & Andrienko, G. (2008) Visually

driven analysis of movement data by progressive clustering. Information Visualization, 7, 3-4,

225-239.

16 Chapter 1

Rodríguez, A. M. (2005) Moving objects databases. In Encyclopedia of Database Technologies and

Applications, eds. L. C. Rivero, J. H. Doorn & V. E. Ferraggine, IGI Global, 378-382.

Sack, J. R., Speckmann, B., Van Loon, E. & Weibel, R. (2010) Abstracts collection – representation,

analysis and visualization of moving objects. In Dagstuhl Seminar 10491, Dagstuhl, Germany:


Saltenis, S., Jensen, C. S., Leutenegger, S. T. & Lopez, M. A. (2000) Indexing the positions of

continuously moving objects. Sigmod Record, 29, 2, 331-342.

Schuurman, N. (2000) Trouble in the heartland: GIS and its critics in the 1990s. Progress in Human

Geography, 24, 4, 569-590.

Shoshany, M., Even-Paz, A. & Bekhor, S. (2007) Evolution of clusters in dynamic point patterns: with a

case study of ants' simulation. International Journal of Geographical Information Science, 21,

7, 777-797.

Shoval, N. (2008) Tracking technologies and urban analysis. Cities, 25, 1, 21-28.

Shoval, N. & Isaacson, M. (2007a) Sequence alignment as a method for human activity analysis in

space and time. Annals of the Association of American Geographers, 97, 2, 282-297.

Shoval, N. & Isaacson, M. (2007b) Tracking tourists in the digital age. Annals of Tourism Research, 34,

1, 141-159.

Timmermans, H., Arentze, T. & Joh, C. H. (2002) Analysing space-time behaviour: new approaches to

old problems. Progress in Human Geography, 26, 2, 175-190.

Tseng, Y.-C., Kuo, S.-P., Lee, H.-W. & Huang, C.-F. (2003) Location tracking in a wireless sensor

network by mobile agents and its data fusion strategies. In Information Processing in Sensor

Networks, eds. F. Zhao & L. Guibas, Springer Berlin / Heidelberg, 554-554.

Van de Weghe, N. (2004) Representing and Reasoning about Moving Objects: A Qualitative

Approach, Doctoral Dissertation, Ghent: Ghent University, 268.

Van de Weghe, N., Billen, R., Kuijpers, B. & Bogaert, P. (2008) Proceedings of the International

Workshop on Moving Objects: From Natural to Formal Language, in conjuntion with

GIScience 2008, Park City, Utah, USA.

Van Kreveld, M. & Luo, J. (2007) Trajectory similarity of moving objects. In Young Researchers Forum,

Proceedings of the 5th Geographic Information Days (GI-DAYS). eds. F. Probst & C. Kessler,

Münster: IfGI prints, 229-232.

Wahle, J. & Schreckenberg, M. (2001) A multi-agent system for on-line simulations based on real-

world traffic data. In Proceedings of the 34th Hawaii International Conference on System

Sciences.

Wang, C.-C., Thorpe, C., Thrun, S., Hebert, M. & Durrant-Whyte, H. (2007) Simultaneous localization,

mapping and moving object tracking. The International Journal of Robotics Research, 26, 9,

889-916.

Weld, D. S. & de Kleer, J. (1989) Readings in qualitative reasoning about physical systems. San

Francisco, CA, USA: Morgan Kaufmann.

Willems, N., van Hage, W. R., de Vries, G., Janssens, J. H. M. & Malaisé, V. (2010) An integrated

approach for visual analysis of a multisource moving objects knowledge base. International

Journal of Geographical Information Science, 24, 10, 1543-1558.

Wilson, C. (2008) Activity patterns in space and time: calculating representative Hägerstrand

trajectories. Transportation, 35, 4, 485-499.

Introduction 17

Wolfson, O. & Mena, E. (2005) Applications of moving objects databases. In Spatial Databases, eds. Y.

Manalopoulos, A. Papadopoulos & M. G. Vassilakopoulos, IGI Global, 186-203.

Yilmaz, A., Javed, O. & Shah, M. (2006) Object tracking: A survey. ACM Computing Surveys, 38, 4, 13.

Zhang, Q. & Lin, X. (2004) Clustering moving objects for spatio-temporal selectivity estimation. In

Proceedings of the 15th Australasian database conference – Volume 27, Dunedin, New

Zealand: Australian Computer Society, 123-130.

Moving Objects

Part I

“Among entities there must be some cause which moves and combines

things. There must be a principle of such a kind that its substance is

activity.” (Aristotle)

A Qualitative Trajectory Calculus to reason about moving point objects 21

2 A Qualitative Trajectory Calculus to reason about moving

point objects

Delafontaine M., Chavoshi S. H., Cohn A. G., Van de Weghe N.

in Hazarika S. M. (Ed.): Qualitative Spatio-Temporal Representation and Reasoning:

Trends and Future Directions (2011)

Copyright © IGI Global

Abstract. A number of qualitative calculi have been developed in order to reason

about space and time. A recent trend has been the emergence of integrated

spatiotemporal calculi in order to deal with dynamic phenomena such as motion. In

2004, Van de Weghe introduced the Qualitative Trajectory Calculus (QTC) as a

qualitative calculus to represent and reason about moving objects. This chapter

presents a general overview of the principal theoretical aspects of QTC, focusing on

the two most fundamental types of QTC. It is shown how QTC deals with important

reasoning concepts, and how the calculus can be employed in order to represent raw

moving object data.

Kewords. Qualitative calculus – Spatio-temporal reasoning – Moving point objects

2.1 Introduction

Reasoning about spatial and temporal information takes a central place in human daily life. A

number of qualitative calculi have been developed to represent and reason about spatial or

temporal configurations. Most of them focus on one of the two domains, whereas a few are

true spatiotemporal calculi that deal with spatiotemporal phenomena. One such is the

Qualitative Trajectory Calculus, which in the remainder of this chapter will be referred to as

QTC. QTC is a qualitative calculus to reason about a specific spatiotemporal phenomenon:

moving objects.

The remainder of this chapter is structured as follows. First, relevant background issues are

discussed. Second, some general characteristics of QTC are explained and a brief overview of

all QTC calculi that have been elaborated so far is given. The two most fundamental QTC

calculi, QTCB and QTCC, are then presented in detail. The following sections discuss

representing and reasoning with QTC, as well as how QTC can be extended. An application

section follows in order to highlight the potential of implementing QTC in information

systems. The final sections mention opportunities for further research and conclusions.

22 Chapter 2

2.2 Background

In Artificial Intelligence, several qualitative calculi exist to reason about either spatial or

temporal information, the most well-known being Allen’s Interval Calculus (Allen 1983),

which has about 1200 citations in the ISI Web of Science by the time of writing. According to

Wolter & Zakharyaschev (2000), an apparent and natural step is to combine both spatial and

temporal formalisms in order to reason about spatiotemporal phenomena. A crucial and

fundamental phenomenon at this cross-pollination of space and time is motion. Note that

motion is an inherently spatiotemporal phenomenon (Peuquet 2001). Dealing with motion is

essential to spatial and geographical information systems, where an evolution from static to

dynamic formalisms and representations has been made. A specific type of motion is

associated with moving objects, i.e. objects whose position moves through space in time.

In the past decade, the modelling of moving objects has been a hot topic in fields such as

GIScience, Artificial Intelligence and Information Systems (Bitterlich et al. 2008). In

qualitative reasoning, however, considerable work has focused on the formalisation of

motion, or moving objects in particular. Some examples are Muller (2002), Ibrahim (2007),

Hallot & Billen (2008), and Kurata & Egenhofer (2009). These approaches have in common

that they rely on topological models such as the Region Connection Calculus (Randell, Cui &

Cohn 1992) or the 9-Intersection model (Egenhofer & Franzosa 1991). However, a general

shortfall of topological models is their inability to further differentiate between disjoint

relations. This makes their applicability to represent and reason about continuously moving

objects questionable, as in many cases moving objects remain disjoint for most of the time.

For instance, cars in a traffic situation are usually disjoint, apart from the exceptional case of

an accident.

In order to overcome this inability, the Qualitative Trajectory Calculus (QTC), was proposed

by Van de Weghe (2004). QTC provides a qualitative framework to represent and reason

about moving objects which enables the differentiation of groups of disconnected objects.

The development of QTC has been inspired by some major qualitative calculi: the Region

Connection Calculus (Randell, Cui & Cohn 1992), the temporal Semi-Interval Calculus (Freksa

1992a), and the spatial Double Cross Calculus (Freksa 1992b, Zimmermann & Freksa 1996).

2.3 The Qualitative Trajectory Calculus

2.3.1 Simplifications

Information systems usually represent knowledge according to an underlying model of the

real world, making simplifications in order to abstract away from the mass of details that

would otherwise obscure essential aspects. To this end, QTC makes four simplifications

(Figure 2.1). First and foremost, QTC considers the relation between two objects, i.e. binary

relations (relational simplification, Figure 2.1b), as is common in spatial and temporal

reasoning (Cohn & Renz 2007). Second, moving objects are spatially simplified into moving


point objects or MPOs (object simplification, Figure 2.1c), as is common in GIScience and

geoinformatics (Laube 2005, Gudmundsson, van Kreveld & Speckmann 2004, Güting et al.

2000, Noyon, Claramunt & Devogele 2007). There are only two topological relations (disjoint

and equal) between two MPOs. Since the relation between two equal MPOs is trivial, the

third simplification in QTC is the restriction to disjoint MPOs (topological simplification).

Finally, in order to understand the temporal dimension in depth, it is important to find out

what happens at one time point. Hence, QTC relations are relations that hold at a particular

time point (temporal simplification, Figure 2.1d).

Figure 2.1 – Simplification in QTC of a real-life situation (a) by taking cumulatively account of the

relational simplification (b), the object simplification (c), and the temporal simplification (d)

(simple arrows for trajectories, double arrows for instantaneous velocity vectors).

2.3.2 Continuity, conceptual neighbours, and transitions

QTC assumes space and time, and thus the motion of objects, to be continuous. As a

consequence, QTC relations change in time according to the laws of continuity. Along with

continuity comes the important concept of conceptual neighbourhood as introduced by

Freksa (1992b). Two QTC relations between the same pair of MPOs are conceptual

neighbours if and only if these relations can directly follow each other through continuous

motion of the MPOs, without the necessity for a third relation to hold at an intermediate

point in time. A transition then denotes the continuous change of one relation into a

conceptual neighbouring relation. Each transition thereby happens at a certain instant or

point in time, which we will term a transition instant. A conceptual neighbourhood can be

represented by a conceptual neighbourhood diagram (CND), i.e. a visualisation of a graph

which nodes represent relations, and where two nodes are connected if they are conceptual

neighbours of each other.

All QTC calculi are associated with a set of jointly exhaustive and pairwise disjoint (JEPD)

base relations. Consequently, there is one and only one relation for each pair of coexisting

MPOs at each time instant. In addition, due to continuity, the concurrent movement of two

MPOs over a given time interval is uniquely mapped to a sequence of conceptually

neighbouring base relations.

24 Chapter 2

All QTC relations are formed by a tuple of labels (representing different primitive qualitative

relations) that all have the same three-valued qualitative domain , which we will

denote as in the remainder of this chapter. A ‘0’ symbol corresponds to a landmark value,

and as Galton (2001) points out, this value always dominates both ‘’ and ‘+’ values. Hence:

A ‘0’ must always last over a closed time interval (of which a time instant is a special

case);

A ‘’ / ‘+’ must always last over an open time interval;

Only transitions to or from ‘0’ are possible (transitions from ‘’ / ‘+’ to ‘+’ / ‘’ are

impossible) and transition instants always correspond with a ‘0’ value.

Based on the notion of topological distance introduced by Egenhofer & Al-Taha (1992), the

conceptual distance can be defined as a measure for the closeness of QTC relations (Van de

Weghe & De Maeyer 2005). We take the conceptual distance between ‘0’ and another

symbol to be one. This is the smallest conceptual distance, apart from zero (i.e. the distance

between a symbol and itself). Since a direct transition is impossible, the conceptual distance

between ‘’ and ‘+’ is equal to two (one for ‘’ to ‘0’ and one for ‘0’ to ‘+’). The overall

conceptual distance between two QTC relations can then be calculated by summing the

conceptual distance over all relation symbols. For instance, for two QTC relations consisting

of four symbols, the conceptual distance ranges from zero to eight.

2.3.3 Types of QTC

Due to the consideration of different spaces and frames of reference, the following types of

QTC have been elaborated:

Basic type – QTCB (Van de Weghe et al. 2006), Figure 2.2a

Double Cross type – QTCC (Van de Weghe et al. 2005a), Figure 2.2b

Network type – QTCN ) (Bogaert et al. 2007), Figure 2.2c

Shape type – QTCS (Van de Weghe et al. 2005b)

The Basic (QTCB) and the Double Cross (QTCC) types both deal with MPOs that have a free

trajectory in an n-dimensional space. QTCB relations are determined by referring to the

Euclidian distance between two MPOs (Figure 2.2a). QTCC relations on the other hand rely

on the double cross, a concept introduced by Zimmerman and Freksa (1996), as a spatial

reference frame (Figure 2.2b). QTCB and QTCC will be discussed in detail in the next two

sections.

QTCN (Network) focuses on the special case of MPOs which trajectories are constrained by a

network, such as cars in a city. Since both the Euclidean distance and the double cross

concepts ignore the spatial configuration of a potential underlying network, they are not

well suited for QTCN. Therefore, QTCN relations rely on the shortest paths in the network

between the considered MPOs (Figure 2.2c). In essence, QTCN employs the philosophy of


QTCB in the context of a space constrained by a network. QTCN will not be considered further

in this chapter.

Finally, QTCS (Shape) employs the double cross concept in order to describe trajectory

shapes or even arbitrary undirected polylines in a qualitative way. Thus, QTCS deals with the

relative configuration of a trajectory, rather than with the relation between MPOs. Due to

this different focus, it is out of the scope of this chapter.

Figure 2.2 – Two MPOs represented in a typical two-dimensional QTCB (a), QTCC (b), and QTCN (c)

setting. The frame of spatial reference is represented by the dashed line.

2.4 QTC – Basic (QTCB)

An MPO is always characterised by an origin and a destination, whether explicit or implicit.

Hence, a basic dichotomy concerning MPOs, perhaps the most fundamental one, is the

distinction between towards and away from relations. This very generic idea underlies QTCB

where this binary relation is evaluated on the basis of Euclidean distance in an

unconstrained n-dimensional space. In addition, also the relative speed between both

objects can be taken into account. As mentioned earlier, QTC relations consist of qualitative

symbols that share the threefold domain . QTCB relations are constructed from

the following relationships:

Assume: MPOs and and time point

denotes the position of an MPO at

denotes the Euclidean distance between two positions and

denotes the velocity vector of at

denotes that is temporally before

A. Movement of with respect to at (distance constraint): −: is moving towards :

(2.1)

+: is moving away from :

(2.2)

26 Chapter 2

0: is stable with respect to (all other cases)

B. Movement of with respect to at (distance constraint), can be described as in A with and interchanged, and hence:

−: is moving towards (2.3)

+: is moving away from (2.4)

0: is stable with respect to (all other cases)

C. Relative speed of with respect to at (speed constraint): −: is moving slower than :

(2.5)

+: is moving faster than :

(2.6)

0: and are moving equally fast:

(2.7)

Two levels of QTCB relations have been proposed: a first level QTCB1 that only considers the

distance constraints (relationships A and B), and a second level QTCB2 taking account of the

speed constraint (relationship C) as well. The resulting relation syntaxes are respectively the

tuples (A B)B1

and (A B C)B2

. Note that relationship C dually represents the relative speed

of l with respect to k, and hence trivialises a fourth relationship.

Relation icons for QTCB are shown in Figure 2.3, where is always on the left side, and on

the right side. The line segments and crescents represent potential motion areas. Note that

their boundaries are open, and, for the crescents, the straight boundaries correspond to

elements of another relation. A filled dot indicates that an MPO might be stationary,

whereas an open dot means that it must be moving. Dashed lines represent uncertain

boundaries that follow from the ignorance of relative speed. The Roman numerals below the

icons specify the minimum number of spatial dimensions required for a relation to be

feasible.

There are 9 (3²) base relations in QTCB1 (Figure 2.3a). All these relations are possible in a

one- or higher-dimensional space. QTCB2 on the other hand has 27 (3³) base relations (Figure

2.3b), which are all possible in two- or higher-dimensional spaces. However, in a one-

dimensional space, only 17 (63.0%) QTCB2 relations can occur. This reduction follows from a

dependency between the distance constraints and the speed constraint in the case of a 1D

space. In a 1D space, the direction of movement is always collinear with the direction of

Euclidean distance, and hence a ‘0’ in the distance constraints always corresponds to a

stationary MPO. As a consequence, it is impossible for an MPO to be stationary and to have

a higher speed than another MPO. In a two- or higher-dimensional space on the other hand,


a ‘0’ distance constraint does not necessarily indicate a stationary object, e.g. in the case of

‘tangential motion’ such as when one MPO is circling around the other MPO.

Figure 2.3 – QTCB1 (a), and QTCB2 (b) relation icons.

2.5 QTC – Double Cross (QTCC)

In addition to the towards / away from dichotomy of QTCB, QTCC employs another

fundamental distinction in navigation, i.e. the left / right dichotomy. Hence, an intrinsic ‡-

shaped frame of reference is obtained, called the Double Cross, after a concept introduced

by Freksa (1992b) (Figure 2.4). The reference line associated with the left / right distinction is

the straight connection line between both MPOs. Besides the left / right dichotomy, QTCC

also takes into account the relative difference in relative motion angle with respect to this

reference line.

28 Chapter 2

Figure 2.4 – Different use of the double cross in the Double Cross Calculus (Galton 2001) (a), and

the QTCC calculus (b).

Assume: MPOs and and time point

denotes the reference line through and

denotes the minimum absolute angle between

and

D. Movement of with respect to at (side constraint): −: is moving to the left side of :

(2.8)

+: is moving to the right side of :

(2.9)

0: is moving along (all other cases)

E. Movement of with respect to at (side constraint), can be described as in D with and interchanged, and hence:

−: is moving to the left side of (2.10)

+: is moving to the right side of (2.11)

0: is moving along (all other cases)

F. Angle constraint:

−:

(2.12)

+:

(2.13)

0: all other cases (2.14)

As for QTCB, two levels of QTCC have been defined: a first level QTCC1 which simply considers

the towards / away from and left / right distinctions and a second level QTCC2 considering

the speeds and angle constraints as well. The relational syntaxes are respectively

(A B D E)C1

and (A B D E C F)C2

. Let us consider relationship F if one of the objects is not

moving at . The object can move in every direction at and at . Assume that F is ‘’ at


and ‘+’ at . Since we assume continuous motion, F has to be ‘0’ at . Thus, if at least one

MPO is stationary, F will be ‘0’.

QTCC1 and QTCC2 respectively have 81 (34) and 729 (36) theoretical JEPD base relations

(Figure 2.5, Figure 2.6). In a one-dimensional space, left and right of the reference line

through and cannot be distinguished, and hence the side and angle constraints will

always be ‘0’. Thus, in essence, QTCC1 reduces to QTCB1 and QTCC2 reduces to QTCB2 for the

one-dimensional case, with respectively 9 (11.1% of the theoretical number) and 17 (2.3%)

base relations.

Figure 2.5 – QTCC1 relation icons.

30 Chapter 2

Figure 2.6 – QTCC2 relations and the minimal number of spatial dimensions supporting them:

respectively the dotted, dashed, and straight boundaries for one, two, and three dimensions.

In two dimensions, all QTCC1 base relations exist (as for all higher dimensions), whereas only

305 (42.4%) QTCC2 relations are possible, due to the interdependence of relational symbols.

Since in 2D space, objects must be stationary whenever their distance and side constraints

are ‘0’, the speed constraint is restricted and the angle constraint must be ‘0’ in that case.

Also, an object with a ‘0’ distance constraint and non-‘0’ side constraint must be moving with

a bigger or equal angle with respect to , and hence the restriction on the angle

constraint. Analogously, objects with a non-‘0’ distance constraint and ‘0’ side constraint

move with smaller or equal angles with respect to . Moreover, when the latter two rules


are combined, the inequality turns into either a strict equality, or a strict inequality, and

thereby restricts the angle constraint to a singleton.

In three-dimensional space, the distance and side constraints are insufficient to deduce the

stationarity of the objects. However, as in 2D, they determine whether the direction of

movement must be along or perpendicular to . From this observation restrictions follow

on the angle constraint. The special case where both the distance and side constraints are ‘0’

may indicate either a stationary object, or an object moving perpendicular to and

perpendicular to both the left / right and towards / away from directions. We obtain 591

(81.1%) feasible QTCC2 relations in 3D.

2.6 Representing and reasoning with QTC

QTC has been confronted with key concepts in qualitative reasoning. In this section, we will

discuss three of these issues, respectively conceptual neighbourhood diagrams (CNDs),

composition tables (CTs), and incomplete knowledge.

2.6.1 Conceptual neighbourhood diagrams

As mentioned earlier, the construction of CNDs for QTC is based on the concepts of

dominance (Galton 2001) and conceptual distance. For an in depth description, we refer to

Van de Weghe and De Maeyer (2005). CNDs for the Basic and Double Cross QTC calculi in 2D

space are respectively shown in Figure 2.7 and Figure 2.8. For each link between conceptual

neighbours the conceptual distance between the adjacent relations has been indicated. The

CND for QTCC1 in 1D has been omitted, since it would be the same as the CND for QTCB1

except for two additional ‘0’ values in each relation. The CND for QTCC2 is also not shown, as

it is too complex to visualise on a two-dimensional medium.

Figure 2.7 – CNDs for QTCB1 in n-dimensional space (a), for QTCB2 in a one-dimensional space (b),

and for QTCB2 in a two- or higher-dimensional space (c). The straight, dashed and dotted lines

respectively represent the conceptual distances one, two and three.

32 Chapter 2

Figure 2.8 – CND for QTCC1 in a two-or higher-dimensional space. Links have been gray-shaded

according to the conceptual distance between the adjacent relations.


From the CNDs, we learn that, due to the laws of continuity, the conceptual neighbours of

each particular relation constitute only a subset of base relations. This set comprises the

candidate relations that may directly precede or follow the relation at hand in time, i.e. the

set of possible transitions from/to this relation. This set of candidates is thereby highly

limited when compared to the set of theoretical possibilities, as can be seen from Table 2.1.

Note that each pair of conceptual neighbours and is associated with two transitions,

i.e. a transition from to , and its converse from to . Similarly to a CND, a transition

graph can be constructed with directed links to represent existing transitions. However, for

QTCB and QTCC, all converse transitions do exist and thus one conceptual neighbour relation

can be counted for two transitions (Table 2.1). Note that this may not be the case for other

types of QTC, e.g. for QTCDN’ (Delafontaine et al. 2008).

Another notable finding is that all CNDs are completely symmetric with respect to the

relation consisting solely of ‘0’ values. We call this symmetric and reflexive relation the zero-

relation. Symmetry with respect to the zero-relation is due to the central position of ‘0’ in

the qualitative set , as well as to the symmetry of conceptual neighbourhood

for converse QTC relations.

QTC calculus # spatial dimensions # base relations # transitions # combinations ratio

B1 1+ 9 32 72 44.4%

B2 1 17 64 272 23.5%

B2 2+ 27 196 702 27.9%

C1 2+ 81 1 088 6 480 16.8%

Table 2.1 – The number of base relations, transitions, theoretical combinations of base relations,

and the ratio transitions / theoretical combinations for the Basic and Double Cross QTC calculi.

Furthermore, every relation is a conceptual neighbour of the zero-relation (and vice versa),

as is consistent with our intuition. For instance, it is highly reasonable that, whatever the

relation between two MPOs at a certain moment, they may always become stationary the

next moment, in which case their relation turns into the zero-relation.

2.6.2 Composition tables

Another important reasoning tool, apart from the CND, is the composition table (CT). The

idea behind a CT is to compose existing relations to obtain new relations, i.e. if two existing

relations and share a common element they can be composed into a new

relation . The composition operation is represented here by the symbol, e.g.

. CTs are cross tables that usually contain the composition

results of all combinations of base relations for a certain calculus, with in the left column,

in the top row, and in each of the entries. CTs are very useful from a

computational point of view, since a simple table look-up can be far more efficient than

complex theoretical deduction (Bennett 1997, Skiadopoulos & Koubarakis 2004, Vieu 1997).

34 Chapter 2

In addition, CTs play an important role when working with incomplete information and

larger inference mechanisms.

The CT for one-dimensional QTCB1 is shown in Table 2.2. Of its 81 (9²) compositions, 20 are

unique, 20 of them are twofold, 4 are threefold, and the remaining 36 yield no solution

(empty set). The empty solutions come along with the inconsistent cases where the common

MPO must be moving in the first relation and must be stationary in the second relation, and

vice versa. Hence, in order to avoid them, one might use two separate CTs: one for the case

of a moving common MPO, the other one for the stationary case.

(--) (0-) (+-) (-0) (00) (+0) (-+) (0+) (++)

(--)

(-+)˅

(+-)

(--)

(0+)˅

(0-)

(0-)

(--)˅

(++)

(+-)

(0-)

(-0)˅

(+0)

(-0) (00) (00)

(-0)˅

(+0)

(+0)

(+-)

(--)˅

(++)

(-+)

(0+)˅

(0-)

(0+)

(-+)˅

(+-)

(++)

(-0)

(-+)˅

(--)˅

(+-)

(0+)˅

(0-)

(--)˅

(+-)˅

(++)

(00) (0+)˅

(0-)

(00) (0+)˅

(0-)

(+0)

(--)˅

(-+)˅

(++)

(0+)˅

(0-)

(-+)˅

(++)˅

(+-)

(-+) (--) (-+)˅

(+-)

(0-) (0+)˅

(0-)

(+-) (--)˅

(++)

(0+) (-0) (-0)˅

(+0)

(00) (00) (+0) (-0)˅

(+0)

(++) (-+) (--)˅

(++)

(++) (0+)˅

(0-)

(++) (-+)˅

(+-)

Table 2.2 – CT for QTCB1 in a one-dimensional space.

Complete CTs can be constructed for QTCB2. However, this would generally be a bad idea,

since the speed constraint (relationship C) is independent from the distance constraints

(relationships A & B). Hence, a more efficient solution is to use separate CTs for the distance

and speed constraints, and then recombine the results afterwards. Table 2.3 presents the CT

for the speed constraint, with seven unique results and two universe results. Note that these

universe sets are further reduced whenever at least one of the objects is stationary, as can

be deduced from the distance constraints in one-dimensional QTCB.


− 0 +

− − − U

0 − 0 +

+ U + +

Table 2.3 – CT for the speed constraint.

The CTs for two-dimensional QTCC1 and QTCC2 would respectively contain 6561 (81²) and

93025 (305²) entries, each of these entries containing a set of up to 81 and 305 elements.

Since CTs soon become very large, a so-called composition-rule table (CRT) was introduced

by Van de Weghe et al. (2005c). A CRT differs from a traditional CT as it does not contain all

individual composition results. Nevertheless, a CRT does provide all the information offered

by a traditional CT. Instead of the full CT, a CRT uses a set of composition rules to generate

the composition results for the relations at hand. These rules can be implemented in

information systems in order to automatically generate compositions, which might be

preferable to CTs due to their extent.

CRTs for QTC can be obtained by using diagrammatic reasoning on the basis of relation icons

(e.g. Figure 2.3 and Figure 2.5). As and are given, their corresponding relation icons

can be translated so that the position of in the icon of matches the position of in the

icon of . Then, in order to find the composition result, two central issues have to be

considered. First, which rotation do we need, such that the velocity vector of in matches

the one of in ? Second, how is moving with respect to in , and how is moving

with respect to in ?

Let us consider the case of two-dimensional QTCC1. For the first issue, nine rotational

possibilities have to be taken into account1: the crisp rotations 0°, 90°, 180°, 270°, the range

rotations ]0°, 90°[, ]90°, 180°[, ]180°, 270°[, ]270°, 360°[, and the option of no possible match

by rotation. The latter case occurs due to the impossibility of inference between a moving

and a stationary MPO. For the second issue, only the first and the third relational symbols of

(relationships A & C) and the second and fourth symbols of (relationships B & D) have

to be considered to determine the composition result.

Table 2.4 presents the CRT for QTCC1 in 2D. It has 324 entries, which is a compression to less

than 5% compared to the original CT with 6561 entries. The CRT consists of two halves: the

upper half to look up the first and third symbol (relationships A & C) of , and the lower

half to determine the second and fourth symbol (relationships B & D).

1 According to trigonometry, we take anti-clockwise angles as being positive.

36 Chapter 2

We briefly explain the CRT with an example. The velocity vector of in the icon of

(+ + 0 0)C1

needs to be rotated over 270° in order to match the vector of in

(− 0 − −)C1

. Hence, to find , we use the column of 270° of Table 2.4.

Then, the relationships A & C of are in the row corresponding to A & C of R1, i.e.

the row of ‘’,’’, and the column of 270°: we obtain for A and ‘’ for C. Analogously, B &

D of depend on B & D of : we get ‘+’ for B, ‘’ for D. Thus, we find

(− + − −)C1, (0 + − −)

C1, (+ + − −)

C1 . Note that results for A & C in one column

always have to be combined with results for B & C in the same column, even when multiple

columns correspond to the same rotation angle, e.g. for 180°. Thus we should not take the

cross product.

0° 90° 180° 270°

0°-

90° 90°- 180° 180°- 270°

270°-

360° X

A C A C A C A C A C A C A C A C A C A C A C A C A C A C A C A C A C A C

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

– 0 – 0 – + – 0 + 0 – – – + – + – + – + 0 + + + + – 0 – – – – – – – – –

– – – – – U – – + + U – – U – U – U – U – + U + + U + – U - U – U – U –

0 – 0 – – – 0 – 0 + + – – – – – – – – – – 0 – + + + + 0 + - + – + – + –

+ – + – U – + – – + + U U – U – U – U – – – – U U + + + + U + U + U + U

+ 0 + 0 + – + 0 – 0 + + + – + – + – + – 0 – – – – + 0 + + + + + + + + +

+ + + + + U + + – – U + + U + U + U + U + – U – – U - + U + U + U + U +

0 + 0 + + + 0 + 0 – – + + + + + + + + + + 0 + – – – – 0 – + – + – + – +

– + – + U + – + + – – U U + U + U + U + + + + U U – – – – U – U – U – U

B D B D B D B D B D B D B D B D B D B D B D B D B D B D B D B D B D B D

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

+ 0 + 0 + + – 0 + 0 + – + + – + 0 + + + + + + + + – + – + – 0 – – – + –

+ + + + U + – – + + + U U + – U – + U + U + U + + U + U + U + – U – + U

0 + 0 + – + 0 – 0 + + + – + – – – 0 – + – + – + + + + + + + + 0 + – + +

– + – + – U + – – + U + – U U – – – – U – U – U U + U + U + + + + U U +

– 0 – 0 – – + 0 – 0 – + – – + – 0 – – – – – – – – + – + – + 0 + + + – +

– – – – U – + + – – – U U – + U + – U – U – U – – U – U – U – + U + – U

0 – 0 – + – 0 + 0 – – – + – + + + 0 + – + – + – – – – – – – – 0 – + – –

+ – + – + U – + + – U – + U U + + + + U + U + U U – U – U – – – – U U –

Table 2.4 – CRT for QTCC1 in a two-dimensional space.

2.6.3 Incomplete knowledge

Not always everything has to be known about a situation to make inferences which are

important for the issue at hand (Frank 1996). Obviously, in these situations information may

lack for offering complete answers to queries. However, ‘a partial answer may be better

than no answer at all.’ as Freksa (1992a) argues. By abstracting away from the mass of

metrical details, qualitative representations are much more appropriate for handling such


incomplete knowledge, rather than quantitative approaches (Cristani, Cohn & Bennett

2000).

As mentioned before, the development of the QTC has been inspired by some major QR

calculi, especially the temporal Semi-Interval Calculus (Freksa 1992a) and the spatial Double-

Cross Calculus (Zimmermann & Freksa 1996, Freksa 1992b). Central in these theories is the

specific attention to incomplete knowledge, and hence, one might expect QTC to be able to

handle incomplete knowledge as well.

One kind of incomplete knowledge results from natural language expressions. Consider the

expression “ is moving towards , which is not slower than ”. This expression can be

represented in QTC, for instance by (− U U+)B2

with . Hence, we obtain a union

of six solutions. Interestingly, these solutions constitute a conceptual neighbourhood, i.e.

they are mutually path-connected through conceptual neighbour relations when isolated

from the complete CND of base relations (see Figure 2.7). According to Freksa (1992a), we

achieve coarse knowledge, i.e. a kind of incomplete knowledge that allows to be represented

by a conceptual neighbourhood of relations at a certain level of granularity. When relations

between MPOs are perceived or described incompletely through natural language, the

resulting knowledge will typically be coarse.

Whenever one expression may lead us to incomplete knowledge, multiple expressions can

be combined in order to deduce finer knowledge. Table 2.5 gives an example of four

expressions, each of which has a coarse result, for which the intersection results in complete

knowledge. In addition, composition offers an appropriate inference mechanism to integrate

expressions about three or more objects.

Natural language expression QTCB2 solution Integrated solution

“ k is moving towards l ” (− U U)B2

(− U U)B2 (U0 U0 U)B2 (U + U)B2 (U U 0)B2 = ( + 0)B2

“ k and l are moving along

the same straight line ” (U0 U0 U)B2

“ l is moving away from k ” (U + U)B2

“ l is moving equally fast as k ” (U U 0)B2

Table 2.5 – Intersection of coarse solutions to obtain fine knowledge, with U0 = U \{0}.

2.7 Extending QTC

Complex real-life motions go far beyond the earlier described simplifications applied in QTC.

Can we relax these constraints? Obviously, not all simplifications can be ignored. Therefore,

we now focus on how QTC can be extended, whilst still accepting the object simplification,

i.e. the abstraction of moving objects to MPOs. In the remainder of this section we will

38 Chapter 2

discuss the respective and cumulative releases of the relational, temporal, and topological

simplifications.

2.7.1 Multiple MPOs

The relations between multiple MPOs can be represented by means of a QTC cross table or

matrix (Table 2.6). An element in this matrix represents the QTC relation between

MPOs and . A QTC matrix can be computed at each time point. The following compression

rules and techniques can be used in order to reduce its size:

The diagonal of the matrix can be excluded, as it is empty due to the topological

constraint.

Only the upper right (or lower left half) of the matrix has to be considered, as is gray

shaded in bold in Table 2.6. The lower part of the matrix holds the converse relations of

the upper part and vice versa and is therefore redundant.

t k l m n

k

--

-+ -0

l -- ++ +0

m +- ++

-0

n 0- 0+

0-

Table 2.6 - QTCB1 matrix for four MPOs k, l, m, and n at time t.

Hence, for objects, the number of elements can be reduced from to - . Note

that research has been done in order to further simplify topological relations (Rodríguez,

Egenhofer & Blaser 2003) and simplifying temporal relations (Rodriguez, Van de Weghe & De

Maeyer 2004) over multiple elements. It could be interesting to combine both in order to

simplify spatiotemporal relations, such as QTC relations. Thus, the number of elements in a

QTC matrix could be further reduced so that it only contains relevant information, i.e. no

redundancies.

2.7.2 Multiple time points and intervals

What if we consider QTC matrices at different time moments? According to the philosophy

of qualitative reasoning, new relations only need to be calculated whenever transitions

occur. As a consequence, it will be the most efficient to compute one initial matrix and to

store only relations which have transitioned in all subsequent matrices.

2.7.3 Multiple topological relations

QTC does not distinguish topological relations, and might hence be complemented by

topological calculi. As mentioned earlier, point objects only have two topological relations:


disjoint and equal. Though QTC is developed to reason about disjoint objects, this constraint

might be relaxed. Note that in case of equal MPOs, we will always obtain zero-relations.

2.8 Example case

This section discusses an example application of QTC in one of the major domains of applied

science that in essence deals with objects moving in a geographical space, namely

transportation research. Ever since their invention, cars have been a focus of research for

numerous traffic engineers that have tried to represent and understand their complex

physics. A typical example is the case of an overtake event (André, Herzog & Rist 1989,

Fernyhough, Cohn & Hogg 2000). In this section, we will analyse this case in QTC starting

from raw trajectory sample points as received from position aware devices. As the left / right

distinction is crucial in overtake events, we will utilise QTCC.

Let us consider two cars and . Table 2.7 gives their two-dimensional sample coordinates

during an overtake event at regular time steps of one second. As QTC assumes continuity,

such a discrete set of sample points has to be interpolated in order to obtain continuous

trajectories. Although several approaches are possible, we will, for this example case, rely on

simple linear interpolation in space and time. This is also shown in Table 2.7.

sample

point

car k

car l

x (m) y (m) t (s) x (m) y (m) t (s)

1 15 0 0 15 10 0

2 15 5 1 15 13 1

3 10 13 2 15 17 2

4 10 23 3 15 23 3

5 10 33 4 15 28 4

6 15 41 5 15 33 5

7 15 46 6 15 38 6

Table 2.7 – Trajectory sample points of two cars k and l during an overtake event.

Figure 2.9 gives an overview of the spatial configuration of the objects and their

instantaneous velocity vector for all sample times during the overtake event. Also, the QTCC1

relations are given at and in between these sample instants. We find the following relation

40 Chapter 2

pattern: (− + 0 0)C1 (− + − +)

C1 (0 0 − +)

C1 (+ − − +)

C1 (+ − 0 0)

C1.

Since this is a pattern of subsequent conceptual neighbours, we call it a conceptual

animation (Van de Weghe et al. 2005a). It consists of five relations, four of which hold over a

time interval, whereas (0 0 − +)C1

occurs instantaneously at 3 s. Although all others last

over intervals, continuity theory induces some subtle differences between them. As pointed

out earlier, a ‘0’ value must always last over a closed time interval (of which a time instant is

a special case), whereas ‘’ and ‘+’ must always hold over an open time interval. Therefore,

it follows that (− + − +)C1

and (+ − − +)C1

persist over open time intervals, whereas

(0 0 − +)C1

occurs at an instantaneous closed time interval. Note that, as Table 2.7 does

not provide a preceding and following sample point for respectively the first and the seventh

sample point, the change in movement direction is unknown at these instants.

Consequently, the beginning of (− + 0 0)C1

and the end of (+ − 0 0)C1

are unknown, and

hence their corresponding time intervals are half-closed (Figure 2.9). With this knowledge, a

more complete description of the complete conceptual animation would be:

]0, 1]:(− + 0 0)C1

]1, 3[:(− + +)C1

[3]:(0 0 − +)C1

]3, 5[:(+ − − +)C1

[5, 6[:(+ − 0 0)C1

.

time 0 s 1 s 2 s 3 s 4 s 5 s 6 s

instantaneous

QTCC1 relation unkown (-+00)

C1 (-+-+)

C1 (00-+)

C1 (+--+)

C1 (+-00)

C1 unkown

interval QTCC1

relation (-+00)

C1 (-+-+)

C1 (-+-+)

C1 (+--+)

C1 (+--+)

C1 (+-00)

C1

Figure 2.9 – Configuration of two cars k and l at sample time stamps during an overtake event.

The overtake event illustrated here would be a legal manoeuvre if we consider right-hand

driving in Continental Europe. What about the case of left-hand driving? In that case, the


trajectories of and are mirrored along the main road axis, and hence left interchanges

with right. As can be expected for QTCC1, we obtain a symmetrical animation with the last

two characters inverted, while the first two remain: (− + 0 0)C1 (− + + −)

C1

(0 0 + −)C1 (+ − + − )

C1 (+ − 0 0)

C1.

Similarly to the overtake event, numerous other traffic situations can be modelled by means

of conceptual animations. A qualitative framework can then be composed of such QTC

patterns in order to reason about, recognise or simulate traffic events.

2.9 Future research directions

A major direction for further research is the extension of QTC theory. New types of QTC,

perhaps application-specific types, can be elaborated. To this end, opportunities lie in the

relaxation of one or more of the simplifications that were made, e.g. to allow moving line,

region and body objects, next to the conventional MPOs. Also, more realistic scenarios,

spatial and temporal constraints, or frames of reference can be taken into account.

Delafontaine et al. (2008) already made an attempt in that direction by studying the

implications for QTCN when considering dynamic instead of static networks.

Other directions lie in the implementation, application and evaluation of QTC. Efforts in that

direction have already been undertaken by Delafontaine et al. (Delafontaine & Van de

Weghe 2008, Delafontaine 2008). We plan to evaluate the usefulness of QTC-based

information systems through extensive case studies.

Finally, future research may consider how QTC relates to other domains, such as

psychological, cognitive and behavioural sciences, linguistics, information visualisation, and

human-computer interaction. It is our aim to study how QTC relates to cognition and natural

language, e.g. in simple prepositions such as ‘towards’ and ‘away from’ (Bogaert et al. 2008).

2.10 Conclusion

This chapter has presented the Qualitative Trajectory Calculus as a qualitative

spatiotemporal calculus to handle the relations between moving objects adequately. The

development of QTC and which spatial and temporal calculi inspired QTC has been

discussed. The chapter has focused on the two most general and fundamental QTC calculi,

i.e. the Basic and Double Cross types, as they constitute the basis of all other types. The

principal reasoning mechanisms such as conceptual neighbourhoodness and composition

have been considered in some detail, as well as the ability for QTC to deal with incomplete

knowledge. The usefulness and applicability of QTC has been illustrated in a simple case

where, starting from raw trajectory data, a conceptual QTC animation is obtained. Finally,

although QTC is not yet fully theoretically well-documented, we presented three useful

directions for future research.

42 Chapter 2

References

Allen, J. F. (1983) Maintaining knowledge about temporal intervals. Communications of the ACM, 26,

11, 832-843.

André, E., Herzog, G. & Rist, T. (1989) Natural language access to visual data: Dealing with space and

movement. In SFB 314, Project VITRA,. Saarbrücken, Germany: German Research Center for

Artificial Intelligence (DFKI), Universität des Saarlandes, 21.

Bennett, B. (1997) Logical representations for automated reasoning about spatial relationships,

Doctoral Dissertation Leeds: University of Leeds, School of Computing, 211.

Bitterlich, W., Sack, J. R., Sester, M. & Weibel, R. (2008) Abstracts collection – representation,



Bogaert, P., Van de Weghe, N., Cohn, A. G., Witlox, F. & De Maeyer, P. (2007) The Qualitative

Trajectory Calculus on Networks. In Spatial Cognition V: Reasoning, Action, Interaction, eds.

T. Barkowsky, M. Knauff, G. Ligozat & D. R. Montello, 20-38.

Bogaert, P., Van der Zee, E., Maddens, R., Van de Weghe, N. & De Maeyer, P. (2008) Cognitive and

linguistic adequacy of the Qualitative Trajectory Calculus. In International Worshop on

Moving Objects : From Natural to Formal Language, eds. N. Van de Weghe, R. Billen, B.

Kuijpers & P. Bogaert. Park City, Utah.


Representation, eds. F. Van Harmelen, V. Lifschitz & B. Porter. Elsevier Science.

Cristani, M., Cohn, A. G. & Bennett, B. (2000) Spatial Locations via morpho-mereology. In Conference

on Principles of Knowledge Representation and Reasoning (KR'2000), Morgan Kaufmann, 15-

25.

Delafontaine, M. (2008) The Qualitative Trajectory Calculus - from theory to practice. In

Representation, Analysis and Visualization of Moving Objects (Dagstuhl Seminar 08451), eds.

W. Bitterlich, J. R. Sack, M. Sester & R. Weibel, 5. Dagstuhl, Germany: Schloss Dagstuhl -

Leibniz-Zentrum für Informatik, Germany.

Delafontaine, M. & Van de Weghe, N. (2008) Towards an implementation of the Qualitative

Trajectory Calculus to analyze moving objects. In Proceedings of the International Conference

Spatial Cognition 2008, Poster Presentations, ed. C. Hölscher, Freiburg, Germany, 117-120.



Sciences, 178, 8, 1997-2006.

Egenhofer, M. J. & Al-Taha, K. K. (1992) Reasoning about gradual changes of topological

relationships. In Theory and Methods of Spatio-Temporal Reasoning in Geographic Space,

eds. A. U. Frank, I. Campari & U. Formentini, Pisa, Italy: Springer-Verlag, 196-219.

Egenhofer, M. J. & Franzosa, R. D. (1991) Point-set topological spatial relations. International Journal

of Geographical Information Systems, 5, 2, 161-174.

Fernyhough, J., Cohn, A. G. & Hogg, D. C. (2000) Constructing qualitative event models automatically

from video input. Image and Vision Computing, 18, 2, 81-103.

Frank, A. U. (1996) Qualitative spatial reasoning: Cardinal directions as an example. International

Journal of Geographical Information Systems, 10, 3, 269-290.

Freksa, C. (1992a) Temporal reasoning based on semi-intervals. Artificial Intelligence, 54, 199-127.


Freksa, C. (1992b) Using orientation information for qualitative spatial reasoning. In Theories and



Galton, A. (2001) Dominance diagrams: a tool for qualitative reasoning about continuous systems.

Fundamenta Informaticae, 46, 1-2, 55-70.

Gudmundsson, J., van Kreveld, M. & Speckmann, B. (2004) Efficient detection of motion patterns in

spatio-temporal data sets. In Proceedings of the 12th Annual ACM International Workshop on

Geographic Information Systems, Washington DC, USA: ACM.

Güting, R. H., Bohlen, M. H., Erwig, M., Jensen, C. S., Lorentzos, N. A., Schneider, M. & Vazirgiannis,

M. (2000) A foundation for representing and querying moving objects. ACM Transactions on

Database Systems, 25, 1, 1-42.

Hallot, P. & Billen, R. (2008) Generalized life and motion configurations reasoning model. In

International Worshop on Moving Objects : From Natural to Formal Language eds. N. Van de

Weghe, R. Billen, B. Kuijpers & P. Bogaert. Park City, Utah.

Ibrahim, Z. & Tawfik, A. (2007) An abstract theory and ontology of motion based on the Regions

Connection Calculus. In Abstraction, Reformulation, and Approximation, 230-242.

Kurata, Y. & Egenhofer, M. J. (2009) Interpretation of behaviours from a viewpoint of topology. In

Behaviour Monitoring and Interpretation - BMI, Ambient Intelligence and Smart

Environments, eds. B. Gottfried & H. Aghajan. Amsterdam, the Netherlands: IOS Press.

Laube, P. (2005) Analysing Point Motion – Spatio-Temporal Data Mining of Geospatial Lifelines,


Muller, P. (2002) Topological spatio-temporal reasoning and representation. Computational

Intelligence, 18, 3, 420-450.

Noyon, V., Claramunt, C. & Devogele, T. (2007) A relative representation of trajectories in

geographical spaces. Geoinformatica, 11, 4, 479-496.

Peuquet, D. J. (2001) Making space for time: Issues in space-time data representation.


Randell, D. A., Cui, Z. & Cohn, A. G. (1992) A spatial logic based on regions and connection. In

Proceedings of the Third International Conference on Principles of Knowledge Representation

and Reasoning, eds. B. Nebel, C. Rich & W. Swartout, 165-176.

Rodríguez, A. M., Egenhofer, M. J. & Blaser, A. D. (2003) Query pre-processing of topological

constraints: Comparing a composition-based with neighborhood-based approach. In

International Symposium on Advances in Spatial and Temporal databases (SSTD 2003), LNCS

2750, Greece: Springer, 362-279.

Rodriguez, A. M., Van de Weghe, N. & De Maeyer, P. (2004) Simplifying sets of events by selecting

temporal relations. In Proceedings of the 3rd International Conference on Geographic

Information Science, LNCS 3234, 269-84|viii+343.

Skiadopoulos, S. & Koubarakis, M. (2004) Composing cardinal direction relations. Artificial

Intelligence, 152, 2, 143-171.



44 Chapter 2

Van de Weghe, N., Cohn, A. G., De Maeyer, P. & Witlox, F. (2005a) Representing moving objects in

computer-based expert systems: the overtake event example. Expert Systems With

Applications, 29, 4, 977-983.

Van de Weghe, N., Cohn, A. G., De Tré, G. & De Maeyer, P. (2006) A Qualitative Trajectory Calculus as

a basis for representing moving objects in geographical information systems. Control and

Cybernetics, 35, 1, 97-119.

Van de Weghe, N. & De Maeyer, P. (2005) Conceptual neighbourhood diagrams for representing

moving objects. In Perspectives in Conceptual Modeling, 228-238.

Van de Weghe, N., De Tré, G., Kuijpers, B. & De Maeyer, P. (2005b) The double-cross and the

generalization concept as a basis for representing and comparing shapes of polylines. In

Proceedings of the 1st International Workshop on Semantic-based Geographical Information

Systems (SeBGIS'05), Agia Napa, Cyprus.

Van de Weghe, N., Kuijpers, B., Bogaert, P. & De Maeyer, P. (2005c) A Qualitative Trajectory Calculus

and the composition of its relations. In Proceedings of the 1st International Conference on

Geospatial Semantics (GeoS), eds. A. M. Rodríguez, I. F. Cruz, M. J. Egenhofer & S. Levashkin,

Springer-Verlag, 60-76.

Vieu, L. (1997) Spatial representation and reasoning in artificial intelligence. In Spatial and Temporal

Reasoning, ed. O. Stock, Dordrecht, The Netherlands: Kluwer, 5-41.

Wolter, F. & Zakharyaschev, M. (2000) Spatio-temporal representation and reasoning based on RCC-

8. In Proceedings of the 7th Conference on Principles of Knowledge Representation and

Reasoning, KR2000.

Zimmermann, K. & Freksa, C. (1996) Qualitative spatial reasoning using orientation, distance, and

path knowledge. Applied Intelligence, 6, 1, 49-58.

Inferring additional knowledge from QTCN-relations 45

3 Inferring additional knowledge from QTCN relations

Delafontaine M., Bogaert P., Cohn A. G., Witlox F., De Maeyer P., Van de Weghe N.

in Information Sciences (2011), Volume 181, Issue 9

Copyright © Elsevier Science

Abstract. It is widely held that people tend to use qualitative rather than quantitative

phrases when raising or answering questions about moving objects. Queries about

whether an object is moving towards or away from another object or whether

objects are getting closer to each other or further away from each other, require

qualitative responses. This characteristic should be reflected in a calculus to be used

to describe and reason about continuously moving objects. In this chapter, we

present a qualitative trajectory calculus of relations between two disjoint moving

objects, whose movement is constrained by a network. The proposed calculus (QTCN)

is formally introduced and illustrated. Particular attention is placed on how to infer

additional knowledge from QTCN relations by means of composition tables and the

transformation of QTCN relations into relations defined by the Relative Trajectory

Calculus on Networks (RTCN).

Keywords. Moving Objects – Qualitative information – Networks – Spatio-temporal

Reasoning

3.1 Introduction

Continuously moving objects are prevalent in many domains such as human movement

analysis (such as traffic planning or sports scene analysis) and animal behaviour science

(Laube, Imfeld & Weibel 2005). Most applications focus on the positional movement of the

object, abstracted to a single point1. Recent advances in various positioning technologies

(e.g. GPS, LBA, wireless communication) (Zeimpekis, Giaglis & Lekakos 2002) allow the

capture and storage of large quantities of such moving point data. Research has addressed

the generation (Brinkhoff 2002, Pfoser & Theodoridis 2003), indexing (Saltenis et al. 2000,

Agarwal, Arge & Erickson 2003, Lee et al. 2007, Francis, Madria & Sabharwal 2008),

modelling (Hornsby & Egenhofer 2002, Güting, de Almeida & Ding 2006, Hornsby & King

2008) and querying (Sistla et al. 1997, Erwig et al. 1999, Laube et al. 2007, Gao et al. 2010) of

moving objects in spatiotemporal databases. However, only recently has work been

conducted in reasoning about the relations between moving point objects and the

1 In the rest of this chapter, when we refer to “moving point objects”, we mean such a moving object whose

spatial extent has been abstracted to a single point, for example its centroid.

46 Chapter 3

transitions between these relations, especially in a qualitative framework (Clementini, Di

Felice & Hernandez 1997, Van de Weghe 2004). A specific proposal for qualitative relations

between disjoint moving point objects is the Qualitative Trajectory Calculus (QTC), which

formally defines qualitative relations between disjoint moving point objects (Van de Weghe

2004).

In this chapter, building on Van de Weghe (2004), QTC is adapted to objects moving in

networks, resulting in QTCN, and its power for representing and reasoning with qualitative

information for objects moving in networks is shown. The chapter is structured as follows.

Section 3.2 describes the difference between qualitative and quantitative information and

explains why qualitative information can be useful. Section 3.3 briefly introduces the

Qualitative Trajectory Calculus (QTC), which is the basis for the Qualitative Trajectory

Calculus for Networks (QTCN) and which is formally outlined in section 3.4. The next two

sections focus on reasoning with QTCN relations. Section 3.5 presents the composition of

QTCN relations, while section 3.6 shows how QTCN relations can be transformed into

relations defined by the Relative Trajectory Calculus on Networks (RTCN). Section 3.7

discusses the usefulness of QTCN in possible applications, leading to conclusions and

directions for further research in section 3.8.

3.2 Qualitative versus quantitative questions

When raising or answering questions about moving objects, both qualitative and

quantitative responses are possible. Typically, when responding to a question in a

quantitative sense, a predefined unit of a quantity on a continuous measuring scale is used

(Goyal 2000). For example, when asked for the speed of a car, the most likely quantitative

answer to that question would be that the car drives at, say, 30 km/h. As Galton (2000) says,

quantitative information is ‘measured by quantity’. In the qualitative approach, the expected

answer will be ‘the car is driving slowly’. Qualitative information is concerned with

information which ‘depends on a quality’ (Galton 2000). A key aspect of qualitative

information, is to find ways to represent continuous aspects of the world (space, time,

quantity, etc.) by a small set of symbols (Forbus 1997, Clementini, Di Felice & Hernandez

1997). In the qualitative approach, continuous information is qualitatively discretised by

landmarks separating neighbouring open intervals, resulting in discrete quantity spaces

(Weld & de Kleer 1989). For instance, one might say that a car driving more than 30 km/h is

driving fast, and a car driving less than 30 km/h is driving slowly.

When describing the movement of objects, a qualitative description can sometimes give a

more satisfactory answer than a quantitative one. For example, if one does not know the

exact speed of a car and a bicycle, but one knows that the speed of the car is higher than the

speed of the bicycle, one can say that the car is moving faster than the bicycle, labelling this

with the qualitative value ‘+’. One could also say that the bicycle is moving slower than the

car, by assigning the qualitative value ‘−’ to this relation. Finally, both objects can also move


at the same speed, resulting in a qualitative value ‘0’. Note that a distinction is only

introduced if it is relevant to the current context (Byrne & Johnson-Laird 1989, Clementini, Di

Felice & Hernandez 1997).

Of particular interest in describing qualitative information, are representations that form a

finite set of jointly exhaustive and pairwise disjoint (JEPD) relations (Renz & Nebel 2007). In a

set of JEPD relations, any two entities are related by exactly one of these relations, and they

can be used to represent definite knowledge with respect to the given level of granularity.

Incomplete or partial knowledge can be specified by coarse relations representing unions

(i.e. disjunctions) of possible JEPD relations.

There are a variety of other grounds why reasoning with qualitative information can be

considered complementary to reasoning in a quantitative way, in areas such as Artificial

Intelligence and Geographic Information Science. A key motive is the fact that human beings

are more likely to prefer to communicate in qualitative categories, supporting their intuition,

rather than using quantitative measures (Freksa 1992b). Representing and reasoning with

qualitative information can overcome information overload. Information overload occurs

whenever more information has to be handled than can be processed (O'Reilly 1980). For

example, it is easier to communicate a certain slope characteristic of a region (e.g. flat,

steep, hilly) than to provide over a thousand height points (Donlon & Forbus 1999). Also,

spatial expressions in natural language are rarely precise (e.g. the library is located in the

centre of the town; he is moving towards the cinema) (Guesgen & Albrecht 2000); in other

words, they usually do not provide enough information to identify the exact geographical

location of an object or event (Kalashnikov et al. 2006). Abstract, non-coordinate-based

methods are necessary to deal with these uncertainties (Frank 1996). Although reasoning

with qualitative information may lead only to a partial answer, such an answer is often

better than having no answer at all (Freksa 1992a). In addition, since the information is more

granular, qualitative reasoning can be computationally easier than its quantitative

counterpart (Freksa 1992b). Finally, qualitative data often provides an ideal way to deliver

insights into a particular problem rapidly, in order to identify potential issues that warrant a

more detailed quantitative analysis (Iwasaki 1997).


Mereotopology is the most developed area of qualitative spatial reasoning (Bennett 1997,

Cohn & Renz 2007). However, when it comes to moving point objects, topological models

such as the 9-intersection model merely distinguish two trivial topological relations between

two point objects: equal and disjoint (Egenhofer & Herring 1991). Since in the real world the

mereotopological relationship between most moving objects is that of being disjoint, and

topological models cannot further differentiate between disjoint objects, nor indeed can any

purely topological representation, important questions remain unanswered. An obvious

example is the case of two airplanes, where it is imperative to know whether both airplanes

48 Chapter 3

are likely to stay in a disjoint relation; if not, the consequences are catastrophic. In order to

represent and reason about moving objects the Qualitative Trajectory Calculus (QTC) was

introduced (Van de Weghe 2004). This calculus deals with qualitative relations between two

disjoint moving point objects. QTC can distinguish a number of basic binary relationships

between two moving objects. An object can be moving towards another object; it can be

moving away from another object; or it can be stable with respect to the other object. In

(Van de Weghe 2004), two QTC calculi are defined. The Qualitative Trajectory Calculus –

Double Cross (QTCC) (Van de Weghe 2004, Van de Weghe et al. 2005a) examines relations

between moving point objects based on three reference lines forming a so-called double

cross. The Qualitative Trajectory Calculus – Basic (QTCB) (Van de Weghe & De Maeyer 2005,

Van de Weghe et al. 2006) defines these relations by comparing differences in distance over

time. In order to elaborate a QTC calculus for network-based moving objects, we will build

on QTCB since QTCC is not suitable to use in a network environment, as it utilises a direction-

based spatial reference for defining relations. In the remainder of this section we will briefly

introduce QTCB as defined in (Van de Weghe 2004).

In QTC, time is assumed to be continuous and linear. This time line can be represented by

the set of real numbers ( ) and it has a total order associated with it. This implies that one

cannot identify two time points next to each other. The density of allows no notion

“nextness” (Mortensen 1999). In order to formally define the qualitative relations available

in QTCB, we introduce the following notations and definitions:

denotes the position of an object at time point .

denotes the speed of at time point .

denotes the distance between two positions and .

Definition 3.1 A relation in QTCB at level 1 between a first object and a second object

at a time point is defined by a two character label. This label represents

the following two relationships:

1. Movement of with respect to at :

−: is moving towards :

(3.1)


(3.2)

0: is stable with respect to : all other cases


Can be described as in 1, with and interchanged, hence:




0: is stable with respect to

Definition 3.2 A relation in QTCB at level 2 between a first object and a second object

at a time point is defined by a three character label. The first two

characters are defined as in Definition 3.1. The third character represents

the relative speed and is defined as follows:

3. Relative speed of with respect to at :

−: is moving slower than :

(3.5)


(3.6)


(3.7)

3.4 The Qualitative Trajectory Calculus on Networks

Having introduced QTC, we will now elaborate the definition of QTC on networks. Moreira et

al. (1999) differentiate between two kinds of moving objects: objects that have a completely

free trajectory, only constrained by the dynamics of the object itself (e.g. a bird flying

through the sky) and objects that have a constrained trajectory (e.g. a train on a railway

track). Many trajectories involving humans are bounded to a network. Hence, there is a need

to develop a calculus that defines qualitative relations between two disjoint moving objects

on trajectories constrained by a network. An informal description and definition of QTCN was

presented in (Van de Weghe 2004, Van de Weghe et al. 2004, Bogaert et al. 2007), while a

conceptual neighbourhood diagram for QTCN was presented in (Bogaert et al. 2007). In this

chapter, QTCN is defined formally. Also, we explore the power of this calculus to infer

additional information from the basic QTCN-relations.

3.4.1 Definitions and restrictions concerning networks and moving objects

A network, such as a road, rail or river network, is usually described as a set of

interconnected linear spatial features; each such linear feature can be regarded as a curve,

describing a linear path through the space it is embedded in. Thus, in essence, a network is a

co-dimensional structure. The concept of co-dimensionality can be used to express the

difference in dimension between spatial entities (point: zero-dimensional; line: one-

dimensional, region: two-dimensional, etc.) and the space they are embedded in (Galton

2000). In the case of a network, one-dimensional structures (a set of interconnected lines)

are embedded in a two dimensional (co-dimension one) or three dimensional space (co-

dimension two). Therefore, we assume an underlying spatial framework S for specifying

locations. Typically this would be , but could be any set with a metric distance function

50 Chapter 3

obeying the triangle inequality, and a notion of curve defined, such that

denotes the set of simple non-closed curves in .

In order to formally define QTCN relations for two moving point objects, using the network in

which they are embedded as a reference frame, three functions are defined on curves. For

any curve :

denotes the length of ;

is true if is an endpoint of ;

if and are two points incident in , then denotes the subcurve of

between and including and .

The network in which objects move in QTCN is characterised by a graph, whose edges

represent a set of linear features and the nodes of the graph represent the endpoints which

bound these linear features (Definition 3.3). A function embeds these nodes and

edges in the spatial framework (Definition 3.4 and 3.5). As stated above, the edges should

represent simple non-closed curves. To formally define this property, we do not allow two

nodes to lie at the same location (Restriction 3.1), the edges should be bounded by two

different nodes (Definition 3.5) and two different edges can only intersect at their respective

endpoints (Restriction 3.2). The number of edges representing curves which intersect at a

node denotes the degree of that node (Definition 3.6).

Definition 3.3 If is a network then is its set of nodes and is its set

of edges.

Definition 3.4 If is a node then is the spatial location of in .

Restriction 3.1 If is a network then .

Definition 3.5 If is a network and then is the curve

denoted by in , and

.

Restriction 3.2 If is a network then

nodes( ).

Definition 3.6 If is a network then the degree of a node ,

.

The movement of objects in QTCN is restricted by the network, which implies that the

location of an object should at all times be situated on an edge (Definition 3.7). As stated in


section 3.3, QTC only considers relations between disjoint objects, thus, two different

objects cannot be at the same place at the same time (Restriction 3.3).

Definition 3.7 An object at a time point is located in a network iff

.

Restriction 3.3 All two non-identical objects and are not instantaneously coincident at

a time point : .

To relate two objects in QTCN, there needs to be at least one path between both objects (see

section 3.4.2). A path is composed of a connected sequence of edges. Since the objects do

not necessarily lie at the endpoint of an edge, a notion of edge segments is required

(Definition 3.8). The notation denotes an edge segment which represents (i.e.

whose location is) that part of an edge between a point and an endpoint of the edge

(including and ). If is the other endpoint of , then the edge segment equals the edge

(as a special case). Thus, a path between two objects is composed of a sequence such that

the first and last elements are edge segments on which the two objects are located (possibly

the same segment), and any intermediate edges form a connected path, such that no edge

occurs more than once (Definition 3.9). The length of a path is defined as the sum of the

length of its edges and edge segments (Definition 3.10). A shortest path is defined as a path

such that there is no path having a shorter length between the same two nodes (Definition

3.11). There can be more than one shortest path between two objects at the same time. If,

in this special case, the first edge segment is different for all of these shortest paths, we

refer to these shortest paths as bifurcating shortest paths (Definition 3.12 and Figure 3.1).

Definition 3.8 If is an edge then is an edge segment of iff

.

Definition 3.9 A path between two different objects and in a network at time

point is a sequence such that

=seg( , | , )

loc( ).

Definition 3.10 is the length of a path .

Definition 3.11 A shortest path in a network from an object to an object at a

time point is a path such that there is no path from to of length less

than . We may write when is such a shortest path.

52 Chapter 3

Definition 3.12 If there are at least two different shortest paths from an object

to an object at a time point , then there is a bifurcating shortest path

from to at iff

.

Figure 3.1 – Bifurcating (a) and non-bifurcating (b) shortest paths.

It is obvious that objects moving on a network do not always move along the same edge

simultaneously. Objects can move from one edge to another. When doing so, they pass a

node (Definition 3.13). If passes a node lying at the intersection of two edges and at

time point , and neither of these edges is along a shortest path from to at , this event is

referred to as a shortest path omitting node pass event (Definition 3.14 and Figure 3.2).

Definition 3.13 An object on a network is in a node pass event along edges at a

time point , iff

.

Definition 3.14 An object on a network is in a shortest path omitting node pass event

with respect to another object at a time point iff

.

Figure 3.2 – A shortest path omitting node pass event.


3.4.2 Definition of QTCN relations

The reference used to qualitatively assess the relation between two objects is the distance

measured along the shortest path. If there is no path between two objects, then there is no

QTCN relation between these objects. Put differently, these objects are either not moving

along a network, or they occupy disjoint parts of a disconnected network and will hence

remain disjoint. The shortest path is chosen because it seems to encode what it means for

one object to approach or recede from another object in a network. (In Euclidean space, one

might naturally define approaching in terms of an angular measure, but this is not applicable

in networks, and shortest path is the appropriate equivalent notion.) In a network, an object

can only approach another object if and only if it moves along a shortest path between these

two objects (Bogaert et al. 2007). Using this property, we can state that an object can only

approach another object at a time point in a network if it does not lie on

immediately before and if it lies on immediately after . moves away from at if

it is on immediately before and if it does not lie on

immediately after . If

lies on only at , but not immediately before and immediately after , or if is on

immediately before and immediately after , then is stable with respect to

(although this relation may only last for an instantaneous moment in time). This property

allows reformulating conditions (3.1, 3.2) of Definition 3.1 for the construction of the first

level relation of QTCB to a QTCN setting.

Definition 3.15 A relation in QTCN at level 1 between a first object and a second object

on a network at a time point is defined by a two character label. This

label represents the following two relationships:


−: is moving towards :

(3.8)


(3.9)

0: is stable with respect to (all other cases):

(3.10)

(3.11)


Can be described as in 1 with and interchanged, hence:

54 Chapter 3



0: is stable with respect to (3.14, 3.15)

The second level relation of QTCN is defined identically to the definition in QTCB – cf.

Definition 3.2 (Definition 3.16).

Definition 3.16 A relation in QTCN at level 2 between a first object and a second object

in a network at a time point is defined by a three character label. The

first two characters are defined as in Definition 3.15. The third character

represents the relative speed and is defined as follows:

3. Relative speed of with respect at :

−: is moving slower than :

(3.16)


(3.17)


(3.18)

Based on Definition 3.16, we can construct all canonical cases for QTCN relations at level 2.

Let us analyse all possible movements of a first object with respect to a second object in

a QTCN relation at time point . can be stationary, i.e. not moving with respect to the

network, or not. If is stationary at , it will be located on a shortest path to at (and

immediately before and immediately after ), and therefore the definition yields ‘0’ for the

first character in the label (i). If is moving at , then by definition there are four possibilities

(ii – v). can be on a shortest path to immediately before and not immediately after ,

which returns ‘+’ for the first character in the label (ii). can be on a shortest path to

immediately after but not immediately before , which returns ‘−’ for the first character in

the label (iii). When is in a shortest path omitting node pass event with respect to , it will

not be on a shortest path to just before and after , resulting in a ‘0’ for the first character

in the label (iv). If there is a bifurcating shortest path from to , then will be on a shortest

path to just before and after , which also yields ‘0’ for the first character in the label (v).

The same five cases exist for the movement of the second object in the relation. Hence,

there exist 25 (5²) canonical cases looking at the first level of QTCN. When considering the

second level, the additional three possibilities for the third label character might be

expected to yield 75 (25*3) canonical cases. However, due to the impossibility for a

stationary object to move faster than or equally as fast as a non-stationary object, 18 of

these relations cannot physically occur. The remaining 57 canonical cases are presented in

Figure 3.3. The first column in the figure presents the QTCN relation. In the other columns, an

icon is sketched for all canonical cases. A ‘0n’ denotes a ‘0’ due to a shortest path omitting

node pass event. A ‘0b’ denotes a ‘0’ due to the existence of a bifurcating shortest path


Figure 3.3 – 57 Canonical cases for QTCN at level 2.

56 Chapter 3

Figure 3.3 (continued)

between the objects. The left and right dots represent the positions of (the first object)

and (the second object), respectively. A dot is filled if the object can be stationary. The

arrow symbols represent the potential movement directions of the objects. The arrows can

have different lengths indicating the difference in relative speed.

3.5 Composition

People often make inferences of and from qualitative relations in daily life (Byrne & Johnson-

Laird 1989). For example, if we know that Nico is taller than Philippe and Frank is taller than

Nico, we infer that Frank is taller than Philippe. A specific type of inference mechanism,

which is a fundamental part of a relational calculus, is the composition of its relations (Tarski

1941). The idea behind composition is to compose a finite set of new facts and rules from

existing ones, i.e. if two existing relations and share a common object ( ),

they can be composed into a new relation , denoted by:

– note that may be a disjunction of base relations. If, for a set of relations, the

compositions of all combinations of base relations can be computed, they are usually stored

in a composition table. Composition tables make sense from a computational point of view,

since a compositional inference can simply be looked up, instead of needing complex

computations (Bennett 1997, Vieu 1997). Ever since their introduction, composition tables

have been precomputed for many different temporal (e.g. the interval calculus (Allen 1983)

and the semi interval calculus (Freksa 1992a)), spatial (e.g. topological calculi (Randell, Cui &

Cohn 1992, Egenhofer 1994), directional calculi (Frank 1991, Freksa 1992b), distance calculi


(Hernández, Clementini & Di Felice 1995)), and spatiotemporal calculi (e.g. QTC (Van de

Weghe et al. 2005b)).

3.5.1 Composition of QTCN relations

Since the composition of relative speed (represented by the third character of a level 2 QTCN

relation) is straightforward, this section will focus on the composition of QTCN at level 1.

Nine (3²) QTCN base relations can be distinguished at level 1. As a consequence, the

composition table at level 1 has 81 (9²) entries, each of which potentially contains a subset

of these nine relations. Thus, 729 (93) possible combinations of three relations need to be

examined for their existence or non-existence. For each possibility that actually exists, a

simple ‘animation’ can be drawn to demonstrate its existence. Examples of such animations

for the composition of (+ −) and (− 0) are shown in Figure 3.4.

Figure 3.4 – Animations for the composition of (+ −) and (− 0); a movement arrow next to an

object indicates that the object is passing a node.

Since each composition yields the entire set of base relations, the construction of a

composition table is trivial. This triviality results from the fact that QTCN relations do not

provide sufficient information about the spatiotemporal configuration of the network.

Therefore, in order to obtain sparser composition tables, additional knowledge of the

relation between the network and the moving objects is required. This can be acquired by

imposing temporal as well as spatial constraints.

3.5.2 Temporal Constraints

As a first approach to achieve sparser composition tables, temporal constraints can be

considered. One valuable temporal constraint, perhaps the only general one, is to consider

which relations last over a time interval (rather than those holding only instantaneously). A

‘0’ in a level 1 QTCN label can only hold over a time interval when an object is stationary with

58 Chapter 3

respect to the network, as can be proven using the constraints of continuity (Bogaert et al.

2007). As a consequence, an object which is stationary with respect to one object will also be

stationary with respect to any other object. The composition table according to this

restriction is provided in Table 3.1. The composition table consists of five fine results (i.e.

singleton base relations), all being (0 0), 18 disjunctions of two relations, 22 disjunctions of

four relations and 36 inconsistent compositions (denoted by the empty set). Thus, the total

number of possibilities is reduced from 729 to 129.

Table 3.1 – Composition table for QTCN at level 1 restricted to relations lasting over time intervals;

A0 and B0 stand for the set {−, +}.

3.5.3 Spatial Constraints

While the composition results in Table 3.1 are already much sparser than those obtained

without constraints, they merely provide five fine results. Therefore, as a second approach,

spatial constraints can be imposed on top of the temporal restriction. As shown in section

3.4, the determination of a level 1 QTCN relation merely involves knowledge about the

relative movement with respect to the shortest path(s) between the objects concerned. In

composition, this relative movement is known for the first two object pairs, while nothing is

known about the shortest path(s) of the third pair, leaving all relations possible to occur. For

three objects , and on a network , assume that the relations and

are given and is unknown, implying that and

are known and that

is unknown. If it is known that is on

or that is on , a simple non-

closed curve can be drawn containing the positions of all three objects at . On this curve,

each object has three movement possibilities: it can be stable or move in one of two

opposite directions. Hence, there are 27 (33) movement configurations of these three

objects. An illustration of each specific configuration is shown in Figures 5 and 6, respectively

illustrating the cases of lying on and lying on

. The associated

composition tables are presented in Table 3.2 and Table 3.3. This kind of composition is very

useful, since it always leads to exact knowledge: both tables contain 27 fine composition

results, whereas 54 compositions are inconsistent.

− − − 0 − + 0 − 0 0 0 + + − + 0 + +

− − A0 B0 A

0 0 A

0 B0 A

0 B0 A

0 0 A

0 B0

− 0 A0 B0 A

0 0 A

0 B0

− + A0 B0 A

0 0 A

0 B0 A

0 B0 A

0 0 A

0 B0

0 − 0 B0 0 0 0 B

0 0 B

0 0 0 0 B

0

0 0 0 B0 0 0 0 B

0

0 + 0 B0 0 0 0 B

0 0 B

0 0 0 0 B

0

+ − A0 B0 A

0 0 A

0 B0 A

0 B0 A

0 0 A

0 B0

+ 0 A0 B0 A

0 0 A

0 B0

+ + A0 B0 A

0 0 A

0 B0 A

0 B0 A

0 0 A

0 B0


Figure 3.5 – Possible relative movement configurations in QTCN for R1(k, l) R2(l, m) where m lies

on the simple shortest path between k and l and none of the objects is located at a node.

− − − 0 − + 0 − 0 0 0 + + − + 0 + +

− − − + − 0 − −

− 0 − + − 0 − −

− + − + − 0 − −

0 − 0 + 0 0 0 −

0 0 0 + 0 0 0 −

0 + 0 + 0 0 0 −

+ − + + + 0 + −

+ 0 + + + 0 + −

+ + + + + 0 + −

Table 3.2 – Composition table for relative movement in QTCN, for R1(k, l) R2(l, m) where m lies on

the simple shortest path between k and l and none of the objects is located at a node.

60 Chapter 3

Figure 3.6 – Possible relative movement configurations in QTCN for R1(k, l) R2(l, m) where k lies

on the simple shortest path between m and l and none of the objects is located at a node.

− − − 0 − + 0 − 0 0 0 + + − + 0 + +

− − + − + 0 + +

− 0 + − + 0 + +

− + + − + 0 + +

0 − 0 − 0 0 0 +

0 0 0 − 0 0 0 +

0 + 0 − 0 0 0 +

+ − − − − 0 − +

+ 0 − − - 0 − +

+ + − − − 0 − +

Table 3.3 – Composition table for relative movement in QTCN, for R1(k, l) R2(l, m) where k lies on

the simple shortest path between m and l and none of the objects is located at a node.

3.6 Transforming QTCN into the Relative Trajectory Calculus on Networks

Having defined the QTCN relations between a pair of moving objects, a set of trivial

qualitative questions can be answered. For example, by looking at the third character of the

label, one can identify which object is moving the fastest. Looking at the first two characters


of the QTCN label, queries such as whether an object is moving towards or away from

another object can be resolved. In addition to these trivial questions, QTCN at level 2 has the

power to answer additional questions using the information contained by all three

characters in the label. This information can be obtained by transforming QTC relations into

relations defined by the Relative Trajectory Calculus (RTC) (Van de Weghe 2004).

In contrast to QTC, where distances between objects at different times are compared (e.g. in

Definitions 3.1 and 3.15), RTC defines relations based on the relative motion of an object

against another object at the same moment in time (Van de Weghe 2004) (Definition 3.17).

Definition 3.17 A relation in RTC between a first object and a second object at a time

point is defined by a single character label. This label represents the

comparison of the distance between and immediately before with the

distance between and immediately after . This results in three

possibilities:

−: the distance between and decreases:

(3.19)

0: the distance between and remains the same:

(3.20)

+: the distance between and increases:

(3.21)

RTCN describes the RTC relations on networks. In what follows, we will show that every QTCN

relation can be mapped onto a single RTCN relation. This allows QTCN at level 2 to answer

questions such as whether two objects are getting closer to each other or whether they are

getting further away from each other. To this end, we will first consider the cases where the

union of all shortest paths over the entire time span can be described as a simple curve

without junctions. Note that this excludes, among others, the case of bifurcating shortest

paths (Figure 3.1) and shortest path omitting node pass events (Figure 3.2). Hence, the

following equalities apply for the QTCN relation between the objects and at time point :

A ‘−’ in the first character of the relation label implies:

(3.22)

A ‘+’ in the first character of the relation label implies:

(3.23)

62 Chapter 3

Analogous reasoning applies for ‘−’ and ‘+’ in the second label character, yielding 3.24 and

3.25. Regardless of the QTCN relation it follows from (3.22-3.25) that:

(3.26)

Theorem 3.1

A QTCN relation (− − −) between the objects and at a time point can be transformed

into an RTCN relation (−), such that the RTCN relation is true whenever the QTCN relation is

true.

Proof:

By definition, the first two characters of (− − −) imply:

(3.27)

(3.28)

From (3.27) and (3.28) it follows that:

(3.29)

(3.30)

(3.31)

Which is by definition equal to the RTCN relation (−).

Analogously, it can be proven that the QTCN relations {(− − 0), (− − +), (− 0 +),

(0 − −)} can be converted into the RTCN relation (−).

Theorem 3.2

A QTCN relation (+ + +) between the objects and at time point can be transformed

into an RTCN relation (+), such that the RTCN relation is true whenever the QTCN relation is

true.

Proof:

By definition, the first two characters of (+ + +) imply:

(3.32)

(3.33)

From (3.32) and (3.33) it follows that:

(3.34)

(3.35)

(3.36)

Which is by definition equal to the RTCN relation (+).

Analogously, it can be proven that the QTCN relations {(+ + 0), (+ + −), (+ 0 +),

(0 + −)} can be converted into the RTCN relation (+).


Theorem 3.3

A QTCN relation (− + −) between the objects and at time point can be transformed

into an RTCN relation (+), such that the RTCN relation is true whenever the QTCN relation is

true.

Proof:

By definition, the third character of (− + −) implies:

(3.37)

(3.38)

(3.39)

(3.40)

(3.41)

(3.42)

(3.43)

Which is by definition equal to the RTCN relation (+).

Analogously, it can be proven that the QTCN relation (− + +) can be converted into the

RTCN relation (+), that the QTCN relations {(+ − −), (+ − +)} can be converted into the

RTCN relation (−), and that the QTCN relations {(− + 0), (+ − 0), (0 0 0)} can be

converted into the RTCN relation (0).

Note that the above mentioned theorems are not valid when the union of shortest paths

does not constitute a simple curve over the considered time span, since equations (3.22-

3.25) are not valid. Based on restrictions imposed by continuity, it can be shown that, in

these cases, there is also a unique transformation from a QTCN relation into a single RTCN

relation. Consider a qualitative variable capable of taking any of the three qualitative values

‘−’, ‘0’ and ‘+’. Due to continuity, this variable cannot make a direct change from ‘−’ to ‘+’

and vice versa, since such a change must always pass the intermediate value ‘0’ (Galton

1995). Let us consider the shortest path omitting node pass event in Figure 3.7. In Figure

3.7a there is a QTCN relation (− 0 +), which can be transformed into the RTCN relation (−),

according to Theorem 3.1. Analogously, (+ 0 +) can be transformed into (+) in Figure 3.7c.

Then, due to the above restriction imposed by continuity, the QTCN relation (0 0 +) in

Figure 3.7b must be an RTCN relation (0).

Similar transformations apply for all QTCN relations occurring at shortest path omitting node

pass events or when there are bifurcating shortest paths. Table 3.4 provides an overview of

the transformations from each canonical case in QTCN to the respective RTCN relation. A ‘0n’

denotes that a ‘0’ is due to a shortest path omitting node pass event. A ‘0b’ denotes that a

‘0’ is due to the existence of a bifurcating shortest path between the objects. A ‘0s’ denotes

64 Chapter 3

a ‘0’ is due to a stationary object. The black cells indicate that no corresponding RTCN

relations physically exist.

Figure 3.7 – A transition in QTCN from (− 0 +) via (0 0 +) to (+ 0 +).

QTCN-label RTCN-label QTCN-label RTCN-label QTCN-label RTCN-label

− − − − 0s 0s 0 0 0n 0n + 0 − − 0 − 0s 0s + 0s + − + − − + − 0b 0s − 0s + 0 − 0s − 0b 0s 0 0s + + − 0s 0 0b 0s + 0 0b + − + − 0s + − 0n 0s − 0b + 0 0 − 0b − 0 0n 0s 0 0b + + 0 − 0b 0 0 0n 0s + 0 0n + − + − 0b + − 0s 0b − 0 0n + 0 0 − 0n − 0 0s 0b 0 0n + + 0 − 0n 0 0 0s 0b + + − − − − 0n + − 0b 0b − 0 + − 0 0 − + − + 0b 0b 0 0 + − + + − + 0 0 0b 0b + 0 + 0s − − + + − 0n 0b − 0 + 0s 0 0s − − − 0n 0b 0 0 + 0s + + 0s − 0 0n 0b + 0 + 0b − 0 0s − + 0s 0n − 0 + 0b 0 0 0b − − − 0s 0n 0 + 0b + + 0b − 0 0 0s 0n + + 0n − 0 0b − + 0 0b 0n − 0 + 0n 0 0 0n − − − 0b 0n 0 0 + 0n + + 0n − 0 0 0b 0n + 0 + + − + 0n − + 0 0n 0n − 0 + + 0 + 0s 0s − 0n 0n 0 0 + + + +

Table 3.4 – Transformations from all QTCN canonical cases to RTCN relations.

Table 3.4 clearly shows that the ‘0s’, ‘0n’, and ‘0b’ labels do not influence the transformation

from QTCN to RTCN. Therefore, Table 3.4 can be reduced to Table 3.5.

Thus, there is a one-to-one mapping from QTCN to RTCN relations. This is notable since for

QTC relations of objects having a free trajectory in , this is not the case (Van de Weghe

2004). The latter is illustrated in Figure 3.8. Since the dotted line has a fixed length, the

figure shows that a QTCB relation (− + 0) can be transformed into all possible RTC relations.


QTCN-label RTCN-label QTCN-label RTCN-label QTCN-label RTCN-label

− − − − 0 − − − + − − − − − 0 − 0 − 0 0 + − 0 0 − − + − 0 − + 0 + − + + − 0 − 0 0 0 − 0 + 0 − 0 − 0 0 0 0 0 0 0 + 0 0 0 − 0 + − 0 0 + 0 + 0 + + − + − + 0 + − + + + − + − + 0 0 0 + 0 0 + + 0 + − + + − 0 + + 0 + + + +

Table 3.5 – Transformations from QTCN into RTCN relations.

Figure 3.8 – Examples of transformations from QTCB to RTC.

3.7 Discussion

On the one hand, defining and examining the properties of a distance based calculus for

moving objects constrained by networks is a worthwhile theoretical investigation into

further aspects of QTC theory. On the other hand, we argue that this calculus is also

convenient for the use in applications. In this section, we will illustrate this usefulness by

means of two examples.

3.7.1 A Police/Gangster Example

In order to show the applicability of the composition of QTCN relations at level 1 and the

usefulness of the temporal and spatial constraints stated in section 3.5, let us consider the

following example where three policemen , and are at different locations in a city

and wish to catch a gangster along a road network (Figure 3.9). It is assumed that the

policemen know their mutual positions and therefore their mutual shortest paths at any

time, but they can only see the gangster if they are in line of sight. At time , while and

are still awaiting instructions, policeman has noticed and started chasing the gangster

who started to escape, thus yielding = (− +) (Figure 3.9a). Since all shortest paths

are simple and is on both

and

, composition can be applied using Table

3.2, such that can give the right orders to and concerning the direction in which

they should move, i.e. directs and to start moving towards (since and know

where is), which causes and to move towards just after . At , is at a junction.

Hence, composition cannot be applied, since one cannot know which turn will take (Figure

3.9b). Immediately after , will have seen turning right, and so still knows at which

66 Chapter 3

edge is, thus enabling composition with respect to and . This situation lasts until

(Figure 3.9c) and will continue after , probably until the gangster gets caught. Table 3.6

lists the respective composition results inferred over . As can be noted, results are

only lacking at , whereas during the rest of the period there is complete information due

to the existing spatiotemporal constraints.

Time Known relations Results inferred from

temporal constraints

Results inferred from

spatial constraints

= (0 −),

= (0 0),

= (− 0),

= (− +)

= (0 −)

(0 +)

= (0 −)

(0 +)

= (0 −),

= (− 0)

= (− −),

= (− +),

= (− −),

= (− +)

= (− −)

(− +)(+ −)(+ +)

= (− −)

(− +)(+ −)(+ +)

= (− −),

= (− −)

= (0 −),

= (0 0),

= (− 0),

= (− +)

None possible None possible

= (0 −),

= (0 0),

= (− 0),

= (− +)

= (− −)

(− +)(+ −)(+ +)

= (− −)

(− +)(+ −)(+ +)

= (− −)

= (0 −),

= (0 0),

= (− 0),

= (− +)

= (− −)

(− +)(+ −)(+ +)

= (− −)

(− +)(+ −)(+ +)

= (− −)

Table 3.6 – Composition results inferred over [t1, t3] due to spatial and temporal constraints.

Figure 3.9 – Simplified animation of three policemen chasing a gangster.


3.7.2 A Collision Avoidance Application

An application where QTCN at level 2 can be useful is in collision avoidance systems. If one

wants to know if two objects are going to collide, then it is useful, as a first step, to restrict

attention to the objects that might meet. In other words, only the objects which are getting

closer to each other, i.e. objects in an RTCN relation (−), are relevant, because otherwise

they cannot collide. Thus, QTCN relations at level 2 eliminate many movements from further

examination, greatly reducing calculation times. Further examination of the remaining

relations gives information on the type of collision. The relations (− + +) and (+ − −)

indicate possible rear-end collisions, whereas (− − −), (− − 0), and (− − +) indicate

possible head-on collisions. The relations (− 0 +) and (0 − −) may indicate collisions with

a stationary object. Note that these QTCN relations indicate potential collisions that do not

necessarily result in real collisions. Related work on collision avoidance has, on the one hand,

focussed on detecting possible collisions between objects which have a completely free

trajectory in a two dimensional space (Schlieder 1995, Gottfried 2005, Dylla & Wallgrun

2007). These approaches mainly focus on the direction of movement. Although they have all

shown their usefulness when the movement of objects is unconstrained, directional

methods can not directly be transformed to networks, since they do not take into account

the spatial structure of a network. The movement in Figure 3.10a, for example, would

announce a possible collision in all the above mentioned directional approaches, while from

QTCN analysis it follows that the objects move away from each other and therefore cannot

collide. Furthermore, none of the methods above incorporates the relative speed between

two moving objects. However, the notion of relative speed is crucial for collision detection in

cases where the objects move in the same direction, while in the other cases, it may offer

appealing insights into a finer subdivision of collision types. Consider the example in Figure

3.10b. When using only directional information, this movement would trigger a collision

detection, but since is moving faster than , the distance between them increases, and

hence, there is no true collision danger. For both these reasons, directional approaches over-

predict possible collisions, while QTCN does not.

Figure 3.10 – Two scenes without collision danger for two moving objects.

Other techniques for collision avoidance considering network-constrained objects mainly

focus on railway networks. Collisions in these systems are avoided by disallowing two trains

to occupy the same track segment (Hansen 1998, Haxthausen & Peleska 2000). First of all,

these methods also over-predict possible collisions, since two trains may travel on the same

track without colliding (e.g. as in Figure 3.10b with moving slower than ). Secondly, this

68 Chapter 3

sole constraint does not capture every possible collision situation. If two trains are on

different segments, they can still be close and moving towards each other. Hence, not all

collisions can be predicted in collision avoidance systems relying on this constraint

(especially for objects colliding at network junctions).

3.8 Conclusions and future work

In this chapter, we have formally presented the Qualitative Trajectory Calculus on Networks

(QTCN) as a qualitative calculus to represent and reason about moving point objects which

are constrained in their movement by networks.

We have shown two techniques to infer additional knowledge from the basic QTCN relations.

On the one hand we have presented the composition of QTCN relations (section 3.5). It was

found that, at level 1, each QTCN base relation is a possible result for each composition of

two relations. While this result, at first, can be considered of limited use, it was shown how

sparser and more powerful composition tables may be obtained by imposing realistic

additional spatial and temporal constraints. By excluding instantaneous relations, we were

able to reduce the total of 729 possibilities to 129 (18%). In addition, by restricting to the

case where the union of shortest paths involved in the composition forms a non-closed

curve, a further reduction was made to 27 (4%) fine results (i.e. singleton base relations).

These sparser composition tables are more powerful and useful with respect to potential

applications, as has been illustrated in section 3.7.1.

On the other hand, we have demonstrated that QTCN is able to answer qualitative questions

such as whether objects on a network are moving towards or away from each other. These

queries are not limited to trivial questions which merely relate to the relationship

represented by a single QTCN relation character. Hence, a QTCN relation conveys more

information than each of its individual label characters separately. As pointed out in section

3.6, each canonical relation in QTCN at level 2 can be uniquely transformed into a RTCN

relation (this is not the case for QTCB in (Van de Weghe 2004)). Therefore, QTCN is

capable of answering questions such as whether two objects are getting closer to each other

or whether they are getting further away from each other. In section 3.7.2, we have

illustrated that the definition of QTCN and the unique transformation of its relations into

single RTCN relations can be useful, for example in collision avoidance systems.

The theoretical contributions in this chapter complement the earlier contributions vis-à-vis

other calculi of the QTC family (see Delafontaine et al. 2011 for an overview) in general, and

regarding QTCN in particular. While QTCN relations have been introduced in a brief and

informal manner in earlier work (Van de Weghe 2004, Bogaert et al. 2007), this chapter

offers a formal axiomatisation of QTCN. In addition to the conceptual neighbourhood

diagrams presented in (Bogaert et al. 2007), we have presented the composition tables for

QTCN as well as the transformation of QTCN into RTCN relations. Furthermore, we have


explored and illustrated the reasoning power of QTCN by means of its ability to answer

qualitative queries. As has been recently shown for QTCB and QTCC (Delafontaine, Cohn &

Van de Weghe 2011), these contributions will allow QTCN to be implemented in an

information system in order to represent and reason about moving objects constrained by

networks.

Among the qualitative calculi that deal with relations between moving objects, QTCN is

unique in its consideration of network-based objects. An exception is the work of Wang et al.

(2005) who extend the Directed Interval Algebra (Renz 2001) to the Road Network Directed

Interval Algebra (RNDIA). Although their algebra is also based on the notion of shortest

paths, RNDIA differs from QTCN as it defines relations among directed network tracks rather

than relations among moving point objects. RNDIA is therefore less appropriate to represent

and reason about instantaneous events occurring among objects along their trajectories.

Collisions, for example, are not unambiguously represented in RNDIA as they may occur in

the case of different RNDIA base relations (e.g. the equal, overlay, and cross relations (Wang

et al. 2005). Given that practically all traffic movements are bounded by networks, QTCN-

based applications are promising in the field of Intelligent Transportation Systems and

Geographic Information Systems for Transportation (GIS-T) (Shaw & Rodrigue 2009).

Ongoing research involving QTCN is being conducted on cognitive aspects of the calculus.

Major questions to be investigated in this respect include what specific terms such as motion

verbs and prepositions do people attach to each of the canonical cases of the calculus.

Future findings on these issues may provide insights on the power of QTCN in natural

language processing and human computer interaction.

References

Agarwal, P. K., Arge, L. & Erickson, J. (2003) Indexing moving points. Journal of Computer and System

Sciences, 66, 1, 207-243.


11, 832-843.

Bennett, B. (1997) Logical representations for automated reasoning about spatial relationships,

Doctoral Dissertation, Leeds: University of Leeds, School of Computing, 211.




Brinkhoff, T. (2002) A framework for generating network-based moving objects. Geoinformatica, 6, 2,

153-180.

Byrne, R. M. J. & Johnson-Laird, P. N. (1989) Spatial reasoning. Journal of Memory and Language, 28,

564-575.

Clementini, E., Di Felice, P. & Hernandez, D. (1997) Qualitative representation of positional

information. Artificial Intelligence, 95, 2, 317-356.

70 Chapter 3



Delafontaine, M., Chavoshi, S. H., Cohn, A. G. & Van de Weghe, N. (2011) A Qualitative Trajectory



USA: IGI Global.



Donlon, J. & Forbus, K. D. (1999) Using a geographic information system for qualitative spatial

reasoning about trafficability. In Proceedings of the 13th International Workshop on

Qualitative Reasoning (QR99), Loch Awe, Scotland.

Dylla, F. & Wallgrun, J. O. (2007) Qualitative spatial reasoning with conceptual neighborhoods for

agent control. Journal of Intelligent & Robotic Systems, 48, 1, 55-78.

Egenhofer, M., J. (1994) Deriving the composition of binary topological relations. Journal of Visual

Languages and Computing, 5, 2, 133-149.

Egenhofer, M. J. & Herring, J. (1991) Categorizing topological relationships between regions, lines,

and points in geographic databases. In Technical Report. University of Maine, Department of

Surveying Engineering.

Erwig, M., Güting, R. H., Schneider, M. & Vazirgiannis, M. (1999) Spatio-temporal data types: an

approach to modeling and querying moving objects in databases. Geoinformatica, 3, 3, 269-

296.

Forbus, K. D. (1997) Qualitative reasoning. In The Computer Science and Engineering Handbook, ed. J.

A. Tucker, CRC Press, 715-733.

Francis, D. H., Madria, S. & Sabharwal, C. (2008) A scalable constraint-based Q-hash indexing for

moving objects. Information Sciences, 178, 6, 1442-1460.

Frank, A., U. (1991) Qualitative spatial reasoning about cardinal directions. In Proceedings of

Autocarto 10, American Congress on Surveying and Mapping, eds. D. Mark & D. White,

Baltimore, Maryland, 148-167.

Frank, A. U. (1996) Qualitative spatial reasoning: Cardinal directions as an example. International

Journal of Geographical Information Systems, 10, 3, 269-290.





Galton, A. (1995) A qualitative approach to continuity. In Time, Space and Movement: Meaning and

Knowledge in the Sensible World, Workshop notes of the 5th International Workshop

(TSM95), eds. P. Amsili, M. Borillo & L. Vieu, Château de Bonas, France.

Galton, A. (2000) Qualitative Spatial Change. Oxford University Press, 410.

Gao, Y., Zheng, B., Chen, G., Li, Q., Chen, C. & Chen, G. (2010) Efficient mutual nearest neighbor query

processing for moving object trajectories. Information Sciences, 180, 11, 2176-2195.

Gottfried, B. (2005) Collision avoidance with bipartite arrangements. In Proceedings of the 2005 ACM

Workshop on Research in Knowledge Representation for Autonomous Systems, Bremen,

Germany: ACM.


Goyal, R. K. (2000) Similarity Assessment for Cardinal Directions between Extended Spatial Objects,

Doctoral Dissertation, The Graduate School, University of Maine, 167.

Guesgen, H. W. & Albrecht, J. (2000) Imprecise reasoning in geographic information systems. Fuzzy

Sets and Systems, 113, 1, 121-131.



Hansen, K. M. (1998) Formalising railway interlocking systems. In Proceedings of the Second FMERail

Workshop, London, United Kingdom, 1-12.

Haxthausen, A. E. & Peleska, J. (2000) Formal development and verification of a distributed railway

control system. IEEE Transactions on Software Engineering, 26, 8, 687-701.

Hernández, D., Clementini, E. & Di Felice, P. (1995) Qualitative distances. In Spatial Information

Theory: A Theoretical Basis for GIS, LNCS 988, 45-57.



Hornsby, K. & King, K. (2008) Modeling motion relations for moving objects on road networks.


Iwasaki, Y. (1997) Real-world applications of qualitative reasoning. IEEE Expert, 12, 3, 16-21.

Kalashnikov, D., Ma, Y., Mehrotra, S., Hariharan, R., Venkatasubramanian, N. & Ashish, N. (2006) SAT:

Spatial awareness from textual input. In Advances in Database Technology (EDBT 2006), eds.

Y. Ioannidis, et al., Springer Berlin / Heidelberg, 1159-1163.

Laube, P., Dennis, T., Forer, P. & Walker, M. (2007) Movement beyond the snapshot - Dynamic

analysis of geospatial lifelines. Computers, Environment and Urban Systems, 31, 5, 481-501.


point objects. International Journal of Geographical Information Science, 19, 6, 639-668.

Lee, S., Park, S., Kim, W.-C. & Lee, D. (2007) An efficient location encoding method for moving objects

using hierarchical administrative district and road network. Information Sciences, 177, 3, 832-

843.

Moreira, J., Ribeiro, C. & Saglio, J.-M. (1999) Representation and manipulation of moving points: An

extended data model for location estimation. Cartography and Geographic Information

Science, 26, 109-124.

Mortensen, M. E. (1999) Mathematics for Computer Graphics Applications. New York, USA: Industrial

Press, 355.

O'Reilly, C. (1980) Individuals and information overload in organizations: Is more necesserily better?

Academy of Management Journal, 23, 4, 684-696.

Pfoser, D. & Theodoridis, Y. (2003) Generating semantics-based trajectories of moving objects.

Computers, Environment and Urban Systems, 27, 3, 243-263.


Proceedings of the Third International Conference on Principles of Knowledge Representation


Renz, J. (2001) A spatial odyssey of the interval algebra: 1. directed intervals. In Proceedings of the

17th International Joint Conference on Artificial intelligence - Volume 1, Seattle, WA, USA:

Morgan Kaufmann.

72 Chapter 3

Renz, J. & Nebel, B. (2007) Qualitative spatial reasoning using constraint calculi. In Handbook of

Spatial Logics, eds. M. Aiello, I. Pratt-Hartmann & J. van Benthem, Berlin: Springer-Verlag,

161-215.

Saltenis, S., Jensen, C. S., Leutenegger, S. T. & Lopez, M. A. (2000) Indexing the positions of

continuously moving objects. Sigmod Record, 29, 2, 331-342.

Schlieder, C. (1995) Reasoning about ordering. In Spatial Information Theory A Theoretical Basis for

GIS, eds. A. Frank & W. Kuhn, Springer Berlin / Heidelberg, 341-349.

Shaw, S. L. & Rodrigue, J.-P. (2009) Geographic information systems for transportation (GIS-T). In The

Geography of Transport Systems, eds. J.-P. Rodrigue & B. Slack, New York: Routledge, 352.

Sistla, A. P., Wolfson, O., Chamberlain, S. & Dao, S. (1997) Modeling and querying moving objects. In

Proceedings of the 13th International Conference on Data Engineering, 422-432.

Tarski, A. (1941) On the calculus of relations. The Journal of Symbolic Logic, 6, 3, 73-89.



Van de Weghe, N., Cohn, A. G., Bogaert, P. & De Maeyer, P. (2004) Representation of moving objects

along a road network. In Proceedings of the 12th International Conference on Geoinformatics

Geospatial Information Research: Bridging the Pacific and Atlantic. Gävle, Sweden.







Van de Weghe, N. & De Maeyer, P. (2005) Conceptual neighbourhood diagrams for representing

moving objects. In Perspectives in Conceptual Modeling, LNCS 3770, Springer, 228-238.

Van de Weghe, N., Kuijpers, B., Bogaert, P. & De Maeyer, P. (2005b) A Qualitative Trajectory Calculus






Wang, S., Liu, D. & Liu, J. (2005) A new spatial algebra for road network moving objects. International

Journal of Information Technology, 11, 12, 47-58.



Zeimpekis, V., Giaglis, G. M. & Lekakos, G. (2002) A taxonomy of indoor and outdoor positioning

techniques for mobile location services. In SIGecom Exchanges - Mobile commerce, ACM, 19-

27.

Qualitative relations between moving objects in a dynamic network 73

4 Qualitative relations between moving objects in a

network changing its topological relations

Delafontaine M., Van de Weghe, N., Bogaert P., De Maeyer P.

in Information Sciences (2011), Volume 178, Issue 8


Abstract. The Qualitative Trajectory Calculus on Networks (QTCN) defines qualitative

relations between two continuously moving point objects (MPOs) moving along a

network. As prevailing in other research, this network is presumed static in QTCN.

Actually, in many cases, networks are dynamic entities. For example in a road

network, the opening of a bridge can temporarily close the connection between two

junctions; traffic jams and traffic lights increase the time needed to travel from A to

B. Therefore, it is interesting to examine what happens with qualitative relations

between two continuously moving point objects if there are changes in the network.

In this chapter, we introduce QTCDN’, being the Qualitative Trajectory Calculus on

Changing Networks able to handle topological network changes. Potential

applications of the calculus in transportation are highlighted, clearly illustrating the

usefulness of the calculus.

Keywords. Qualitative calculus – Moving point objects – Changing networks –

Topological relations

4.1 Introduction

In recent years, time and space have grown into scarce items, being now factors taking part

in widely divergent human decisions. Choices require weighing space and time against each

other. This is possible due to their relation in the notion of ‘change’. A suchlike change, that

we are familiar with, is the movement of an object in time through space. Movements can

occur in a free space or can be spatially restricted by certain factors. A network, e.g. a road

or a river network, being a set of interconnected linear features, is an example of a space in

which object movements are restricted. Mostly, these moving objects are studied in a static

network (Monferrer & Lobo 2002, Pfoser & Jensen 2005, Güting, de Almeida & Ding 2006,

Kim et al. 2006, Li & Lin 2006, Liu, Do & Hua 2006, Lee et al. 2007). Due to this,

spatiotemporal changes of our complex and dynamic reality are neglected, which makes

static models difficult to justify and hardly tenable in a changing world counting in

nanoseconds. Therefore, this chapter concentrates on setting up a calculus of relations

74 Chapter 4

between moving objects in a network changing its topological relations. Topological

relations are the geometric relations between spatial objects that are invariant under

homeomorphisms such as translation, rotation and scaling (Bennett 1997, Vieu 1997). Since

topological relations determine the entire structure of a network, and of a changing network

as well, this chapter focuses on changes of topological relations in a network. Such changes

are present in many real world networks. Consider for example railway barriers closing a

street segment in a road network. The street concerned, first being modelled as a connected

linear feature in the network, becomes interrupted due to this event. This street now has to

be represented by two different lines being no longer connected with each other.

For the setting up of a calculus of relations in this chapter, a qualitative calculus was

preferred to a quantitative one, because qualitative information is the most essential and

pithy kind of information (Clementini, Di Felice & Hernandez 1997, Cohn & Renz 2007) and it

is the most rapidly processed by humans (Monferrer & Lobo 2002). In addition, qualitative

reasoning techniques are becoming increasingly important e.g. in Geographical Information

Science (Saygin, Ulusoy & Yazici 1999, Claramunt & Theriault 2004, Duckham et al. 2006,

Nedas, Egenhofer & Wilmsen 2007) and Artificial Intelligence (Gerevini 2005, Rebolledo

2006, Badaloni & Giacomin 2006). Appeal has been made to an existing qualitative

approach, the Qualitative Trajectory Calculus (Van de Weghe 2004), explained in section 4.2.

This calculus has already been elaborated for static networks by the introduction of the

Qualitative Trajectory Calculus on Networks (Bogaert et al. 2007), briefly stated in section

4.3. In section 4.4, we present the Qualitative Trajectory Calculus on Changing Networks able

to undergo topological change. Finally, conclusions and possible future work are mentioned

in section 4.5.


The Qualitative Trajectory Calculus (Van de Weghe 2004), shortly QTC, is a qualitative

calculus of relations between two disjoint point objects in space. Every object can be given a

relation describing its motion with respect to another object. Depending on the level of

detail and the number of spatial dimensions taken into consideration, different types of QTC

have been worked out in (Van de Weghe 2004). Since this chapter deals with networks, we

will focus on the Qualitative Trajectory Calculus on Networks or briefly QTCN.

4.3 The Qualitative Trajectory Calculus on Networks

4.3.1 Definition

The Qualitative Trajectory Calculus on Networks (Bogaert et al. 2007), shortly QTCN,

considers two point objects in a static network. The objects have the ability to move


continuously along the network, which remains unaltered. Bogaert et al. (2007) use the

following definitions and assumptions for further formalisation of QTCN1:

A graph is a set of edges and a set of nodes .

A network is a connected graph and a finite set of objects.

Each edge connects a pair of nodes in a network.

Each node has a degree, which is the number of edges connected to it.

At any time, each object has a position in the network, which is either at a node in ,

or is along an edge in , in which case the network at is augmented with an

additional dynamic node of degree 2 cutting the edge in two, representing .

A dynamic node is a node representing the position of the object in a network

A subgraph of a network is a set of edges and a set of nodes , such that is a subset

of the set of edges of the network and is a subset of the set of nodes of the network

A path from to at is a subgraph of the network at time , such that every node in

is of degree 2 except two nodes representing the position of and , which are of

degree 1. Thus, a path is a sequence of nodes and edges from to .

Every edge has an associated length, which is a positive number.

The length of a path is the sum of the lengths of the edges in the path.

If is a path of length and there is no path with length less than between the

same two nodes, then is a shortest path2.

A cycle is a subgraph that has at least three non dynamic nodes and contains the same

number of edges and nodes, whereby each edge is of degree 2.

In accordance with the above mentioned, a QTC network is a graph, which itself is not a

spatial structure, but needs to be embedded in a space or must be ‘spatialised’ (Galton &

Worboys 2005). For that, a function can be used, which maps each node of the graph onto a

point in the defined space, and maps each edge of the graph onto a curve segment (Galton

& Worboys 2005).

In a network, a moving object can only approach another object, if and only if it moves along

a shortest path between these two objects (Bogaert et al. 2007). Therefore, the shortest

path between two QTCN objects is used to determine relative movements of the objects with

1 We introduce the following notations for QTC:

denotes the position of an object at time ;

denotes the distance between two positions and ;

denotes the speed of at time ;

denotes that is temporally before ;

denotes the time period immediately before ;

denotes the time period immediately after ;

denotes the shortest path at time between objects and .

2 Note that multiple shortest paths between two objects might be possible.

76 Chapter 4

respect to each other. When an object approaches another object , it moves along the

shortest path between and . In that case, we can state that during and

during . Object moves away from if it lies on

during and does not lie

on during . If lies on

only at but not during or , or if it lies on

throughout , then the object will be stationary with respect to .

4.3.2 Relations in QTCN

A QTCN relation, representing the qualitative relation between two moving objects in a QTC

network, is expressed in a typical three character label. This label compromises the following

three relationships (Bogaert et al. 2007):

Assume two objects and .

1. Movement of the first object , with respect to the position of the second object at

time point :

−: moves along a shortest path:

(4.1)

+: does not move along a shortest path:

(4.2)

0: is stationary with respect to :

(4.3)

(4.4)

2. Movement of the second object , with respect to the position of the first object at

time point can be described as in case 1 with and interchanged, hence:

−: moves along a shortest path

+: does not move along a shortest path

0: is stationary with respect to

3. Relative speed of the first object at time point , with respect to the second object

at time point :

−: is slower than :

(4.5)

+: is faster than :


(4.6)

0: and are equally fast:

(4.7)

Thus, a (+ − 0)-label means that a first object is moving away from a second object (+),

while the second object is approaching the first object (−), and that both objects have the

same speed (0). Since a label contains three characters which can all take on three values,

there are mathematically 3³ (27) different possible relationships in QTCN. In (Bogaert et al.

2007), it is stated that all of the mathematically possible relations exist in QTCN, although not

all of them can last over an interval of time. 17 relations can hold over a time interval, while

10 relations can only exist at a certain point in time.

4.3.3 Transitions in QTCN

Freksa (1992) defines two relations between objects to be conceptual neighbours if they can

be directly transformed into one another by continuously deforming the objects in a

topological sense. The transformation of one relation into a conceptual neighbour is called a

transition. A combination of a transition between a relation A and B and a transition

between B and A, is denoted a transition pair.

A transition can only occur in QTCN because of the movement of at least one of both objects.

Bogaert, Van de Weghe and De Maeyer (2004) distinguish three possible events3 that can

cause transitions in QTCN:

1. Speed Change Event: the relative speed of the objects changes. Figure 4.1 illustrates a

Speed Change Event.

2. Node Pass Event: an object passes a node with degree of 3 or higher, whereby the

movement of the object with respect to the shortest path changes. Figure 4.2 illustrates

a Node Pass Event.

3. Continuous4 Shortest Path Change Event: the shortest path between the objects

changes, due to the continuous movement of at least one of both objects, in such way

that the movement of an object with respect to the shortest path changes. Figure 4.3

illustrates a Continuous Shortest Path Change Event.

Transitions can graphically be represented by means of a Conceptual Neighbourhood

Diagram (CND). In a CND, relations are displayed as nodes, transitions as arrows and

transition pairs as undirected lines joining two conceptual neighbours. The use of CNDs is

well established in AI applications (i.e. in Qualitative Spatial Reasoning (QSR)) to represent

3 For a full understanding of the figures presenting the events, one has to be mindful of the constraints

imposed by continuity formulated further in the ‘Theory of Dominance’. 4 Although the above defined events are all marked by continuous change, in this case the continuous

movement of the objects, the adjective ‘Continuous’ has been added here to indicate the difference with the Discontinuous Shortest Path Change Event defined in section 4.

78 Chapter 4

and reason about qualitative properties (e.g. to predict possible future events) (Randell &

Mitkowski 2004, Dylla & Wallgrun 2007). Figure 4.4 shows the CND of QTCN.

Figure 4.1 – Speed Change Event.

Figure 4.2 – Node Pass Event.

Figure 4.3 – Continuous Shortest Path Change Event.

The CND is totally bidirectional5 and it clearly shows that all of the 27 (3³) mathematically

possible relations exist in QTCN. As stated before, not all of them can last over an interval.

The ten dashed nodes represent the relations that can only exist at a specific point in time.

Not all the relations are conceptual neighbours to each other: of the 702 mathematically

possible transitions (351 transition pairs), only 152 (76 transition pairs) are possible in QTCN.

Much of these limitations can be explained by means of the theory of dominance.

5 All transitions are grouped in transition pairs


Figure 4.4 – The CND of QTCN.

4.3.4 Theory of Dominance

The concept of ‘dominance’ was introduced by Galton (1995b), based on Forbus’ work

(1984). Galton described the temporal nature of transitions between qualitative variables,

which are the QTCN relation characters in this context. Some important restrictions

concerning the dominance between binary qualitative relations were stated. Central in his

theory of dominance are the constraints imposed by continuity, which consequently apply to

all kinds of continuous changes. Transitions in QTCN are subject to these constraints as the

objects can only move continuously and only the objects can cause transitions in QTCN.

We will illustrate the idea of dominance with the following example. Consider a qualitative

variable capable of taking on the values ‘−’, ‘0’ and ‘+’ and able to change continuously

between them. It is clear that a direct change from ‘−’ to ‘+’ and vice versa is impossible,

since such a change must always pass the qualitative value ‘0’. This value ‘0’ only needs to

hold for a certain point in time. On the other hand, a ‘+’ or ‘−’ value must always hold over

an interval (Galton 1995a). Let us briefly explain this point. Consider two different points of a

continuous trajectory. One can always find another intermediate point in between these

points. In fact, an infinite number of points lie in between two different points. Consider now

a number line with a marked ‘0’ point. Since a ‘+’ value can stand for either positive number,

there is always an infinite number of points on the number line between ‘0’ and ‘+’. It now

follows that a ‘+’ value always holds over an interval in time. Dual reasoning applies for a ‘−’

80 Chapter 4

value. Using Galton’s (1995a) terms, we say that ‘0’ dominates ‘−’ and ‘+’, and that ‘−’ and ‘+’

are dominated by ‘0’.

Applied to QTCN, we see the impossibility of a transition between a relation with ‘−’ or ‘+’ in

one character and a relation with respectively ‘+’ or ‘−’ in the corresponding character.

Bringing this into account, 506 mathematically possible transitions become left out in QTCN,

which makes only 196 theoretically possible transitions (98 transition pairs) rest in the CND.

In addition, another 44 transitions are omitted due to restrictions imposed by the network,

which is not a free, more-dimensional space, reducing the total number of possible

transitions to 152 (76 transition pairs) (Figure 4.4).

4.4 Topological changes in networks: QTCDN’

4.4.1 Topological Change and Dynamic Networks

A topological change in a network is a change in the topological relations of a network. As

stated yet, a QTC network is a connected graph. A graph fully determines the topological

relations of a network when embedded in a space. Consequently, every topological change

of a network corresponds with a change in the graph that describes it and vice versa. The

only changes a graph, which is a set, can undergo are the addition and the deletion of one or

more of its elements. As such, we can consider every topological change of a network as an

edge addition6, an edge deletion7 or a combination of both. Additions and deletions of nodes

can be disregarded as they always imply the additions or deletions of edges in a connected

graph.

An important characteristic of topological changes is that they are discontinuous and by

consequence temporally restricted to time points: the change of a topological relation

always happens at a certain point in time and cannot take place over a time interval.

Reckoning with the theory of dominance this means that topological changes either happen

at the same time or that there is a time interval separating them.

A changing network is a network capable of undergoing change on every possible point in

time t (which does not mean that the network does change on every possible point in time).

It then follows that all relations and transitions possible in static networks (QTCN) are also

possible in dynamic networks as dynamic networks can always behave as static networks.

Where QTCN applies to static networks, we define the Qualitative Trajectory Calculus on

Changing Networks able to undergo topological changes (QTCDN’8) to be the calculus of

6 Addition of an edge includes the addition of node or (explicit) node if that node doesn’t belong to

the network yet. 7 Deletion of an edge includes the deletion of node or (explicit) if that node was only connected to

the network by . 8 In QTCDN’, N’ stands for dynamic networks (versus N for static networks) and D stands for discontinuous, as

topological changes are discontinuous changes.


changes in qualitative relations between two point-like disjoint objects in a changing

network able to undergo topological changes.

4.4.2 Relations in QTCDN’

Since all 27 mathematically possible relations exist in QTCN, they consequently exist in

QTCDN’. As for QTCN, 10 of these relations are restricted to time points in QTCDN’ (dashed

nodes in Figure 4.4). This restriction is due to the spatial restraints of a network, which is in

essence a one-dimensional structure embedded in a more-dimensional space.

4.4.3 Transitions in QTCDN’

As stated before, in QTCN there are three possible events causing transitions: a Speed

Change Event, a Node Pass Event and a Continuous Shortest Path Change Event. To find out

which transitions can be caused by topological network changes, one has to ask the question

which of these events can be caused by topological network changes. It is self-evident that a

topological change cannot alter the speed of the objects, what makes a Speed Change Event

to be excluded. Also a Node Pass Event is impossible since an object itself determines how it

will pass a node with degree of 3 or more. Unlike the two mentioned aspects, a topological

change in a network can certainly change the shortest path between two objects.

Nevertheless, it cannot be stated that a topological change can cause a Continuous Shortest

Path Change Event. This is because of the discontinuous nature of a topological change. Let

us briefly illustrate this point. A Continuous Shortest Path Change Event is, following from

the theory of dominance, characterized by a continuous transition of a relation character

from ‘−’ via ‘0’ to ‘+’ or vice versa. That way, there is always a time point, corresponding with

the ‘0’, on which (at least) two different shortest paths exist simultaneously in the network

(Figure 4.3). Consider now a shortest path change due to a topological change in a network

as illustrated in Figure 4.5. It shows that there is no longer a continuous transition, but a

direct change between ‘−’ and ‘+’ without passing ‘0’. Also, a time point is missing on which

two shortest paths exist at the same time. Therefore, we term such an event as a

Discontinuous Shortest Path Change Event.

Note that new transitions possible in topological changing networks are not restricted to

those caused uniquely by Discontinuous Shortest Path Change Events, but also include all

transitions due to combinations of Discontinuous Shortest Path Change Events with all other

events. Fig. 6, for example, shows a combination of a Discontinuous Shortest Path Change

Event with a Node Pass Event. Fig. 7, 8 and 9 give, by means of CNDs, an overview of all

transitions possible in QTCDN’ and impossible in QTCN. Combining all these CNDs with the

CND of QTCN (Figure 4.4) would yield the CND of QTCDN’ which is not visualized here because

of its complexity. It contains 256 transitions of which the 152 transitions of QTCN and 104

new transitions (Fig. 7, 8, 9). Of these 104 new transitions, 64 transitions cannot form

82 Chapter 4

transition pairs and therefore the CND of QTCDN’ is not bidirectional, as was the case for

QTCN.

Figure 4.5 – Discontinuous Shortest Path Change Event.

Figure 4.6 – Transition in QTCDN’ due to a combination of a Discontinuous Shortest Path Change

Event with a Node Pass Event.

4.5 Conclusions and Future work

In this chapter, we defined the Qualitative Trajectory Calculus on Changing Networks able to

undergo topological changes (QTCDN’). The possible relations and transitions in topological

changing networks were derived and presented in CNDs and conceptual figures. Note that

although the same relations exist in QTCDN’ as in QTCN, 256 transitions are possible in QTCDN’;

that is 168% of the total number of possible QTCN transitions. This illustrates the complexity

of a dynamic network versus a static network, which mirrors the complexity of a dynamic

reality versus a shortcoming static model of reality.

We strongly believe that QTCDN’ is useful in representing moving objects in the framework of

a topological changing network. Focusing for instance on transportation networks, many

changes in real world transportation networks can be considered as topological network

changes. First of all, many events caused by human management of transportation networks

can be modelled as a topological change. Next to the example of railway barriers closing a

street segment in a road network (cf. section 4.1), the same splitting up or elimination of

paths in a network can be considered when traffic lights turn red, roads are temporally

fenced off for road maintenance, bridges are opened over a waterway or floodgates in a

river network are closed. Complementary to each of these ‘network breaking’ events, one

can always find a corresponding ‘network joining’ event. In the given examples, network


Figure 4.7 – Possible QTCDN’ transitions due to a Discontinuous Shortest Path Change Event

(combined and/or otherwise) (a) and due to the combination of a Discontinuous Shortest Path

Change Event with a Speed Change Event (b).

Figure 4.8 – Possible QTCDN’ transitions due to a combination of a Discontinuous Shortest Path

Change Event with a Node Pass Event or (exclusive) with a Continuous Shortest Path Change Event.

84 Chapter 4

Figure 4.9 – Possible QTCDN’ transitions due to the combination of a Speed Change Event with a

combined Discontinuous Shortest Path Change Event (a) and due to the combination of a Speed

Change Event with the combination of a Discontinuous Shortest Path Change Event and a Node

Pass Event or (exclusive) a Continuous Shortest Path Change Event (b).

paths will be added or become connected again when railway barriers open, traffic lights

turn green, roads become reopened after maintenance operations, bridges over a waterway

are closed or floodgates in a river network are opened. Reversing a switch in a railway

network means the deletion of a network path together with the addition of another

network path. In addition to the temporary addition or deletion of existing paths of the

network, new paths can be (permanently) added (e.g. when a new road is laid or a new canal

is dug) or deleted (e.g. when a road is dug up or a canal is filled in).

Secondly, many applications can be found in human or natural hazards happening in

transportation networks. All kinds of events where a certain obstacle suddenly obstructs the

passage can be seen as a topological network change. The most obvious example is a

crashed vehicle blocking a street in a road network, but one should also think about

collapsing bridges and buildings, bomb attacks, demonstrations, etc. Although there can be

thought of many human–caused events, also nature phenomena, such as the blocking of

network segments by forest fires, by flooding, by a volcanic eruption, by trees that were cast

down by lightning, etc. may not be forgotten here.

Yet, the above made distinction may not be mutually exclusive, it certainly gives an idea of

the huge number of possible applications for QTCDN’ in real world transportation networks.

Given that nearly all traffic movements are bounded by a network, QTCDN’’s application field


in Geographic Information Systems for Transportation (GIS-T) seems to offer great potential.

We plan to evaluate QTCDN’ in this domain. We have presented QTCDN’ in a relatively informal

way concentrating on presenting ideas illustrated with simple examples. In future work, we

will fully formalize QTCDN’.

References

Badaloni, S. & Giacomin, M. (2006) The algebra IAfuz: a framework for qualitative fuzzy temporal

reasoning. Artificial Intelligence, 170, 10, 872-908.

Bennett, B. (1997) Logical Representations for Automated Reasoning about Spatial Relationships,

Doctoral Dissertation, Leeds: University of Leeds, School of Computing, 211.




Bogaert, P., Van de Weghe, N. & De Maeyer, P. (2004) Description, definition and proof of a

qualitative state change of moving objects along a road network In Münster GI-Days:

Geoinformation and Mobility, from Research to Applications, eds. M. Raubal, A. Sliwinski &

W. Kuhn, Münster, Germany, 239-248.

Claramunt, C. & Theriault, M. (2004) Fuzzy semantics for direction relations between composite

regions. Information Sciences, 160, 1-4, 73-90.

Clementini, E., Di Felice, P. & Hernandez, D. (1997) Qualitative representation of positional

information. Artificial Intelligence, 95, 2, 317-356.



Duckham, M., Lingham, J., Mason, K. & Worboys, M. (2006) Qualitative reasoning about consistency

in geographic information. Information Sciences, 176, 6, 601-627.

Dylla, F. & Wallgrun, J. O. (2007) Qualitative spatial reasoning with conceptual neighborhoods for

agent control. Journal of Intelligent & Robotic Systems, 48, 1, 55-78.

Forbus, K. D. (1984) Qualitative process theory. Artificial Intelligence, 24, 1-3, 85-168.

Freksa, C. (1992) Temporal reasoning based on semi-intervals. Artificial Intelligence, 54, 199-127.

Galton, A. (1995a) A qualitative approach to continuity. In Time, Space and Movement: Meaning and

Knowledge in the Sensible World, Workshop notes of the 5th International Workshop

(TSM95), eds. P. Amsili, M. Borillo & L. Vieu, Château de Bonas, France.

Galton, A. (1995) Towards a qualitative theory of movement. In Spatial Information Theory: A

Theoretical Basis for GIS, LNCS 988, Springer, 377-396.

Galton, A. & Worboys, M. (2005) Processes and events in dynamic geo-networks. In Proceedings of

the 1st International Conference on Geospatial Semantics (GeoS), eds. A. Rodriguez, I. Cruz,

M. Egenhofer & S. Levashkin, Mexico City, Mexico: Springer-Verlag, 45-59.

Gerevini, A. (2005) Incremental qualitative temporal reasoning: Algorithms for the point algebra and

the ORD-Horn class. Artificial Intelligence, 166, 1-2, 37-80.



86 Chapter 4

Kim, K.-S., Lopez, M., Leutenegger, S. & Li, K.-J. (2006) A network-based indexing method for

trajectories of moving objects. In Advances in Information Systems, eds. T. Yakhno & E.

Neuhold, Springer Berlin / Heidelberg, 344-353.

Lee, S., Park, S., Kim, W.-C. & Lee, D. (2007) An efficient location encoding method for moving objects

using hierarchical administrative district and road network. Information Sciences, 177, 3, 832-

843.

Li, X. & Lin, H. (2006) Indexing network-constrained trajectories for connectivity-based queries.


Liu, F., Do, T. & Hua, K. (2006) Dynamic range query in spatial network environments. In Database

and Expert Systems Applications, eds. S. Bressan, J. Küng & R. Wagner, Springer Berlin /


Monferrer, T. E. & Lobo, F. T. (2002) Qualitative velocity. In Proceedings of the 5th Catalonian

Conference on AI: Topics in Artificial Intelligence, Springer-Verlag, 29-39.

Nedas, K. A., Egenhofer, M. J. & Wilmsen, D. (2007) Metric details of topological line-line relations.


Pfoser, D. & Jensen, C. S. (2005) Trajectory indexing using movement constraints*. Geoinformatica, 9,

2, 93-115.

Randell, D. A. & Mitkowski, M. (2004) Tracking regions using conceptual neighbourhoods. In

Proceedings of ECAI 2004, Workshop on Spatial and Temporal Reasoning, 63-71.

Rebolledo, M. (2006) Rough intervals--enhancing intervals for qualitative modeling of technical

systems. Artificial Intelligence, 170, 8-9, 667-685.

Saygin, Y., Ulusoy, Ö. & Yazici, A. (1999) Dealing with fuzziness in active mobile database systems.

Information Sciences, 120, 1-4, 23-44.





Implementing a qualitative calculus to analyse moving point objects 87

5 Implementing a qualitative calculus to analyse moving

point objects

Delafontaine M., Cohn A. G., Van de Weghe N.

in Expert Systems With Applications (2011), Volume 38, Issue 5


Abstract. Due to recent technological advances in position-aware devices, data about

moving objects is becoming ubiquitous. Yet, it is a major challenge for spatial

information systems to offer tools for the analysis of motion data, thereby evolving

from static to dynamic frameworks. This chapter aims to contribute to this area by

introducing an implementation prototype for an information system based on the

Qualitative Trajectory Calculus, a spatiotemporal calculus to represent and reason

about moving point objects.

Keywords. Qualitative calculus – Moving point objects – Implementation

5.1 Introduction

Capabilities to track individual moving objects have recently developed, along with the

technological advances concerning position-aware devices, navigation systems, electronic

transaction networks and surveillance systems (Laube et al. 2007). Nowadays, hi-tech

devices such as mobile phones, digicams, GPS receivers and RFIDs, are omnipresent and

allow for a low cost capture of high resolution trajectories1 of moving objects, whether these

are human beings (Wang, Hu & Tan 2003, Gau et al. 2004, Nielsen & Hovgesen 2004,

Michael et al. 2006), animals (DeCesare, Squires & Kolbe 2005, Yasuda & Arai 2005, Kritzler,

Raubal & Kruger 2007, Laube et al. 2007, Gagliardo et al. 2007), vehicles (Brunk & Davis

2002, Brakatsoulas et al. 2005, Hvidberg 2006), or even projectiles (Grace 2000). As is

generally recognized, this large potential of individually-based trajectory data heralds a new

era of movement analysis (Eagle & Pentland 2006, Laube et al. 2007) in order to feed a

broad range of application fields from ethology over traffic management to sport scene

analysis and weapon guidance.

In the past decade, GIScientists from multiple disciplines have created a sound theoretical

basis regarding the modelling, representation, analysis and extraction of knowledge from

1 Although also denoted as geospatial lifelines (Mark 1998, Hornsby & Egenhofer 2002, Laube, van Kreveld &

Imfeld 2005) others refer to trajectories (Gottfried 2008, Orlando et al. 2007, Brakatsoulas, Pfoser & Tryfona 2004, Spaccapietra et al. 2008, Gudmundsson, van Kreveld & Speckmann 2007), as we will do for consistency with the QTC calculus.

88 Chapter 5

motion data (see among others (Laube, Imfeld & Weibel 2005, Güting, de Almeida & Ding

2006, Giannotti & Pedreschi 2008, Spaccapietra et al. 2008) for an overview).

Despite these considerable efforts, common analyses of trajectory data remained limited

with respect to scope and sophistication (Laube et al. 2007), and much of this theoretical

work is not well reflected in tools offered by current spatial information systems (Wentz,

Campbell & Houston 2003).

One of the research fields which until now has remained largely theoretical is the domain of

qualitative reasoning (QR). However, one of the key motivations for QR lies in its applicability

for user interactive information systems, where qualitative information tallies much more

with human intuition, communication and decision making than quantitative information

(Egenhofer & Mark 1995, Renz, Rauh & Knauff 2000, Monferrer & Lobo 2002). In the past,

several qualitative spatial and temporal calculi have been introduced, first and foremost as a

reasoning tool: the Interval Algebra (Allen 1983), the Point Algebra (Vilain & Kautz 1986), the

Cardinal Direction Calculus (Frank 1991), the Doublecross Calculus (Freksa 1992b), the

Region Connection Calculus (Randell, Cui & Cohn 1992) and the Oriented Point Reasoning

Algebra (Moratz, Dylla & Frommberger 2005) to name but a few.

Yet, the usefulness of these calculi often remains questionable and needs a thorough

evaluation in terms of suitability, relevance and scope of potential applications. Wallgrün et

al. (2007) already made a general attempt in that direction with the development of a

qualitative spatial reasoning toolbox SparQ to allow for an easy integration in applications.

Another effort comes from El-Geresy and Abdelmoty (2004) with the introduction of a

qualitative spatial reasoning engine SPARQS for the automatic derivation of composition

tables. Another relevant line of work is that of Renz and Li (2008) who have largely

automated the task of determining the maximal tractable fragments for qualitative calculi.

Whereas most of the above mentioned calculi either stick to spatial or temporal issues, just

a few of them combine both to allow for spatiotemporal reasoning. One of them of

particular interest to the domain of moving objects is the Qualitative Trajectory Calculus

(QTC) (Van de Weghe 2004), which considers disjoint moving points objects (MPOs). We

believe that QTC constitutes a basis to represent and reason about moving objects, and thus

its implementation in an information system would provide a practical tool to support the

analysis of moving objects.

This chapter introduces an implementation prototype for the Basic (QTCB) and Double-Cross

(QTCC) calculi (Van de Weghe et al. 2006). Our aim is to show how QTC can be implemented

in an information system in a generic way, to introduce a methodology for handling

continuous data sampled at discrete times suitable for QTC, and to demonstrate the

applicability of such a system. The remainder of this chapter is organised as follows. Section

5.2 sketches a brief overview of QTC and its different types, including an informal account of


QTCB and QTCC (section 5.2). Section 5.3 introduces a conceptual modal and a prototype

QTC-based information system. In section 5.4, the use of this system is illustrated in two

different case studies. Section 5.5 presents a detailed discussion, and finally, section 5.6

draws some conclusions and considers possible future work.

5.2 The Qualitative Trajectory Calculus (QTC)

5.2.1 Types of QTC

QTC was introduced by Van de Weghe (2004) as a qualitative calculus to represent and

reason about moving objects. The QTC formalism defines relations between a pair of disjoint

MPOs. These MPOs are assumed to evolve continuously in space and time. Due to the

consideration of different spaces and frames of reference, the following types of QTC have

been elaborated (Van de Weghe 2004):

Basic type – QTCB

Double-Cross type – QTCC

Network type – QTCN

Shape type – QTCS

QTCB (Basic) and QTCC (Double-Cross) both deal with MPOs having a free trajectory in an n-

dimensional space. In QTCB, relations are determined referring to the Euclidian distance

between two MPOs (Figure 5.1a) (Van de Weghe et al. 2006), while QTCC relations use the

double cross between them (Figure 5.1b) (Van de Weghe et al. 2005a), as introduced by

Zimmerman and Freksa (1996).

QTCN (Network) (Bogaert 2008, Delafontaine et al. 2008) focuses on the special case of

MPOs which trajectories are constrained by a network, such as cars in a city. Since both the

Euclidean distance and the double cross concepts ignore the spatial configuration of a

potential underlying network, they are not well suited for QTCN. Therefore, QTCN relations

rely on the shortest paths in the network between the considered MPOs (Figure 5.1c).

Figure 5.1 – Two MPOs represented in a typical QTCB (a), QTCC (b), and QTCN (c) setting. The frame

of spatial reference is represented by the dashed line.

Finally, QTCS (Shape) is a calculus to represent and compare trajectory shapes, completely

abstracting from the actual MPOs (Van de Weghe et al. 2005b).

90 Chapter 5

In QTC, space and time (and thus the motion of MPOs) are assumed to be continuous.

Therefore, QTC relations may change over time according to the laws of continuity. In what

follows, we will use the term transition to denote the continuous change of one relation into

a conceptual neighbouring relation (Freksa 1992a), thus without passing intermediate

relations. Each transition occurs at an instant, i.e. point in time, which we will term transition

instant.

All QTC calculi are associated with a set of jointly exhaustive and pairwise disjoint (JEPD)

base relations. Consequently, there is one and only one relation for each pair of coexisting

MPOs at each time instant. In addition, due to continuity, the concurrent movement of two

MPOs over a time interval is uniquely mapped to a sequence of conceptual neighbouring

base relations.

5.2.2 Unconstrained movement

Both QTCB and QTCC were developed to represent and reason about MPO movements in a

free Euclidean space. Van de Weghe et al. (2006, 2005c) introduced four types (B11, B12,

B21, B22) of QTCB, and two types (C21, C22) of QTCC, although more subtypes could be

defined on the same basis. All relations in each of these six types are composed of multiple

relation symbols, each of which has the three-valued qualitative domain . These

symbols rely on (a subset of) the following relationships:

For a pair of MPOs and , and a time instant (Figure 5.2):

denotes the point location of at

denotes the velocity vector of at

denotes the straight line between and

denotes the positive angle between and

denotes the positive angle between and

denotes the minimum absolute angle between and

denotes the minimum absolute angle between and

Figure 5.2 – Properties of two MPOs k and l at a time instant t.

Then at :

A. : is moving towards (5.1)



0: all other cases ( is stable with respect to )

B. : is moving towards (5.3)



C. : is moving to the left of (5.5)

+: is moving to the right of

(5.6)


D. : is moving to the left of (5.7)

+: is moving to the right of (5.8)


E. : is moving faster than

(5.9)

+: is moving slower than

(5.10)

0: all other cases ( is moving equally fast as )

F. : is moving at a smaller angle with respect to than (5.11)

+: is moving at a bigger angle with respect to than (5.12)

0: all other cases ( and are moving at the same angle with respect to )

Thus, the assessment of these six relation symbols requires knowledge on the instantaneous

location, and velocity (i.e. speed and motion azimuth) of both MPOs. Table 5.1 presents the

syntax of relations for all QTCB and QTCC types, according to the above mentioned

relationships A–F. Note that B11 and B12 have the same syntax as respectively B21 and B22:

they differ in the number of spatial dimensions taken into account. According to these rules,

a configuration where at time a zebra is moving away from a lion which in turn is

approaching and catching up with the zebra can be described in B22 by ‘+’ for A ( away

from ), ‘’ for B ( towards ), and ‘’ for E ( slower than ), which we will write as

= (+ )B22

.

92 Chapter 5

From an application point of view (cf. the lion and the zebra), the order of objects in the

relation often does not matter. Hence, converse relations have to be taken into account.

Converse relations in QTCB and QTCC can be obtained by interchanging the relation symbols

A with B, C with D, and by replacing E and F with their inverse symbols. The inverse symbol

for ‘’ is ‘+’, for ‘0’ is ‘0’, and for ‘+’ is ‘’. In the above example, the converse of

would be = ( + +)B22

.

QTC type Relation syntax

B11 (A B) B12 (A B E) B21 (A B) B22 (A B E) C21 (A B C D) C22 (A B C D E F)

Table 5.1 – Relation syntax for QTCB and QTCC subtypes.

5.3 A QTC-based information system

5.3.1 Trajectory representations

As QTC assumes spatial and temporal continuity, the location, the speed, and the motion

azimuth of an MPO are assumed to be continuous functions of time. Hence, an MPO

trajectory is a continuous set of points in space and time, which corresponds to the

conventional mathematical notion of a curve at the spatial level, and to a simple closed

interval at the temporal level.

Yet, in order to implement QTC in an information system, we need to consider how

information systems, and GISs in particular, store and represent MPO trajectories. Longley et

al. (2005, p. 70) argue that any representation is discrete, stating that “the world is infinitely

complex, but computer systems are finite”. To date, by far the most common way to store a

trajectory, is as a set of spatial locations at consecutive time steps (Orlando et al. 2007,

Turchin 1998, Yu et al. 2004, Yu & Kim 2006, Gudmundsson, van Kreveld & Speckmann 2007)

which we will term fixes, according to Laube et al. (2005). Obviously, such a discrete set of

fixes conflicts with the assumption of spatial and temporal continuity underlying QTC.

Hence, fixes need to be interpolated in space and time to obtain continuous trajectories.

5.3.2 Conceptual model

In order to implement QTC in an information system, an object-oriented design is proposed,

shown in Figure 5.3. Part of this model has been based on the MPO modelling domain after

Laube et al. (2005) where trajectories are build of a set of fixes (see section 5.3.3).

The MPO class represents dimensionless moving objects, whose spatiotemporal properties

are described by one or more trajectories (instances of Trajectory). Each Trajectory


maintains a list of one or more fixes (instances of Fix), that describe locations in space

(Point) and time (Instant). Each Trajectory has a timeSpan which equals the time interval

between its first and last fix. In order to represent continuous trajectories, the Trajectory

class may have its own detached functions to interpolate in between fixes. The MPO’s

location, speed and motion azimuth at a specific time instant are respectively returned by

the getLocation, getSpeed, and getAzimuth methods (constraint: time parameter must be

within timeSpan).

getLocation(in time) : Point

getSpeed(in time)

getAzimuth(in time)

fixes[1..*] : Fix

\timeSpan[1] : Interval

Trajectory

trajectories[1..*] : Trajectory

MPO

location[1] : Point

timeStamp[1] : Instant

Fix

1

Point

getRelation(in calculus : QTCCalculus, in time : Instant) : QTCRelation

getTransitions(in calculus : QTCCalculus, in interval : Interval)

firstTrajectory[1] : Trajectory

secondTrajectory[1] : Trajectory

\timeSpan[1] : Interval

TrajectoryPair

getSymbol(in index)

QTCRelation

1..*

1

2

0..*

numberOfSymbols[1]

relations[*] : QTCRelation

QTCCalculus

1

*

B11

C22

C21

B22

B21

B12

Instant

Interval

1

1

1

1..*

1

2

Figure 5.3 – UML class diagram for a QTC-based information system

As QTC applies to relations between two MPOs, a TrajectoryPair class is considered to

embody an ordered pair of coexisting trajectories. The firstTrajectory and secondTrajectory

properties refer to the respective Trajectory instances (constraints: firstTrajectory and

secondTrajectory belong to a different MPO; firstTrajectory and secondTrajectory have an

overlapping timeSpan). Each TrajectoryPair has a timeSpan which equals the temporal

overlap between the timeSpan of firstTrajectory and seconTrajectory. Starting from the

principles of continuity and JEPD (see section 5.2), we consider two basic operations that

comprise the necessary conditions for an implementation of QTC:

At each time instant there exists one and only one QTC relation between two MPOs

(section 5.2.1). The getRelation method returns this relation for a given type of QTC at a

given input time (constraint: the input time must be within the timeSpan of the

TrajectoryPair).

Each TrajectoryPair can be associated with a chronologically ordered set of QTC

relations and corresponding transition times (i.e. the instants at which the relations

change) over a time interval during its timeSpan. This ordered mapping is returned by

94 Chapter 5

the getTransitions method for a given type of QTC (constraint: the input time interval

must be during the timeSpan of the TrajectoryPair).

Specific types of QTC are modelled as subclasses of an abstract QTCCalculus class. They

implement two properties: relations returns their set of base relations; numberOfSymbols

returns the number of relation symbols in a relation.

QTC relations are represented by QTCRelation objects, which have a getSymbol method to

return the individual relation symbol at the specified index (constraint: the index parameter

must not exceed the numberOfSymbols of the QTCCalculus at hand).

5.3.3 Implementation prototype

Building on the conceptual model of section 5.3.2, we developed QTCAnalyst, a prototype

QTC-based information system. In the remainder of this section, we give an overview of the

assumptions and restrictions that underlie this implementation.

Trajectories

Although one can apply several methodologies to interpolate trajectory fixes in space and

time, e.g. (Yu et al. 2004), QTCAnalyst relies on the following assumptions, being the most

obvious and robust:

Assumption 5.1 – Trajectory polyline: In between two fix times, an MPO moves continuously

along the straight line segment connecting both fixes.

Assumption 5.2 – Segment speed: In between two fixes, the speed of an MPO is constant.

Thus, a trajectory is represented as a polyline of which each vertex represents a fix, as shown

in Figure 5.4. Though Assumptions 5.1 and 5.2 determine the trajectory of an MPO as a

continuous function of time, they entail two discontinuities for MPOs at fixes: a discontinuity

of motion azimuth due to Assumption 5.1 and a discontinuity of speed due to Assumption

5.2. Hence, contrary to getLocation, the getSpeed and getAzimuth methods are not defined

for time instants that correspond to trajectory fixes of the MPO at hand. In order to get

round this problem to determine the QTC relation at these instants, we will make use of a

transition table, as discussed later in this section.

To enable an objective comparison of trajectories, QTCAnalyst assumes concurrency of fixes:

Assumption 5.3 – Concurrent observation: All trajectories are sampled at the same set of fix

instants.

Whenever this assumption is not satisfied, fixes can always be resampled (interpolating as

necessary) according to Assumptions 5.1 and 5.2 so that Assumption 5.3 is met.


Figure 5.4 – A continuous MPO trajectory (a) and a representation of it according to Assumption

5.1 with fixes (crosses) per second (b).

Relations

As mentioned in section 5.3.2, an implementation of QTC requires a getRelation and a

getTransition method. getRelation can be determined according to relationships A–F (section

5.2.2). However, this will be impossible for MPOs at fixes, since getSpeed and getAzimuth are

ambiguous in that case due to Assumptions 5.1 and 5.2. In order to deduce relations for

MPOs at fixes, QTCAnalyst relies on the laws of continuity, where Galton (2001) points out

that ‘’ and ‘+’ are ‘dominated by’ ‘0’, from which follow these restrictions:

Restriction 5.1a – Intermediate ‘0’: A transition from ‘’ to ‘+’ must always pass the

intermediate value ‘0’.

Restriction 5.1b – Intermediate ‘0’: A transition from ‘+’ to ‘’ must always pass the

intermediate value ‘0’.

Restriction 5.2a – Dominated ‘’: A ‘’ lasts over an open time interval.

Restriction 5.2b – Dominated ‘+’: A ‘+’ lasts over an open time interval.

Restriction 5.2c – Dominant ‘0’: A ‘0’ lasts over either a closed time interval, or a time

instant.

Restriction 5.3a – Intermediate interval: There is always a closed time interval in between

two ‘’ relations.

Restriction 5.3b – Intermediate interval: There is always a closed time interval in between

two ‘+’ relations.

There is always an adjacent open time interval before and after a time instant. For an instant

, let us denote these intervals respectively and . Then at transition instant , due

restrictions 5.1-5.3, we obtain the relation symbols presented in Table 5.2. The

implementation of getRelation at in QTCAnalyst is now as follows:

For not at a fix time: getRelation uses relationships A – F (equations 5.1-5.12).

For at a fix time: getRelation first computates the before and after relationships (A – F)

using the locations at together with the speed and motion azimuth at respectively the

96 Chapter 5

preceding and following segment. Next, the transition table is employed to return the

relation at .

Relation symbol at t Relation symbol during t+

0 +

Relation symbol

during t

0 0 0 0 0 0 + 0 0 +

Table 5.2 – Transition table for QTC relation symbols at transition instant t

Transitions

The getTransitions method returns the chronological sequence of QTC relations and the

corresponding transition instants over a given valid time interval for the TrajectoryPair at

hand. Due to dominance theory (Galton 2001), each transition instant corresponds to a ‘0’

relationship symbol. By consequence, it suffices to assess at which instants a relationship

symbol changes to or from ‘0’. Due to Table 5.2, zero to two transitions might occur for each

relationship symbol at one time instant (e.g. at fix times).

For time instants in between consecutive fixes, relationship A will be ‘0’ when:

is stationary (intra-object coinciding fixes, no transitions);

and coincide. According to Assumptions 5.1-5.3, this situation occurs either at one

intermediate time instant (collision, two transitions), or over the complete segment

(inter-object coinciding fixes, no transitions);

is perpendicular to (equations 5.1-5.2). Due to Assumptions 5.1-5.3, this

situation occurs either at one intermediate time instant (two transitions), or over the

complete segment (no transitions).

The cases with two transitions (one from ‘’ or ‘+’ to ‘0’, the other one from ‘0’ to

respectively ‘+’ or ‘’) are mutually exclusive and can be solved analytically on the basis of

equations such as in Appendix A. Analogous to relationship A, it can be shown that there will

be at most two transitions for B – D, and four transitions for F for time intervals in between

two consecutive fixes. Obviously, no transitions can occur for E due to Assumption 5.2 (only

at fix times).

Thus, a TrajectoryPair consisting of pairs of concurrent fixes, will in a worst case scenario

have – – transitions over its total timeSpan.

Prototype application

QTCAnalyst was implemented in Visual Basic 6.5 using AutoCAD for visualisation and MS

Excel for data input and output. Through a GUI, trajectories that answer Assumptions 5.1-

5.3, can be loaded from fix data, and can be visualised in a conventional two-dimensional

space (top view perspective), or in a space-time cube. TrajectoryPair instances can then be


automatically generated for each canonical pair of coexisting Trajectory instances. Finally,

the output of the getRelation and getTransitions methods can be exported, or visualised. In

addition, QTCAnalyst is able to calculate and export simple summaries (see section 5.4.1), as

well as relation patterns (see section 5.4.2), i.e. chains of subsequent relations, from the set

of relations resulting from getTransitions.

5.4 Case studies

In this section, we utilise QTCAnalyst to analyse QTC relations in two completely different

contexts. The first case focuses on the QTCB relations between moving vehicles on a four

lane one-way street. The second case deals with QTCC relations of players in a squash

contest.

5.4.1 Cars on a street

The study area is a straight section of about 130 m of a four lane one-way road in Ghent

(Belgium), as schematized in Figure 5.5. This road is the south-north directed tail end of a

highway exit for the centre of Ghent. Another single lane road converges with it immediately

south of the study area, whereas there are traffic lights at the north end.

Figure 5.5 – Schematic sketch of the study area.

During the morning rush hour, a movie of the study area has been recorded with a steady

camera from a high building in the neighbourhood for two minutes. This movie has been

georeferenced to a local two-dimensional reference system in order to assess the relative

positions of cars – treated as MPOs – on snapshots taken at a regular time step of 1 s. The x-

axis of this system is aligned with the road’s centreline, whereas the y-axis is along the width

dimension. The resolution in y has intentionally been kept coarse, in order to eliminate

insignificant shifts of cars that stay within their lane. Hence, we obtain a data set of 44 car

trajectories with different time spans but with concurrent fixes (Assumption 3).

Of the 946 canonical trajectory pairs that exist for 44 trajectories, 503 have a temporal

overlap, and hence enable the calculation of QTC relations. Table 5.3 and Table 5.4 list some

of the QTCAnalyst results about the relations between these 503 valid pairs for the B21 and

98 Chapter 5

B22 calculi. The tables summarise the number of instantaneous occurrences, the number of

occurrences over a time interval, the total number of occurrences, and the total duration for

each relation aggregated over all valid pairs.

Relation Instants Intervals Total Duration (s)

( )B21 0 1 1 0.2

( +)B21 0 104 104 328.4

( 0)B21 3 3 6 3.0

(+ )B21 0 362 362 1 581.7

(+ +)B21 0 4 4 0.7

(+ 0)B21 58 132 190 534.0

(0 )B21 146 344 490 2 089.6

(0 +)B21 49 172 221 738.4

(0 0)B21 567 204 771 3 178.0

Total 823 1 326 2 149 8 454.0


frequencies, and duration for 503 car pairs.

From Table 5.3, we may learn that all nine B21 base relations do have at least one

occurrence. However, the occurrences are not equally distributed over this universe set.

Since there is no significant natural order for cars in a street, we will focus our discussion on

groups of converse relations. A first group is represented simply by the symmetric (0 0)B21

relation. It is the most common relation in the data set, lasting for almost 40% of the

cumulative time. Perhaps this indicates the importance of collective stops (both cars

standing still). A ‘0’ relation symbol, however, does not imply object stationarity. For

example, two cars driving next to each other in different parallel lanes are also in a (0 0)B21

relation, while both are moving. The same applies for (0 )B21

, (0 +)B21

, and their converse

relations ( 0)B21

, and (+ 0)B21

, which constitute another important group (40% of the total

time). In these cases, at least one car is moving, whereas this is unknown for its associate.

The last significant group consists of the relation ( +)B21

and its converse (+ )B21

. They

represent the regular situation of cars following one another. For the remaining two

symmetric relations, the table indicates that situations where cars are converging [( )B21

]

or diverging [(+ +)B21

] are rare: they respectively occur once and four times, lasting for only

fractions of seconds.

As shown in Table 5.4, only 21 of the 27 base relations occur in QTC-B22. The relative speed

symbol of these relations can now be used in order to further refine the interpretations

made for QTC-B21. Let us reconsider the groups of converse relations. For (0 0)B21

, we can

see that all intervals must be (0 0 0)B22

since both share the same number of interval

occurrences and have equal total duration. The remaining relations in this group, (0 0 )B22


and (0 0 +)B22

, only occur instantaneously. Due to the difference in relative speed, at least

one object must be moving in this case. These are the typical transition relations of cars

passing by each other. There number of occurrences gives a first indication of the number of

overtake events in the dataset, although relation sequences would be needed for an exact

assessment.

Relation Instant Interval Total Duration

( )B22 0 1 1 0.2

( +)B22 0 0 0 0.0

( 0)B22 0 0 0 0.0

( + )B22 0 110 110 306.5

( + +)B22 0 13 13 13.0

( + 0)B22 28 9 37 9.0

( 0 )B22 1 0 1 0.0

( 0 +)B22 1 3 4 3.0

( 0 0)B22 1 0 1 0.0

(+ )B22 0 376 376 1 197.7

(+ +)B22 0 157 157 290.1

(+ 0)B22 250 79 329 94.0

(+ + )B22 0 4 4 0.7

(+ + +)B22 0 0 0 0.0

(+ + 0)B22 0 0 0 0.0

(+ 0 )B22 3 0 3 0.0

(+ 0 +)B22 45 132 177 534.0

(+ 0 0)B22 10 0 10 0.0

(0 )B22 131 344 475 2 089.6

(0 +)B22 0 0 0 0.0

(0 0)B22 15 0 15 0.0

(0 + )B22 48 172 220 738.4

(0 + +)B22 0 0 0 0.0

(0 + 0)B22 1 0 1 0.0

(0 0 )B22 179 0 179 0.0

(0 0 +)B22 3 0 3 0.0

(0 0 0)B22 385 204 589 3 178.0

Total 1 101 1604 2 705 8 454.0


frequencies, and duration for 503 car pairs.

For the next group, we find the following correspondences for interval occurrences and

durations: ( 0)B21

with ( 0 +)B22

, (+ 0)B21

with (+ 0 +)B22

, (0 )B21

with (0 )B22

, and

(0 +)B21

with (0 )B22

. Hence, the car that is certainly moving always has the highest

100 Chapter 5

speed. Presumably, this means that in most, if not all, of the cases the other car is standing

still.

The group associated with cars that follow each other, has no instantaneous occurrences in

B22 where the relative speed symbol is ‘’ or ‘+’, as could be expected from restriction 5.2

(section 5.3.3) since those relations have no ‘0’ symbols.

Finally, the two remaining relations ( )B22

and (+ + )B22

belong to the least

represented groups, associated with convergence and divergence patterns. Due to their rare

occurrence, four base relations are not represented in these groups.

5.4.2 Squash rally

In this case study, we analyse the relation of two squash opponents in a championship duel

in QTC-C22. Therefore, we employ the public standard CVBase’06 dataset (Pers, Bon &

Vuckovic 2006). In this dataset, the trajectories of two squash players were sampled from

video frames taken at regular time steps of 0.04 seconds, by automatic computer vision

based tracking under field expert supervision. The resulting trajectories were smoothed by a

Gaussian kernel and have a positional RMS error of about 0.3 m.

Since there is only one pair of players, there is no need for a cumulative summary table as in

section 5.4.1. To simplify the discussion, we will consider the QTC-C22 relations between

both players during a rally lasting 37 s. For a complete chronological sequence of QTC-C22

relations during this rally, we refer to the Appendix B.

As stated in section 5.3.3, QTCAnalyst has the ability to compute relation patterns, i.e. chains

of two or more subsequent relations. Let us now consider some simple permutable patterns.

With simple patterns, we mean patterns that do not contain a repetition of subpatterns of a

lower order2 (i.e. complex patterns). A permutable pattern represents a pattern and all

permutations of it. For example, the patterns → → , → → , or → → all represent

the same permutable pattern. Since the smallest order is two, patterns of order two and

three are by definition simple patterns.

For the opponents in the rally, a total of 196 simple permutable QTC-C22 patterns of order

four have been found, and they are distributed non uniformly both in terms of frequency

and duration. 124 of them occur just once, i.e. only 72 patterns have at least one repetition.

Figure 5.6 presents a graph of the frequency and the total duration for the 24 patterns with

the longest total duration. All remaining patterns have a duration of less than 1.5 s, and a

frequency of eight or less. The graph shows that the three most frequent patterns also have

the highest durations. Two patterns prevail: ( + )C22

→ ( 0 )C22

→ ( )C22

→

( 0 )C22

with 40 occurrences over 7.8 s, and (+ )C22

→ (0 )C22

→

2 The number of relations a pattern consists of.


( )C22

→ (0 )C22

with 20 occurrences over 8.9 s. Interestingly, they are each

other’s converse pattern, and hence we learn that a prevailing movement behaviour during

the rally, is that one player (follower) is following its opponent (leader) until the leader

temporarily changes its moving direction towards the follower. Both players thereby

continuously remain moving to the left of each other (i.e. to the left of the reference line

connecting them). An alternation of both patterns may occur whenever the opponents are

alternatively running in clockwise cycles around each other. In squash, this behaviour may

arise whenever both players are alternating a forward move to play the ball with a backward

move to let the opponent play, taking account of the interference rule.3

Note that both patterns have ( )C22

in common: the relation with the longest overall

duration and second most occurrences (see Appendix B). Taking into account that the

patterns are permutable, it follows that they might overlap with each other.

Figure 5.6 – Duration (gray bars) and frequency (black bars) for 24 fourth order simple permutable

patterns in QTC-C22.

5.5 Discussion

This chapter has addressed the implementation of a QTC-based information system: we

proposed a conceptual model, set up a prototype system, and demonstrated its applicability 3 According to the official rules of squash (World Squash Federation 2009), “to avoid interference, the

opponent must try to provide the player with unobstructed direct access to the ball, a fair view of the ball, space to complete a swing at the ball and freedom to play the ball directly to any part of the front wall”.

102 Chapter 5

by two case studies. In what follows, we will point out some strengths and weaknesses of

our approach.

(a) Although this chapter confines itself to an implementation for QTCB and QTCC, the

proposed conceptual model is based on the principles of continuity, and of jointly

exhaustiveness and pairwise disjointness (JEPD), and is therefore generic for all QTC

calculi. QTCAnalyst is not pretended to be an end-user information system. It is a use

case independent prototype that may constitute the core of such a system, but would

need enhanced processing capabilities and automatic interpretation mechanisms in

order to become a fully fledged application. To illustrate the generality of this approach,

we chose two completely different use cases in section 5.4.

(b) QTCAnalyst provides unambiguous and consistent results. Although there are no explicit

implementations of conceptual neighbourhood diagrams (CNDs), QTCAnalyst results

(e.g. Table 5.3, Table 5.4, and Figure 5.6) are consistent with conceptual

neighbourhoodness, since the data respected the assumptions of continuity which

conceptual neighbourhoodness captures, and no gaps in recording occurred. Explicit use

of conceptual neighbourhoods could be useful in the case of incomplete data. For

instance, if at some instants the position of some MPOs is not known, possible relations

may be inferable through the assumptions of continuity as encoded in the CNDs.

Alternatively, interpolation on the actual positions could of course be used.

(c) While being a key and much studied operation in qualitative reasoning generally, the

composition of relations is not supported by QTCAnalyst. The starting point for

QTCAnalyst is trajectory data, and hence, in order to determine the relations

and , the trajectory data of all objects , , and is required. Consequently,

rather than applying the composition of and , a direct computation of

is more convenient, more efficient, and often more precise. We do not ignore

the usefulness of composition, and it provides another method, in addition to the use of

conceptual neighbourhoods mentioned in (b) above to inferring missing data; however,

composition has not been the focus in this work.

(d) Although Assumptions 5.1 and 5.2 can be used to interpolate MPO trajectories, some

open problems still remain in the MPO modelling domain. According to Laube, Imfeld

and Weibel (2005) these include the presence of uncertain and/or missing fixes as well

as granularity related issues. The granularity issue is worth discussing. Consider for

instance case A in Figure 5.7, where (0 )B22

(0 0 )B22

(0 + )B22

,

and hence has a higher speed as it covers a longer distance in reality (Figure 5.7a).

However, due to a sampling satisfying Assumptions 5.1-5.3, this case may be

represented as in Figure 5.7b, where = (0 0 0)B22

. Another example is case B,

where is circling around a stationary , and thus = (0 0)B21

(Figure 5.7c).


However, such a circular trajectory can never be represented by straight segments, and

thus will never equal (0 0)B21

over a time interval in Figure 5.7d. In both

cases, wrong relations are obtained due to the sampling of fixes and the application of

Assumptions 5.1-5.3. Moreover, they illustrate how relative speed as well as relative

direction may be influenced by a sampled representation. Note that both cases deal

with pertaining stable relations, i.e. relations with a ‘0’ symbol holding over a time

interval: in case A, ‘0’ erroneously arises, whereas in case B, ‘0’ is erroneously missed.

Yet, there is another important difference: in case A, the error could be avoided by

sufficient sampling granularity, whereas this does not apply for case B. In order to obtain

the desired stable relations, for situations such as case B, there are several possible

solutions. A reasonable one could be to introduce spatiotemporal limits or thresholds,

where stable relations occur whenever movements (such as relative speeds, or relative

directions) remain within these presumed thresholds. Depending upon the field of

application, suitable thresholds may be based on the precision or accuracy of the

trajectory data, the user-intended analysis granularity, the limits of the object’s (human,

animal, robot, etc.) perception, etc. This approach will also increase the chance of stable

relations actually occurring, where otherwise the usefulness of these so called

borderline cases is sometimes questioned (Gottfried 2008).

(e) While Assumptions 5.1-5.2 are applicable to every set of fixes, Assumption 5.3 is the

only one restricting the data collection method. In addition, this assumption may

sometimes be unrealistic, for instance when multiple unsynchronised sensors are used

or in case of missing fixes. However, as mentioned earlier, one can easily obtain

concurrency by applying first the Assumptions 5.1-5.2, and then resample the resulting

trajectory in order to fulfil Assumption 5.3.

Figure 5.7 – Trajectories of two objects k and l during a time interval for two situations (A and B)

according to two representations: realistic representation (a), (c); representation satisfying

Assumptions 5.1-5.3 (b), (d). Crosses represent fixes.

104 Chapter 5

(f) Throughout this chapter, the usual, absolute notion of time has been employed.

However, since QTC considers relative relationships, a relative time notion could be

useful in some cases, e.g. to compare movements with different time spans.

(g) In an applied setting, a user’s interest in QTC relations will be limited to those objects

that interact with each other. The assessment of interacting objects, i.e. the issue of

determining exactly which objects are interacting with each other, has been indicated as

an open problem (Andrienko et al. 2008). Hence, the advances made on that issue might

improve further implementations.

(h) The case studies in section 5.4 have shown that QTCAnalyst might be a useful tool for

the analysis of trajectory data within diverse contexts, such as traffic monitoring or

sports performance analysis. It is commonly accepted that qualitative and quantitative

formalisms should complement each other. This idea also underlies the results in section

5.4, were we analysed the quantitative properties of qualitative relations or patterns.

5.6 Conclusions and outlook

The contribution of this chapter is threefold:

A generic conceptual model for the analysis of moving point objects through a

Qualitative Trajectory Calculus was introduced.

An implementation methodology was proposed for the QTCB and QTCC calculi and a

prototype was developed (QTCAnalyst).

The applicability for a QTC-based information system was highlighted in two case

studies.

In future work, we intend to extend QTCAnalyst to other QTC calculi, especially QTCN. Since

QTCS abstracts from the actual moving objects, its implementation is not our first priority,

though there may be promising applications, e.g. in the field of trajectory similarity

measurement.

Also, a more advanced implementation may call for an explicit representation of conceptual

neighbourhood diagrams as well as composition tables.

As mentioned in the discussion, a fully fledged information system should implement

advanced mechanisms for post-processing and automatically interpreting raw QTC relations

and/or patterns. Moreover, its input modalities should go beyond conventional trajectory

data: whereas the intuitiveness and suitability for human decision making is a key motivation

for qualitative reasoning systems, possibilities for user-interactive and intuition-based data

input, such as query-by-sketch (Egenhofer 1996) should be considered. On the other hand,

these extensions would in turn benefit from increased output capabilities such as advanced

visualisation and communication means, e.g. animations.


References


11, 832-843.

Andrienko, N., Andrienko, G., Wachowicz, M. & Orellana, D. (2008) Uncovering interactions between

moving objects. In Proceedings of the 5th International Conference on Geographic

Information Science, eds. T. J. Cova, H. J. Miller, K. Beard, A. U. Frank & M. F. Goodchild, Park

City, Utah, 16-26.

Bogaert, P. (2008) A Qualitative Calculus for Moving Point Objects Constrained by Networks, Doctoral

Dissertation, Ghent: Ghent University, 155.

Brakatsoulas, S., Pfoser, D., Salas, R. & Wenk, C. (2005) On map-matching vehicle tracking data. In

Proceedings of the 31st International Conference on Very Large Data Bases, Trondheim,

Norway: VLDB Endowment, 853-864.

Brakatsoulas, S., Pfoser, D. & Tryfona, N. (2004) Modeling, storing, and mining moving object

databases. In Proceedings of the International Database Engineering and Applications

Symposium, IEEE Computer Society, 68-77.

Brunk, B. & Davis, B. (2002) SDAT enterprise: Application of geospatial network services for

collaborative airspace analysis. In CADD/GIS Symposium Proceedings, San Antonio.

DeCesare, N. J., Squires, J. R. & Kolbe, J. A. (2005) Effect of forest canopy on GPS-based movement

data. Wildlife Society Bulletin, 33, 3, 935-941.



Sciences, 178, 8, 1997-2006.

Eagle, N. & Pentland, A. (2006) Reality mining: sensing complex social systems. Personal and

Ubiquitous Computing, 10, 4, 255-268.

Egenhofer, M. J. (1996) Spatial-Query-by-Sketch. In Proceedings of the 1996 IEEE Symposium on

Visual Languages, 60-67.

Egenhofer, M. J. & Mark, D. (1995) Naive geography. In Spatial Information Theory: A Theoretical

Basis for GIS, eds. A. U. Frank & W. Kuhn, Berlin / Heidelberg: Springer-Verlag, 1-15.

El-Geresy, B. A. & Abdelmoty, A. I. (2004) SPARQS: a qualitative spatial reasoning engine. Knowledge-

Based Systems, 17, 2-4, 89-102.

Frank, A., U. (1991) Qualitative spatial reasoning about cardinal directions. In Proceedings of

Autocarto 10, American Congress on Surveying and Mapping, eds. D. Mark & D. White,

Baltimore, Maryland, 148-167.





Gagliardo, A., Ioale, P., Savini, M., Lipp, H. P. & Dell'Omo, G. (2007) Finding home: the final step of

the pigeons' homing process studied with a GPS data logger. Journal of Experimental Biology,

210, 7, 1132-1138.

Galton, A. (2001) Dominance diagrams: a tool for qualitative reasoning about continuous systems.

Fundamenta Informaticae, 46, 1-2, 55-70.

106 Chapter 5

Gau, R. J., Mulders, R., Ciarniello, L. J., Heard, D. C., Chetkiewicz, C. L. B., Boyce, M., Munro, R.,

Stenhouse, G., Chruszcz, B., Gibeau, M. L., Milakovic, B. & Parker, K. L. (2004) Uncontrolled

field performance of televilt GPS-Simplex (TM) collars on grizzly bears in western and

northern Canada. Wildlife Society Bulletin, 32, 3, 693-701.

Giannotti, F. & Pedreschi, D. (2008) Mobility, Data Mining and Privacy: Geographic Knowledge

Discovery, Springer, 410.

Gottfried, B. (2008) Representing short-term observations of moving objects by a simple visual

language. Journal of Visual Languages and Computing, 19, 3, 321-342.

Grace, J. (2000) GPS guidance system increases projectile accuracy. IEEE Aerospace and Electronic

Systems Magazine, 15, 6, 15-17.







Hvidberg, M. (2006) Tracking human exposure to ultrafine particles in Copenhagen using GPS.

Epidemiology, 17, 6, S38-S38.

Kritzler, M., Raubal, M. & Kruger, A. (2007) A GIS framework for spatio-temporal analysis and

visualization of laboratory mice tracking data. Transactions in GIS, 11, 5, 765-782.

Laube, P., Dennis, T., Forer, P. & Walker, M. (2007) Movement beyond the snapshot - Dynamic



point objects. International Journal of Geographical Information Science, 19, 6, 639 - 668.

Laube, P., van Kreveld, M. & Imfeld, S. (2005) Finding REMO - Detecting relative motion patterns in

geospatial lifelines. In Developments in Spatial Data Handling, ed. P. Fisher, Berlin: Springer-

Verlag, 201-215.

Longley, P. A., Goodchild, M. F., Maquire, D. J. & Rhind, D. W. (2005) Geographic Information Systems

and Science. John Wiley & Sons, 519.

Mark, D. M. (1998) Geospatial lifelines. In Integrating Spatial and Temporal Databases. Dagstuhl

Seminars.

Michael, K., McNamee, A., Michael, M. G. & Tootell, H. (2006) Location-based intelligence - modeling

behavior in humans using GPS. In IEEE International Symposium on Technology and Society

(ISTAS 2006) 97-104.

Monferrer, T. E. & Lobo, F. T. (2002) Qualitative velocity. In Proceedings of the 5th Catalonian

Conference on AI: Topics in Artificial Intelligence, Springer-Verlag, 29-39.

Moratz, R., Dylla, F. & Frommberger, L. (2005) A relative orientation algebra with adjustable

granularity. In Proceedings of the Workshop on Agents in Real-Time and Dynamic

Environments (IJCAI 05), Edinburgh, Scotland.

Nielsen, T., S. & Hovgesen, H., H. (2004) GPS in pedestrian and spatial behaviour surveys. In Cities for

People, Proceedings of the 5th International Conference on Walking in the 21st Century, 13.

Copenhagen, Denmark.


Orlando, S., Orsini, R., Raffaeta, A., Roncato, A. & Silverstri, C. (2007) Trajectory data warehouses:

design and implementation issues. Journal of Computing Science and Engineering, 1, 2, 211-

232.

Pers, J., Bon, M. & Vuckovic, G. (2006) CVBASE '06 Dataset, available online: http://vision.fe.uni-

lj.si/cvbase06/dataset.html.


Proceedings of the 3rd International Conference on Principles of Knowledge Representation


Renz, J. & Li, J. J. (2008) Automated complexity proofs for qualitative spatial and temporal calculi. In

Proceedings of the 11th International Conference on Principles of Knowledge Representation

and Reasoning (KR'08), Sydney, Australia, 715-723.

Renz, J., Rauh, R. & Knauff, M. (2000) Towards cognitive adequacy of topological spatial relations. In

Spatial Cognition II, LNCS 1849, 184-197.

Spaccapietra, S., Parent, C., Damiani, M. L., de Macedo, J. A., Portoa, F. & Vangenot, C. (2008) A

conceptual view on trajectories. Data & Knowledge Engineering, 65, 1, 126-146.

Turchin, P. (1998) Quantitative Analysis of Movement: Measuring and Modeling Population

Redistribution in Animals and Plants. Sunderland, MA: Sinauer, 396.









Van de Weghe, N., De Tré, G., Kuijpers, B. & De Maeyer, P. (2005b) The double-cross and the

generalization concept as a basis for representing and comparing shapes of polylines. In

Proceedings of the 1st International Workshop on Semantic-based Geographical Information

Systems (SeBGIS'05), Agia Napa, Cyprus.

Van de Weghe, N., Kuijpers, B., Bogaert, P. & De Maeyer, P. (2005c) A Qualitative Trajectory Calculus




Vilain, M. & Kautz, H. (1986) Constraint propagation algorithms for temporal reasoning. In AAAI-86

Proceedings, 377-382.

Wallgrün, J. O., Frommberger, L., Wolter, D., Dylla, F. & Freksa, C. (2007) Qualitative spatial

representation and reasoning in the SparQ-toolbox. In Spatial Cognition V: Reasoning, Action,

Interaction, eds. T. Barkowsky, M. Knauff, G. Ligozat & D. R. Montello, 39-58.

Wang, L., Hu, W. & Tan, T. (2003) Recent developments in human motion analysis. Pattern

Recognition, 36, 3, 585-601.

Wentz, E. A., Campbell, A. F. & Houston, R. (2003) A comparison of two methods to create tracks of

moving objects: linear weighted distance and constrained random walk. International Journal

of Geographical Information Science, 17, 7, 623-645.

108 Chapter 5

World Squash Federation (2009) World Squash Singles Rules, World Squash Federation, 33.

Yasuda, T. & Arai, N. (2005) Fine-scale tracking of marine turtles using GPS-argos PTTs. Zoological

Science, 22, 5, 547-553.

Yu, B. & Kim, S. (2006) Interpolating and using most likely trajectories in moving-objects databases. In

Database and Expert Systems Applications, LNCS 4080, 718-727.

Yu, B., Kim, S. H., Bailey, T. & Gamboa, R. (2004) Curve-Based representation of moving object

trajectories. In Proceedings of the International Database Engineering and Applications

Symposium, IEEE Computer Society, 419-425.

Zimmermann, K. & Freksa, C. (1996) Qualitative spatial reasoning using orientation, distance, and

path knowledge. Applied Intelligence, 6, 1, 49-58.


Appendix A

Consider two MPOs and with , , ,

, , , , , , , as defined in

section 5.2.2.

Let us consider a two-dimensional space, so that . Let t1, t2 be the time instants of

two consecutive fixes, so that:

,

,

.

Then, due to Assumptions 5.1-5.3:

with

– (5.13)

=

– (5.14)

(

) – (5.15)

(

– (5.16)

For ,

, , , , , , , as functions of , it follows from (5.13-5.16):

(5.17)

(5.18)

(5.19)

deg (5.20)

(5.21)

Hence, due to (5.17-5.21):

(5.22) (5.23) (5.24) (5.25)

110 Chapter 5

Appendix B

Relation Time Duration

unknown 28.00 (- + - +)

C21 0.04

(- 0 - +)C21 28.04

(- - - +)C21 0.16

(- 0 - +)C21 28.20

(- + - +)C21 0.20

(- 0 - +)C21 28.40

(- - - +)C21 0.12

(- 0 - +)C21 28.52

(- + - +)C21 0.68

(- + - 0)C21 29.20

(- + - -)C21 0.80

(- 0 - -)C21 30.00

(- - - -)C21 0.20

(- 0 - -)C21 30.20

(- + - -)C21 0.08

(- 0 - -)C21 30.28

(- - - -)C21 0.16

(- - 0 -)C21 30.44

(- - + -)C21 0.12

(- 0 + -)C21 30.56

(- + + -)C21 0.12

(- 0 + -)C21 30.68

(- - + -)C21 0.24

(- - + 0)C21 30.92

(- - + +)C21 0.28

(0 - + +)C21 31.20

(+ - + +)C21 0.40

(+ - 0 +)C21 31.60

(+ - - +)C21 0.12

(+ 0 - +)C21 31.72

(+ + - +)C21 0.24

(0 + 0 +)C21 31.96

(- + + +)C21 0.20

(- + + 0)C21 32.16

(- + + -)C21 0.36

(- + 0 -)C21 32.52

(- + - -)C21 0.16

(- + - 0)C21 32.68

(- + - +)C21 0.52

(0 + - +)C21 33.20

(+ + - +)C21 0.16

(0 + - 0)C21 33.36

(- + - -)C21 0.03

(0 + - -)C21 33.39

(+ + - -)C21 0.01

(0 + - -)C21 33.40

(- + - -)C21 0.28

(- 0 - -)C21 33.68

(- - - -)C21 0.24

(0 - - -)C21 33.92

(+ - - -)C21 0.16

(0 - - -)C21 34.08

(- - - -)C21 0.55

(0 - - -)C21 34.63

(+ - - -)C21 0.15

(+ 0 - -)C21 34.78

(+ + - -)C21 0.02

(+ + 0 -)C21 34.80

(+ + + -)C21 0.76

(+ 0 + -)C21 35.56

(+ - + -)C21 0.08

(0 - + 0)C21 35.64

(- - + +)C21 0.04

(- - 0 +)C21 35.68

(- - - +)C21 0.04

(- 0 - +)C21 35.72

(- + - +)C21 0.04

(- + - 0)C21 35.76

(- + - -)C21 0.16

(- 0 - -)C21 35.92

(- - - -)C21 0.59

(0 - - -)C21 36.51

(+ - - -)C21 0.02

(+ 0 - -)C21 36.53

(+ + - -)C21 0.31

(+ + - 0)C21 36.84

(+ + - +)C21 0.12

(+ 0 - +)C21 36.96

(+ - - +)C21 0.08

(+ - - 0)C21 37.04

(+ - - -)C21 0.24

(0 - - -)C21 37.28

(- - - -)C21 0.04

(- - 0 -)C21 37.32

(- - + -)C21 0.12

(- 0 + -)C21 37.44

(- + + -)C21 0.27

(- + 0 -)C21 37.71

(- + - -)C21 0.01

(- + 0 -)C21 37.72

(- + + -)C21 0.02

(- + 0 -)C21 37.74

(- + - -)C21 0.02

(- 0 - -)C21 37.76

(- - - -)C21 0.02

(- 0 - -)C21 37.78

(- + - -)C21 0.02

(- 0 - -)C21 37.80

(- - - -)C21 0.11

(- 0 - -)C21 37.91

(- + - -)C21 0.01

(- 0 - -)C21 37.92

(- - - -)C21 0.01

(- 0 - -)C21 37.93

(- + - -)C21 0.09

(0 + - -)C21 38.02

(+ + - -)C21 0.46

(+ 0 - -)C21 38.48

(+ - - -)C21 0.12

(0 - - -)C21 38.60

(- - - -)C21 0.60

(0 - - -)C21 39.20

(+ - - -)C21 0.12

(0 - - -)C21 39.32

(- - - -)C21 0.28

(- 0 - -)C21 39.60

(- + - -)C21 0.24

(0 + - -)C21 39.84

(+ + - -)C21 0.00

(0 + - 0)C21 39.84

(- + - +)C21 0.01

(0 + - +)C21 39.85

(+ + - +)C21 0.39

(+ 0 - 0)C21 40.24

(+ - - -)C21 0.04

(+ - - 0)C21 40.28

(+ - - +)C21 0.04

(+ - - 0)C21 40.32

(+ - - -)C21 0.04

(+ 0 - -)C21 40.36

(+ + - -)C21 0.36

(+ 0 - -)C21 40.72

(+ - - -)C21 0.08

(+ - 0 -)C21 40.80

(+ - + -)C21 0.12

(+ 0 + -)C21 40.92

(+ + + -)C21 0.12

(+ 0 + -)C21 41.04

(+ - + -)C21 0.09

(+ - + 0)C21 41.13

(+ - + +)C21 0.55

(0 - + +)C21 41.68

(- - + +)C21 0.08

(- - 0 +)C21 41.76

(- - - +)C21 0.20

(- - - 0)C21 41.96

(- - - -)C21 0.16

(0 - - -)C21 42.12

(+ - - -)C21 0.28

(+ 0 - -)C21 42.40

(+ + - -)C21 0.00

(+ 0 - -)C21 42.40

(+ - - -)C21 0.00

(+ 0 - -)C21 42.40

(+ + - -)C21 0.04

(0 + - -)C21 42.44

(- + - -)C21 0.31


(0 + - -)C21 42.75

(+ + - -)C21 0.05

(+ 0 - -)C21 42.80

(+ - - -)C21 0.12

(+ - - 0)C21 42.92

(+ - - +)C21 0.40

(+ - - 0)C21 43.32

(+ - - -)C21 0.08

(+ - 0 -)C21 43.40

(+ - + -)C21 0.56

(+ - 0 -)C21 43.96

(+ - - -)C21 0.08

(0 - - -)C21 44.04

(- - - -)C21 0.24

(0 - - -)C21 44.28

(+ - - -)C21 0.20

(0 - - -)C21 44.48

(- - - -)C21 0.16

(- 0 - -)C21 44.64

(- + - -)C21 0.00

(- 0 - -)C21 44.64

(- - - -)C21 0.00

(- 0 - -)C21 44.64

(- + - -)C21 0.10

(0 + - -)C21 44.74

(+ + - -)C21 0.02

(+ + - 0)C21 44.76

(+ + - +)C21 0.84

(+ + - 0)C21 45.60

(+ + - -)C21 0.04

(+ 0 - -)C21 45.64

(+ - - -)C21 0.04

(+ - 0 -)C21 45.68

(+ - + -)C21 0.20

(+ 0 + -)C21 45.88

(+ + + -)C21 0.08

(0 + + -)C21 45.96

(- + + -)C21 0.04

(- + 0 -)C21 46.00

(- + - -)C21 0.08

(- 0 - -)C21 46.08

(- - - -)C21 0.59

(- 0 - -)C21 46.67

(- + - -)C21 0.01

(- 0 - -)C21 46.68

(- - - -)C21 0.00

(- 0 - -)C21 46.68

(- + - -)C21 0.01

(0 + - -)C21 46.70

(+ + - -)C21 0.10

(+ + 0 -)C21 46.80

(+ + + -)C21 0.60

(+ 0 + 0)C21 47.40

(+ - + +)C21 0.04

(0 - + +)C21 47.44

(- - + +)C21 0.04

(- 0 0 +)C21 47.48

(- + - +)C21 0.04

(- + - 0)C21 47.52

(- + - -)C21 0.24

(- 0 - -)C21 47.76

(- - - -)C21 0.47

(0 - - -)C21 48.23

(+ - - -)C21 0.01

(+ 0 - -)C21 48.24

(+ + - -)C21 0.28

(+ + - 0)C21 48.52

(+ + - +)C21 0.36

(+ + - 0)C21 48.88

(+ + - -)C21 0.08

(+ 0 - -)C21 48.96

(+ - - -)C21 0.40

(0 - - -)C21 49.36

(- - - -)C21 0.08

(- - 0 -)C21 49.44

(- - + -)C21 0.05

(- - 0 -)C21 49.49

(- - - -)C21 0.11

(- 0 - -)C21 49.61

(- + - -)C21 0.03

(- 0 - -)C21 49.64

(- - - -)C21 0.02

(- 0 - -)C21 49.66

(- + - -)C21 0.02

(- 0 - -)C21 49.68

(- - - -)C21 0.12

(- 0 - -)C21 49.80

(- + - -)C21 0.00

(- 0 - -)C21 49.80

(- - - -)C21 0.02

(- 0 - -)C21 49.82

(- + - -)C21 0.02

(0 + - -)C21 49.84

(+ + - -)C21 0.08

(+ 0 - -)C21 49.92

(+ - - -)C21 0.03

(+ 0 - -)C21 49.95

(+ + - -)C21 0.01

(+ 0 0 -)C21 49.96

(+ - + -)C21 0.08

(+ 0 + -)C21 50.04

(+ + + -)C21 0.29

(+ + 0 -)C21 50.33

(+ + - -)C21 0.03

(+ + 0 -)C21 50.36

(+ + + -)C21 0.03

(+ + 0 -)C21 50.39

(+ + - -)C21 0.01

(+ + 0 -)C21 50.40

(+ + + -)C21 0.24

(+ + + 0)C21 50.64

(+ + + +)C21 0.24

(0 + + +)C21 50.88

(- + + +)C21 0.08

(- + 0 +)C21 50.96

(- + - +)C21 0.12

(- + - 0)C21 51.08

(- + - -)C21 0.08

(- 0 - -)C21 51.16

(- - - -)C21 0.81

(- 0 - -)C21 51.97

(- + - -)C21 0.03

(0 + - -)C21 52.00

(+ + - -)C21 0.00

(0 + - -)C21 52.00

(- + - -)C21 0.01

(0 + - -)C21 52.01

(+ + - -)C21 0.11

(+ + - 0)C21 52.12

(+ + - +)C21 0.30

(+ + - 0)C21 52.42

(+ + - -)C21 0.02

(+ + - 0)C21 52.44

(+ + - +)C21 0.40

(+ + - 0)C21 52.84

(+ + - -)C21 0.04

(+ 0 - -)C21 52.88

(+ - - -)C21 0.08

(+ - 0 -)C21 52.96

(+ - + -)C21 0.12

(0 - + -)C21 53.08

(- - + -)C21 0.04

(- - + 0)C21 53.12

(- - + +)C21 0.04

(0 - + +)C21 53.16

(+ - + +)C21 0.08

(+ - + 0)C21 53.24

(+ - + -)C21 0.12

(+ - 0 -)C21 53.36

(+ - - -)C21 0.24

(0 - - -)C21 53.60

(- - - -)C21 0.12

(- 0 - -)C21 53.72

(- + - -)C21 0.02

(0 + - -)C21 53.74

(+ + - -)C21 0.10

(+ 0 - -)C21 53.84

(+ - - -)C21 0.56

(0 - - -)C21 54.40

(- - - -)C21 0.04

(- - 0 -)C21 54.44

(- - + -)C21 0.16

(- 0 + -)C21 54.60

(- + + -)C21 0.06

(- + 0 -)C21 54.66

112 Chapter 5

(- + - -)C21 0.02

(- + 0 -)C21 54.68

(- + + -)C21 0.01

(- + 0 -)C21 54.69

(- + - -)C21 0.03

(- + 0 -)C21 54.72

(- + + -)C21 0.24

(- + 0 -)C21 54.96

(- + - -)C21 0.56

(- + - 0)C21 55.52

(- + - +)C21 0.04

(0 + - +)C21 55.56

(+ + - +)C21 0.08

(+ + - 0)C21 55.64

(+ + - -)C21 0.03

(+ + - 0)C21 55.67

(+ + - +)C21 0.01

(0 + - 0)C21 55.68

(- + - -)C21 0.12

(- 0 - -)C21 55.80

(- - - -)C21 0.12

(- 0 - -)C21 55.92

(- + - -)C21 0.04

(0 + - -)C21 55.96

(+ + - -)C21 0.04

(+ 0 0 -)C21 56.00

(+ - + -)C21 0.24

(+ - + 0)C21 56.24

(+ - + +)C21 0.12

(+ - + 0)C21 56.36

(+ - + -)C21 0.84

(+ - 0 -)C21 57.20

(+ - - -)C21 0.16

(0 - - -)C21 57.36

(- - - -)C21 0.60

(- 0 - -)C21 57.96

(- + - -)C21 0.24

(- + - 0)C21 58.20

(- + - +)C21 0.16

(0 + - +)C21 58.36

(+ + - +)C21 0.04

(+ + - 0)C21 58.40

(+ + - -)C21 0.12

(+ 0 - 0)C21 58.52

(+ - - +)C21 0.16

(+ - - 0)C21 58.68

(+ - - -)C21 0.16

(+ - 0 -)C21 58.84

(+ - + -)C21 0.56

(+ - + 0)C21 59.40

(+ - + +)C21 0.42

(+ - 0 +)C21 59.82

(+ - - +)C21 0.02

(+ - 0 +)C21 59.84

(+ - + +)C21 0.36

(0 - + +)C21 60.20

(- - + +)C21 0.28

(- 0 + +)C21 60.48

(- + + +)C21 0.52

(- + + 0)C21 61.00

(- + + -)C21 0.56

(- 0 + -)C21 61.56

(- - + -)C21 0.12

(- - + 0)C21 61.68

(- - + +)C21 0.08

(- - + 0)C21 61.76

(- - + -)C21 0.08

(0 - + -)C21 61.84

(+ - + -)C21 0.16

(+ - + 0)C21 62.00

(+ - + +)C21 0.12

(+ - + 0)C21 62.12

(+ - + -)C21 0.44

(+ - 0 -)C21 62.56

(+ - - -)C21 0.20

(0 - - -)C21 62.76

(- - - -)C21 0.23

(0 - - -)C21 62.99

(+ - - -)C21 0.29

(0 - - -)C21 63.28

(- - - -)C21 0.01

(0 - - -)C21 63.29

(+ - - -)C21 0.03

(0 - - -)C21 63.32

(- - - -)C21 0.06

(- 0 - -)C21 63.38

(- + - -)C21 0.10

(- + - 0)C21 63.48

(- + - +)C21 0.02

(0 + - +)C21 63.50

(+ + - +)C21 0.86

(+ 0 - +)C21 64.36

(+ - - +)C21 0.08

(+ - 0 0)C21 64.44

(+ - + -)C21 0.16

(0 - + -)C21 64.60

(- - + -)C21 0.08

(- - 0 -)C21 64.68

(- - - -)C21 0.24

(- 0 - -)C21 64.92

(- + - -)C21 0.08

unknown 65.00

Table 5.5 – Complete sequence, transition time and duration of QTC-C21 relations between two

squash opponents during a rally lasting 37 s.

Modelling moving objects in geospatial sketch maps 113

6 Modelling moving objects in geospatial sketch maps

Delafontaine M., Van de Weghe N.

in Tomko M., Richter K.-F. (Eds.): International Workshop on Adaptation in Spatial

Communication (2009)

Copyright © SFB/TR 8 Spatial Cognition

Abstract. Freehand sketching of spatial scenes is a natural way of everyday human

communication, and an important representation used in many geospatial reasoning

tasks. However, besides their spatial semantics, people tend to use sketch maps to

explain things that happen in time as well. Until now, this temporal aspect has been

neglected to a considerable extent. Motion – again a common aspect of human daily

life – is one such issue where time enters the picture. This chapter focuses on

opportunities for representing moving point objects (a specific subcategory of

motion) in geospatial sketch maps.

Keywords. Sketch maps – Moving point objects – Geospatial lifelines

6.1 Introduction

For a long time, sketch maps have appeared to be a powerful tool for recovering information

about spatial environments (Golledge & Stimson 1997), attracting attention from numerous

fields such as geography, planning and psychology. Nowadays, new technologies replace

traditional pencil-and-paper-based methods, creating new opportunities for data collection,

integration, and analysis (Huynh & Doherty 2007). Moreover, there is a need for computers

to be able to deal with sketch maps as people do.

To date, some researchers have been studying sketch maps in a geospatial context (Blaser

2000, Huynh & Doherty 2007, Huynh et al. 2008, Schlaisich & Egenhofer 2001, Sezgin,

Stahovich & Davis 2006, Egenhofer 1997a, Egenhofer 1997b, Davis 2007, Forbus, Usher &

Chapman 2003, Okamoto, Okunuki & Takai 2004), and a few systems have been developed

(Haarslev & Wessel 1998, Davis 2002, Forbus et al. 2008, Hammond & Davis 2005) (Figure

6.2 and Figure 6.4), allowing for basic reasoning and/or querying. These efforts share a

primary focus on spatial information, and hence somehow overlook the capabilities to

communicate temporal information by sketching as well. However, people tend to use

sketch maps to make inferences which involve information far beyond purely static spatial

scenes. Particularly, this applies to spatiotemporal phenomena, i.e. aspects that relate space

114 Chapter 6

to time or vice versa1. For example, consider the key role of temporal information in a soccer

coach’s sketch of an opponent attack or an eyewitness’s sketch of a car crash.

Note that both examples focus on moving objects which relate to the spatiotemporal

concept of motion. Over the past decade, the modelling of moving objects has been a hot

topic in fields as GIScience, Artificial Intelligence and Information Systems (Bitterlich et al.

2008). Recent technological advancements have enabled the low-cost capture of motion

data and thereby triggered the need for well-adapted analysis tools. In order to reflect this

tendency, sketch-based information systems should be able to represent and reason about

moving objects. In this chapter, we aim to contribute to this development by examining the

spatial and temporal properties of moving objects as represented in geospatial sketch maps.

The restriction to geospatial sketch maps thereby briefly implies the following three

assumptions:

Elements are drawn from a top view perspective.

Elements are drawn in a geographical space at an approximated spatial scale.

Moving objects can be represented as moving point objects (MPOs) at the approximated

scale of the geospatial sketch map.

The remainder of this chapter is structured as follows. In section 6.2, we explicate and

extend the concept of sketch maps and the related ontology of glyphs. In section 6.3, the

concepts of moving point objects and geospatial lifelines are first introduced, and then

utilised in order to determine the spatiotemporal characteristics of lifeline glyphs. Finally,

section 6.4 mentions conclusions as well as avenues for future research.

6.2 Extended Sketch Maps

Sketch maps can be defined from several perspectives, and according to different research

focuses. We will base on the alternative given by Forbus, Usher and Chapman (2003), where

sketch maps are considered to be “compact spatial representations that express the key

spatial features of a situation for the task at hand, abstracting away the mass of details that

would otherwise obscure the relevant aspects.” They consider sketch maps to be composed

of glyphs (entities) which on their turn consist of ink (drawing strokes) and content (the

conceptual entity that the glyph represents).

Sketch maps are maps in the sense that they depict features in their spatial context.

However, just as with cartography, where maps have evolved from paper to digital maps (1)

and from static to dynamic representations (2), we believe that sketch maps can be

extended in the same way. Although by definition, sketch maps are not precluded from

being paper maps, we assume them, according to contemporary standards, to be digital

1 Conversely, sketching would not make up a terribly good means to deal with abstract phenomena, i.e. aspects

that exist only in time, such as thoughts, feelings, and business relations.


representations managed by an information system. Furthermore, we assume that they are

freehand drawn by means of a one-handed2 input device (e.g. a mouse, a touch pad or a

digital pen), with a standard click-and-drag line drawing tool in a two-dimensional space.

Though these assumptions are definitely constraining, they offer the same facilities as

common sketching with a pencil on a sheet of paper.

Concerning the evolution from static to dynamic representations, we basically agree with

Forbus et al.’s definition except for the spatial keyword, which we propose to replace with

spatiotemporal, in the sense that spatiotemporal features are features that exist both in

space and time (cf. 1). Temporality, in the sense of discourse sequentiality “controls an

assortment of media, art forms, representations”, quoting Sternberg (2004). This certainly

applies to sketching, which is as a kind of narrative or dialogue between the sketcher and its

audience, although an audience is not always required, for instance in design (Cross 1999).

The assumptions of one-handed input and line drawing mode inevitably impose an absolute

chronological order of drawing. Consequently, sketch maps are not to be restricted to spatial

knowledge, but should store temporal information as well. Hence follows the extended

sketch map ontology, where time has entered the picture in several ways, as shown in Figure

6.1.

First and foremost, there is temporal information involved with the ink concept. Like a

human observer, but vis-à-vis a conventional sheet of paper, an information system is able

to capture when a pen hits a tablet or when a mouse button is pressed or released. Each

stroke thus can be associated with a certain interval of drawing time (Figure 6.2 and Table

6.1). By consequence, ink can be considered as composed of spatial and temporal ink. On

the other hand, temporal knowledge can be associated with the content part. For instance,

this is the case when two or more separate glyphs model the consecutive states of one and

the same object. Next to temporal information, content may be characterised by spatial and

thematic, i.e. non-spatial and non-temporal, semantics.

While ink inherently constitutes what is sketched on a sketch map, content is usually

provided using a secondary modality (e.g. speech) or directly interpreted by the listener in

the case of a straight human-to-human communication. Consequently, in order to develop

intelligent and natural sketch interpretation systems, systems require the ability to interpret

glyphs as much automatically as possible, while avoiding significant error and/or information

loss. Therefore, this chapter will neglect the option of having additional content input. In

addition, the remainder of this chapter restricts to geospatial sketch maps, which are

considered to be sketch maps that represent features in a geographical space at an

approximated spatial scale from a top view perspective.

2 According to HCI research, it is natural to assume that only one (preferred) hand is used to draw sensu stricto,

while the other one performs complementary tasks such as leading and referencing (MacKenzie 2003).

116 Chapter 6

Figure 6.1 – ER diagram of the extended sketch map ontology.

6.3 Moving objects in geospatial sketch maps

6.3.1 Moving point objects and geospatial lifelines

From a geospatial background, a moving point object (MPO) is the most basic and commonly

used representation of motion (Laube 2005). This container concept can be used to

represent whatever individual object or subject moving in a geographical space, whether this

is a vehicle, an animal, a human being, or an earthquake epicentre. The most basic

conceptualisation of an MPO trajectory is the geospatial lifeline, or briefly lifeline (Laube

2005) (Figure 6.3). According to Mark (1998) a lifeline is a continuous set of positions that an

object occupies in space over a certain period of time. As a lifeline models a moving point, it

is equivalent to a continuous spatial curve which maps to a continuous time range.

However, in many, if not all cases, lifelines are approximated as a discrete set of space-time

locations, or fixes (Laube et al. 2007). A lifeline describes location as a function of time, and

hence, each time instant corresponds to a unique spatial location, while the reverse is not

true. In other words, for lifelines, time determines space.


Note that the notion of geospatial lifelines drawn in top view (Figure 6.3) differs substantially

from approaches with other scientific backgrounds. In physics, for instance, a side view is

predominant, and the motion of objects is dictated by external forces, instead of being

predefined by a lifeline (Davis 2002), as illustrated in Figure 6.4.

Figure 6.3 – Map of a geospatial lifeline of a butterfly moving from A to B, passing flowers on its

way (own illustration after (Laube 2005)).

Ink Point X Ink Point Y Ink Point Timestamp (s)

1.22 1.10 130.44 1.39 1.03 130.50 1.44 0.98 130.53 1.44 0.81 130.59 1.42 0.64 130.62 1.34 0.47 130.65 1.27 0.34 130.69 1.24 0.23 130.72 1.24 0.13 130.75 1.27 0.02 130.78 1.36 -0.20 130.84 1.40 -0.32 130.87 1.40 -0.57 130.94 1.41 -0.66 130.97 1.41 -0.75 131.00 1.43 -0.83 131.03 1.43 -1.01 131.13 1.45 -1.06 131.15 1.46 -1.10 131.19 1.46 -1.10 131.22

Table 6.1. – Export of spatial and temporal ink of the

stroke in Fig. 2 as a set of timestamped polyline

vertices.

Figure 6.2 – Single-stroke glyph drawn in

CogSketch (Forbus et al. 2008).

118 Chapter 6

Figure 6.4 – A Shrewd Sketch Interpretation and Simulation Tool (ASSIST) (Davis 2002).

6.3.2 Lifeline glyphs

This section addresses the research question of how lifelines can be represented through

glyphs in geospatial sketch maps. To this end, a number of characterising binary distinctions

will be considered according to the relationship between these representations and the

lifeline of the underlying MPO they model. These distinctions can be regarded as

dichotomies for a user to choose from when sketching about an MPO in a geospatial

context. Of particular interest are the relationships which hold between the spatial and

temporal properties of a lifeline and respectively the spatial and temporal ink that

represents it.

Explicit vs. implicit

A major division can be made between implicit and explicit lifeline representations. Explicit

representations are glyphs that embody (part of) a lifeline, i.e. true lifeline glyphs. Implicit

representations are glyphs or groups of glyphs that do not directly represent a lifeline, but

instead imply one, just as road signs imply the route you should follow in the case of a traffic

diversion. Unless mentioned otherwise, the term lifeline glyph will refer to an explicit

representation in what follows. Examples of explicit representations are illustrated in Figure

6.5a-c; an implicit representation is shown in Figure 6.5d.

Single-stroke vs. multi-stroke

The most basic and uncomplicated lifeline glyphs consist out of one single drawing stroke

(Figure 6.5a). Otherwise, lifelines may be composed out of multiple strokes, for some

reasons (Figure 6.5b-d). The temporal (and perhaps spatial) gaps in between two successive

strokes may for instance model important breaks in the motion path of the underlying

object, e.g. stops, events, turning or decision points, etc. (Figure 6.5b). In addition, a single-

stroke approach will be inappropriate whenever the lifeline becomes too complex, e.g. when

the sketcher makes reflections about it while drawing. Also, glyphs with disconnected parts

must be multi-stroke (Figure 6.5c).


Figure 6.5 – Sketch map representations of the butterfly lifeline in Figure 6.3: explicit single-stroke

lifeline glyph (a), explicit multi-stroke lifeline glyph (b), explicit multi-stroke lifeline glyph (c),

implicit representation by means of six flower glyphs and four arrow glyphs.

Continuous vs. Discrete

Although lifelines are by definition continuous spatiotemporal entities (section 6.3.1), their

representations may be either continuous or discrete. This distinction can be made both at

the spatial and the temporal level, i.e. with respect to spatial and temporal ink respectively.

Continuous spatial ink consists of one or more connected curves, whereas discrete spatial

ink comprises at least two disconnected elements. Due to the restrictions of conventional

sketching (assumptions of 6.2), there is always a temporal gap in between two successive

drawing strokes. Hence, for temporal ink, the continuous/discrete division is equivalent to

single-stroke/multi-stroke division. In addition, since discrete spatial ink has to be multi-

stroked, it cannot co-exist with continuous temporal ink. Thus, the following three

configurations are realisable according to this dichotomy:

Continuous spatial ink, continuous temporal ink, i.e. a simple single-stroke glyph (most

basic glyph, e.g. Figure 6.5a).

Continuous spatial ink, discrete temporal ink, i.e. a spatially connected multi-stroke

glyph (e.g. Figure 6.5b).

Discrete spatial ink, discrete temporal ink, i.e. a spatially disconnected multi-stroke

glyph (e.g. Figure 6.5c).

So far, one might ask for the difference between a discrete lifeline glyph (explicit

representation) and a (discrete) implicit representation. The spatial ink of a discrete lifeline

glyph is a discontinuous representation of a continuous curve, such as a dashed or dotted

line (Figure 6.5). By definition, an implicit representation has no lifeline glyph(s) but other

120 Chapter 6

glyphs that imply a lifeline instead: the flower and arrow glyphs in Figure 6.5d are

autonomous entities, whereas a dash segment in Figure 6.5c has no significance on its own.

Aligned vs. non-aligned

Without doubt one of the most valuable derivatives of temporal ink is the chronological

order of drawing. As is common in human communication, this communicative order often

reflects the chronology of the underlying content (Sternberg 2004). We will term this the

alignment relation: an element is aligned if its drawing chronology respects the order

(positive alignment) or reverse order (negative alignment) of the chronology in the

underlying content. Note that a negative alignment differs from the case of no alignment

which applies when neither the right nor the reverse order matches the actual chronology.

Three hierarchical levels of alignment can be distinguished within the context of sketch

maps: inter-glyph, inter-stroke, and intra-stroke alignment. Note that although Huynh et al.

(Huynh et al. 2008, Huynh & Doherty 2007) already emphasized the significance of drawing

sequences, they merely considered inter-glyph alignment.

The drawing evolution of aligned lifeline glyphs reflects the order of locations taken

chronologically by the underlying MPO. For lifeline glyphs, the alignment relations imply an

absolute ordering, i.e. a complete internal spatiotemporal chronology for properties such as

motion azimuth or events such as performing a specific movement pattern. Thereby, they

enable geospatial reasoning, allowing for making inferences like “the object took this bend

before heading north”. Note that single-stroke lifeline glyphs are always aligned, be it

positively or negatively.

Scaled vs. distorted

Alignment can be considered the key qualitative relationship between temporal ink and the

temporal semantics of the underlying content. Next to alignment, numerous quantitative

relationships may exist, which enable the extraction of high level information. However, it is

highly probable that quantitative relations – despite their existence – will not be intended by

the sketcher, and hence are meaningless. Nevertheless, the relationship of linear

proportionality (fixed scale) merits our specific attention for two reasons. First, a linear

proportionality is one of the simplest3 relationships between two quantitative variables.

Second, as elements in geospatial sketch maps are drawn at an approximated spatial scale,

then why would it not be straightforward and natural for people to be able to draw them at

an approximated time scale as well? Obviously, if intended so, perfect linear relationships

are unrealistic, instead of approximate correlations.

3 The simplest one would be the equality relation, which does not make sense, except for the trivial case where

the MPO of interest is the pointer of the input device at hand.


As for the continuous/discrete dichotomy, the scaled/distorted division applies to both the

level of spatial and temporal ink. In geospatial sketch maps, spatial ink is believed to have an

approximate fixed scale. At the temporal level, alignment is a necessary condition for time-

scaled glyphs. Time-scaled lifeline glyphs, allow for inferences about relative speed and

travel time in statements such as “the object spent most of its time on this part of its

trajectory”, or “the speed of the object in the bends is half of its speed in the straight parts”.

At an intermediate information level, in between aligned and time-scaled representations,

temporal ink can be used to segment glyphs according to clearly distinguishable categories

such as slow, moderate, and rapid drawing speed. For lifeline glyphs, these categories, when

meaningful, reflect the actual speed of the modelled MPO.

6.3.3 Typology of lifeline representations

On the basis of the distinctions made in section 6.3.2, a typology of lifeline representations

in geospatial sketch maps can be deduced, as shown in Figure 6.6. A lifeline is modelled

through one or more glyphs (dashed relationship in Figure 6.6). These glyphs will be either

explicit, or implicit representations. Within both subtypes, aligned representations can be

distinguished from others (non-aligned). Explicit aligned glyphs can be further subdivided in

continuous and discrete types. Finally, continuous cases may be scaled or distorted.

Figure 6.6 – Typology of lifeline representations in geospatial sketch maps.

6.3.4 Multiple lifelines

So far, we considered the characterisation of individual lifeline glyphs. However, reasoning

about interactions between moving objects, requires relating multiple lifelines to each other.

These inter-lifeline relations have to be temporal, as time determines space for lifelines, and

not vice versa (section 6.3.1). In section 6.3.2 we have shown that alignment properties can

Lifeline

Glyph(s)

Explicit

Aligned

Continuous

Scaled Distorted

Discrete

Non-aligned

Implicit

Aligned Non-aligned

122 Chapter 6

be used to describe temporal relations within and among glyphs. However, lifeline

representations are not always aligned. More than that, the assumptions of one-handed

input and line drawing tool preclude a sketcher from drawing two separate elements

simultaneously. Hence, temporal inter-glyph relations cannot be expressed by means of

alignment, apart from the exceptional cases restricted to before and after relations.

Conversely, interactions between multiple MPOs will be especially relevant for lifelines that

happen simultaneously or at least have a temporal overlap. Therefore, these relationships

need to be imposed by means of additional content such as found in annotations, meta-

layers, or specialised interfaces, which is out of the scope of this chapter as stated earlier.

6.4 Conclusions and outlooks

In this chapter, we extended the static concept of sketch maps, and the related ontology of

glyphs carrying ink and content, to a dynamic framework. Temporal information – next to

spatial information – takes a key role in this renewed model, where it can be found in both

ink and content associations. In order to focus on the representation of MPOs in geospatial

sketch maps, we relied on the well-known notion of geospatial lifelines. The extended model

has then been utilised to elaborate a set of characteristic binary distinctions about lifeline

representations. They can be regarded as dichotomies for a sketcher to choose from when

sketching about MPOs in a geospatial context. Throughout the chapter, there is a focus on

the interrelations between the spatial and temporal properties of lifelines and the respective

spatial and temporal ink representing it. We believe that such interrelations are important

for information systems in order to improve the automatic interpretation of the content of

lifeline glyphs by their ink, thereby making extensive use of its temporal ink, next to its

spatial component.

Above all, this chapter can be considered a basis for further research. Its content has been

underpinned by theoretical concepts, literature and common sense arguments. Nonetheless,

the authors are well aware of the fact that empirical research is a necessary next step in

order to elucidate and assess how people do represent and reason about moving objects

through sketches. Therefore, we are planning to set up appropriate test cases and build a

tool to acquire and analyse the according sketch map data. This will enable to answer

questions such as to what extent do human sketchers respect alignment relations, or do

humans have the ability to reproduce time-scaled representations in sketch maps.

Sketching is often seen as a multi-modal, multi-domain and multi-disciplinary issue.

Consequently, in further stages, this work can be extended in numerous ways. To begin with,

special cases of lifelines have been overlooked. Examples are periodic displacements, e.g.

cycles and to-and-fro movements, and lifelines (partially) shared by multiple objects such as

for a herd of animals. In addition, several interpretative aspects are still to be assessed, such

as the abilities to inter- and extrapolate lifelines, or the integration of multiple lifelines and

their underlying interaction patterns. Furthermore, the restriction to MPOs and two-


dimensional top view can be abandoned, and replaced with other motion concepts and

perspectives from different backgrounds. In time geography for instance, the predominating

perspective is that of a three-dimensional (two spatial and one temporal dimensions) space-

time cube (Kraak 2003), and, to our knowledge, the ability of people to draw sketch maps in

such setting has not been examined yet. In other future work, this work could be extended

beyond motion, to other concepts and applications which relate space and time such as

change assessment and physical planning. Finally, the applied data acquisition restrictions

may be adjusted. We have applied the constraints of conventional pencil-and-paper

sketching. Instead, different assumptions could be employed in order to reflect for instance

the opportunities offered by the latest or planned technological developments with respect

to multi-modal sketching interfaces.

References

Bitterlich, W., Sack, J. R., Sester, M. & Weibel, R. (2008) Abstracts collection – Representation,



Blaser, A. D. (2000) A study of people's sketching habits in GIS. Spatial Cognition and Computation, 2,

4, 393-419.

Cross, N. (1999) Natural intelligence in design. Design Studies, 20, 1, 25-39.

Davis, R. (2002) Sketch Understanding in Design: Overview of Work at the MIT. In AAAI Spring

Symposium. AAAI.

Davis, R. (2007) Magic paper: sketch-understanding research. Computer, 40, 9, 34-41.

Egenhofer, M. J. (1997a) Multi-modal spatial querying. In 7th International Symposium on Spatial

Data Handling (SDH 96), ed. M.-J. Kraak & M. Molenaar, Delft, Netherlands: Taylor & Francis,

785-799.

Egenhofer, M. J. (1997b) Query Processing in Spatial-Query-by-Sketch. Journal of Visual Languages &

Computing, 8, 4, 403-424.

Forbus, K. D., Usher, J. E. & Chapman, V. (2003) Qualitative spatial reasoning about sketch maps. In

15th Innovative Applications of Artificial Intelligence Conference (IAAI-03), Acapulco, Mexico:

American Association for Artificial Intelligence, 61-72.

Forbus, K. D., Usher, J. E., Lovett, A., Lockwood, K. & Wetzel, J. (2008) CogSketch: Open-domain

sketch understanding for cognitive science research and for education. In Eurographics

Workshop on Sketch-Based Interfaces and Modeling, eds. C. Alvarado & M.-P. Cani.

Golledge, R. G. & Stimson, R. J. (1997) Spatial Behavior: A Geographic Perspective. New York: The

Guilford Press, 620.

Haarslev, V. & Wessel, M. (1998) VISCO-querying GIS with spatial sketches. In Proceedings of

Formalizing Reasoning with Visual and Diagrammatic Representations, Orlando, FL, USA:

AAAI Press, 103-104.

Hammond, T. & Davis, R. (2005) LADDER, a sketching language for user interface developers.

Computers & Graphics-UK, 29, 4, 518-532.

124 Chapter 6

Huynh, N. T. & Doherty, S. T. (2007) Digital sketch-map drawing as an instrument to collect data

about spatial cognition. Cartographica: The International Journal for Geographic Information

and Geovisualization, 42, 4, 285-296.

Huynh, N. T., Hall, G. B., Doherty, S. T. & Smith, W. W. (2008) Interpreting urban space through

cognitive map sketching and sequence analysis. Canadian Geographer / Le Géographe

canadien, 52, 2, 222-240.

Kraak, M. J. (2003) The space-time cube revisited from a geovisualization perspective. In Proceedings

of the 21st International Cartographic Conference (ICC), Durban, South Africa, 1988-1996.

Laube, P. (2005) Analysing Point Motion – Spatio-Temporal Data Mining of Geospatial Lifelines,


Laube, P., Dennis, T., Forer, P. & Walker, M. (2007) Movement beyond the snapshot – Dynamic


MacKenzie, S. (2003) Motor behaviour models for human-computer interaction. In HCI Models,

Theories, and Frameworks, ed. J. M. Carroll, Morgan Kaufmann.

Mark, D. M. (1998) Geospatial lifelines. In Integrating Spatial and Temporal Databases, Dagstuhl

Seminar 98471, Schloss Dagstuhl, Wadern, Germany.

Okamoto, K., Okunuki, K. & Takai, T. (2004) Sketch map analysis using GIS buffer operation. In Spatial

Cognition IV. Reasoning, Action, Interaction. International Conference Spatial Cognition 2004.

Revised Selected Papers, eds. C. Freksa, M. Knauff, B. Krieg-Bruckner, B. Nebel & T.

Barkowsky, Frauenchiemsee, Germany: Springer-Verlag, 227-244.

Schlaisich, I. & Egenhofer, M. J. (2001) Multimodal spatial querying: What people sketch and talk

about. In Proceedings of the 1st International Conference on Universal Access in Human-

Computer Interaction, ed. C. Stephanidis, New Orleans, LA, 732-736.

Sezgin, T. M., Stahovich, T. & Davis, R. (2006) Sketch based interfaces: early processing for sketch

understanding. In ACM SIGGRAPH 2006 Courses, Boston, Massachusetts: ACM.

Sternberg, M. (2004) Telling in time (I) Chronology and narrative theory. In Narrative Theory. Critical

Concepts in Literary and Cultural Studies., ed. M. Bal, 93-137.

Travelling subjects

Part II

“Many a trip continues long after movement in time and space have ceased”

(John Steinbeck)

Analysing spatiotemporal sequences in Bluetooth tracking data 127

7 Analysing spatiotemporal sequences in Bluetooth

tracking data

Delafontaine M., Versichele M., Neutens T., Van de Weghe N.

in Environment and Planning B, submitted for publication

Abstract. The use of Bluetooth technology as a technique to collect data about the

movement of individuals is increasingly gaining attention. This chapter explores the

potential of sequence alignment methods to analyse data obtained from Bluetooth

tracking. To this end, an empirical case study is elaborated which applies sequence

alignment methods to examine the behavioural patterns of visitors tracked by

Bluetooth at a major trade fair in Belgium. The results and findings underline the

validity of Bluetooth tracking to collect data from visitors at mass events, as well as

the ability of sequence alignment methods to extract insightful information from

sequences within such data.

Keywords. Spatiotemporal patterns – Bluetooth tracking – Sequence alignment

7.1 Introduction

This chapter will use sequence alignment methods (SAM) to analyse patterns within tracking

data obtained from Bluetooth sensing. Although existing as a communication technology

since the mid-nineties, Bluetooth has only recently been employed for the tracking of

individual movement (O’Neill et al. 2006, Hermersdorf et al. 2006, Van Londersele,

Delafontaine & Van de Weghe 2009, Fallast, Scholz & Ekam 2008, Wasson, Sturdevant &

Bullock 2008, Bullock et al. 2010, Furbach, Maron & Read 2008). Despite its limited

positional accuracy, Bluetooth tracking is a low-cost alternative for true location-aware

technologies. A major advantage of this technique is that it allows for the distinction of

tracked subjects at the individual level. This is because Bluetooth-enabled devices broadcast

a unique MAC (48-bit physical address). Furthermore, due to its widespread standard

integration in nowadays personal wearable devices such as cellphones, PDA’s and headsets,

Bluetooth allows for unannounced tracking, i.e. tracking of subjects who are not aware of

being tracked. It therefore offers researchers valuable potential to conduct unbiased

experiments and gather uninfluenced observations of a large number of individuals.

In this chapter, we consider the most common approach to employ Bluetooth technology as

a tracking system. It consists of a number of Bluetooth access points, henceforth denoted as

nodes, installed at fixed strategic locations throughout the area of interest. Each node

continuously searches for nearby devices. Whenever a Bluetooth-enabled device enters the

128 Chapter 7

radio range of a node, its MAC address is logged, such that the presence of devices at nodes

can be recorded along the time line. From these records, the trajectory of an individual may

be approximated as the spatiotemporal sequence of node observations of the device (s)he is

carrying. In addition to this basic tracking system, optional supplementary attributes may be

logged such as the device class1 and the user-friendly name2, although these might demand

additional lookup time. To date, most Bluetooth tracking projects documented in the

literature have relied on this approach (e.g. Fallast, Scholz & Ekam 2008, Wasson, Sturdevant

& Bullock 2008, Van Londersele, Delafontaine & Van de Weghe 2009, Bullock et al. 2010). On

the other hand, apart from being robust and plain, the approach is appealing due to its easy

and low-cost implementation which requires merely a number of Bluetooth dongles3,

computational units and storage units. Furthermore, the approach is efficient in its passive

data collection as it does not set up true connections with devices, and thereby avoids any

interaction with the individuals being tracked.

In the large body of research on movement behaviour, considerable work has been

dedicated to the definition and extraction of patterns from movement data (e.g. Laube,

Wolle & Gudmundsson 2007, Gudmundsson, van Kreveld & Speckmann 2007, Dodge, Weibel

& Lautenschutz 2008, Dodge, Weibel & Forootan 2009). Most of these approaches stem

from a cross-pollination of GIScience, computational geometry, knowledge discovery in

databases, data mining, spatial cognition, and artificial intelligence (Laube, Wolle &

Gudmundsson 2007, Gottfried & Aghajan 2009, Miller & Han 2008). However, much of these

techniques may not be suitable to analyse Bluetooth tracking sequences. This is because

Bluetooth tracking sequences may be incomplete or inconsistent due to data failure of the

nodes (e.g. signal obstructions, data loss) and tracked devices (e.g. limited battery lives,

disabled by the carrier) on the one hand, and due to the limited coverage of the study area

in terms of node radio ranges on the other hand. REMO (Laube, van Kreveld & Imfeld 2005,

Laube, Imfeld & Weibel 2005), a generic geographic knowledge discovery approach to

describe relative motion patterns through a matrix, for example, would not be a suitable

formalism to represent and explore Bluetooth tracking sequences as it would require the

location of each device to be known at regular time stamps. Another example is the

Qualitative Trajectory Calculus (Delafontaine et al. 2010, Delafontaine, Cohn & Van de

Weghe 2011), which, despite its potential to handle incomplete information, is not eligible

for handling Bluetooth sequences as it builds on higher level motion attributes such as

motion azimuth and velocity.

This chapter will explore the potential of sequence alignment methods (SAM) for the

extraction of patterns within Bluetooth tracking sequences. SAM is a relatively new

1 The device class is a 3-byte value that describes a device by a hierarchical classification, e.g. Phone: Cellular,

Computer: Laptop. 2 A user-friendly name is an arbitrary word or phrase most often configurable by the user. 3 A Bluetooth receiver integrated into a USB stick.


technique in the research field focusing on movement patterns. In the next section, we will

briefly highlight the background and basics of SAM. Then, in section 7.3, we will apply SAM

to analyse Bluetooth tracking sequences gathered at a 5-day trade fair in Ghent (Belgium).

Finally, conclusions are drawn in section 7.4.

7.2 Sequence Alignment Methods

7.2.1 Background

Having a tradition in bioinformatics to measure the distance between DNA strings or protein

strands (Morrison 2010), SAM was first applied in social science by Abbott (1995) to analyse

career patterns. In turn, Abbott’s pioneer contribution has triggered an important body of

SAM studies within sociology (see (Abbott & Tsay 2000) for an overview). From that point

onwards, SAM has been considered a promising methodology to analyse the sequential

aspects of human space-time activities, which is evidenced, among others, through

contributions by Wilson (1998, 2001, 2008), Joh et al. (Joh, Arentze & Timmermans 2001a,

Joh, Arentze & Timmermans 2001b, Joh et al. 2002, Joh, Arentze & Timmermans 2007), and

Shoval et al. (Shoval & Isaacson 2007, Shoval et al. 2008).

Within the abundant research on human activity and travelling behaviour, SAM is usually

applied to data collected by means of questionnaires, activity-travel diaries and position-

aware devices. The application of SAM to empirical data obtained from passive wireless

tracking systems has, until present, not been scrutinised. An exception is the recent work of

Choujaa and Dulay (2009b, 2009a) who consider activity sequences inferred from cellphone

data. However, they employ SAM as a novel approach to predict gaps in the activity logs,

rather than to analyse these logs.

7.2.2 Methodology

Sequence alignment is the process of equating two or more sequences of elements of a well-

defined universe using a set of eligible operations (Morrison 2010). Sequence alignment

methods (SAM) seek for optimal alignments by employing dynamic programming algorithms

to either maximise a similarity measure, or to minimise a distance measure (Wilson 2008).

This distance measure is usually referred to as Levenshtein distance (Schlich 2003,

Levenshtein 1966) or biological distance (Shoval & Isaacson 2007, Bargeman, Joh &

Timmermans 2002). There exist two categories of SAM algorithms. Global alignment

methods force the alignment to span the entire length of the sequences, while local

alignment methods focus on the similar parts within sequences that may differ significantly

overall (Choujaa & Dulay 2009a).

The conventional operations eligible for a pairwise alignment, i.e. the alignment of two

sequences, are identity, substitution, insertion, and deletion. As they always occur together,

the latter two operations are known as indels and are accommodated by gaps in one of both

130 Chapter 7

sequences. Sequences are usually represented as a string of elements consisting of one or

more characters. A pairwise alignment of two single-character strings ‘Bluetooth’ and

‘Blåtand’4 is illustrated in Figure 7.1. It features three identities, four substitutions and two

indels. A multiple alignment, i.e. an alignment of three or more sequences, is usually

approximated by a procedure of multiple pairwise alignments, known as progressive

alignment (Wilson 2006).

To determine whether an alignment is optimal, the operations have to be weighted by a

priori defined similarity scores. Typically, some additive scoring scheme is adopted in which

the identity operation represents the highest similarity and is thus given the highest score.

Substitutions are mostly associated to zero scores and indels to penalties (negative scores).

However, depending on the nature of sequenced elements, combination-specific

substitution scores (or indel penalties) may be useful. For instance with respect to the

alphabet characters in the example (Figure 7.1), from an etymological-linguistic point of

view, the t-d substitution might be assigned a higher similarity score then the o-n

substitution. Specific similarity values are usually described by a scoring matrix which

contains all pairwise substitution scores.

Contrary to traditional measures such as Euclidean, Manhattan, or Hamming distances,

Levenshtein distances systematically capture the entire sequential dimension to assess the

similarity among two sequences (Shoval & Isaacson 2007). This is the principal advantage of

SAM with respect to other methods. In addition, the alignment process allows for

discovering hidden patterns buried within the dataset (Wilson 1998). This is a particularly

valuable characteristic within the context of this chapter, given the frequent gaps in

Bluetooth tracking logs.

According to Shoval and Isaacson (2007), two types of analysis can be conducted on the

basis of SAM. The most common one is an analysis of clusters of similar sequences and/or

representative sequences. Another possibility consists of detecting hypothetical behavioural

patterns within the sequence data at hand. The former use of SAM will be considered in the

next section of this chapter.

4 Bluetooth is named after the Danish king Harald Blåtand (940 – 981 A.D.).

B l u e t o o t h identity substitution

indel B l å t a n d

Figure 7.1 – Pairwise alignment.


7.3 Case study

In this case study we will apply sequence alignment methods to analyse the behavioural

patterns of visitors tracked by means of Bluetooth at the Horeca Expo in Ghent (Belgium).

The Horeca Expo is the most important annual trade fair for the hotel and catering industry

in Belgium, and it is particularly well-chosen as a setting for the examination of visitor

movement patterns for several reasons. To begin with, the fair is a well-organised and

controlled indoor event which is exclusively accessible for paying visitors, exhibitors and

crew members. This strongly limits the potential interference and data noise due to all kinds

of passers-by devices out of the study scope, which is, for instance, less evident in outdoor

environments (e.g. Van Londersele, Delafontaine & Van de Weghe 2009, Furbach, Maron &

Read 2008). Secondly, the fair organisers allowed us to passively track participants without

their prior knowledge5, such that the experiment is by no means biased in that sense. In

addition, the daily variation and extent of additional smaller events that may cause

temporary deviant behaviour of visitors during the fair is strongly limited. The data

collection, preparation and results are discussed in depth in the remainder of this section.

7.3.1 Data collection

The data for this case study have been collected during the 21st edition of the Horeca Expo

(November 22-26, 2009). This edition has counted 53 146 visitors, most of them being

professionals in the catering industry, for 607 exhibition stands. The Horeca Expo takes place

at the Flanders Expo exhibition centre in Ghent (Belgium). The centre has eight exhibition

halls over an area of about 56 000 m² (Figure 7.2). Each hall groups exhibition stands of a

specific theme (e.g. hall 1: breweries, hall 5: kitchen contractors). 22 Bluetooth nodes,

denoted A – T6, have been discreetly installed throughout the entire site. The nodes are

equipped with power class 2 Bluetooth dongles which are developed to cover a radio range

of about 20m, although experiments have shown that this range may vary substantially,

among others due to indoor reflections. Given this presumption, it follows that the study

area is not completely covered by all nodes, and that some node pairs have an overlap in

their covered areas (Figure 7.2).

The Bluetooth nodes continuously scan for nearby devices and log all discovered MAC

addresses with the timestamp of discovery. Over the entire 5-day course of the fair, 14 498

unique devices have been observed, most of which are mobile phones and the like (95%)

(Figure 7.3). Although at most 2%7 of the observed devices are not wearable (e.g. desktop

computers), these will be detained for further analysis since their tracking logs are not

5 Unanounced Bluetooth tracking complies with the statutory privacy legislation on personal information

protection imposed by the Belgian Privacy Commission (http://www.privacycommission.be), since Bluetooth tracking data relates to devices and as such does not allow for identifications at the individual level. 6 Node H has been left out as it is located out of the study area in this case study.

7 Including the devices for which the class is unknown.

132 Chapter 7

expected to reflect visitor movements. 89% of all devices have been observed only on one

day (Figure 7.4), which suggests a large majority of one-day participants. In terms of unique

devices per day, the dataset consists of 20 148 device-days. A histogram of device-day

duration, i.e. the duration between the first and last node observation of a device on a day,

is depicted in Figure 7.5. Two notable remarks can be drawn. First, almost 20% of the device-

days have been observed for less than fifteen minutes. This can be explained among others

by a quick disabling of devices of persons entering the fair and by short Bluetooth-enabled

episodes of devices of people who intentionally make use of the Bluetooth functionality.

Since this case study aims to analyse visitor behavioural patterns, such fragmented device-

day observations can be considered unrepresentative and have therefore been excluded.

Second, over 10% of the device-days have observations that cover over eight hours, which is

about the daily opening duration of the fair. Since these devices most probably accrue to

exhibitors, crew members and/or are non-wearable, they have been excluded as well.

Figure 7.2 – Schematic map of Flanders Expo with indication of entrances and exits for visitors

(arrows), exhibition halls (H1-H8, black rectangles), and Bluetooth nodes (A-T, x-marks) with 20m

radio range (black circles).


Figure 7.3 – Distribution of Bluetooth device classes across observed devices

Figure 7.4 – Histogram of observed days per device

Figure 7.5 – Histogram of device-day duration.

7.3.2 Data preparation

For each remaining device-day we have determined the chronological sequence of node

observations. To filter for noise in the data, subsequent observations by the same node that

are less than one minute apart have been concatenated to one observation lasting over the

entire interval. Some additional preparative steps have been taken to extract representative

2%

76%

1% 18%

0%0% 1% 0% 2%

Audio

Cellular phone

Cordless phone

Smart phone

Desktop computer

Handheld computer

Laptop computer

Palm sized computer

Unknown

0

2000

4000

6000

8000

10000

12000

14000

1 2 3 4 5

Freq

uen

cy o

f o

bse

rved

dev

ices

Days

0

500

1000

1500

2000

2500

3000

3500

4000

< 0.25 0.25 - 1 1 - 2 2 - 3 3 - 4 4 - 5 5 - 6 6 - 7 7 -8 > 8

Freq

uen

cy o

f o

bse

rved

dev

ice

-day

s

Observation duration (h)

134 Chapter 7

sequences for visitors and to exclude as much as possible the sequences of exhibitors, crew

members and outlier sequences. The following restrictions have been imposed:

The first and last observations in the sequence are observed at node P or R which are

located near the visitor entrances and exits (Figure 7.2);

The time span of a sequence is within the official opening hour intervals of the fair, i.e.

each day from 10:30 AM to 7:00 PM;

The time gaps in between two subsequent observations in the sequence have a

maximum duration of 15 minutes;

The sequence contains observations of at least eight different nodes.

Further, the observation sequences that satisfy the above restrictions have been transcoded

to single-character sequences to facilitate sequence alignment. To this end, a temporal unit

of 3 minutes has been postulated as being the minimum duration for visiting a certain

location within the fair. Hence, the observation sequences have been divided into 3-minute

episodes, each of which has been allocated a character according to the following rules:

If more than 50% of an episode is covered by observations of the same node, the node’s

character is allocated to the episode;

If more than 50% of an episode is covered by observations of two nodes, the character

of the node which observations cover the greater share is allocated to the episode;

If an interval has observations of three or more nodes, a character V is allocated to the

interval;

In all other cases a gap character (-) is assigned.

Figure 7.6 presents some of the resulting sequences. The interpretation of sequence

characters is as follows. A node character represents a visiting event in the neighbourhood

of the corresponding node; a V character represents a travelling episode, i.e. a visitor

travelling through the fair (e.g. in between two visiting events); and gaps represent the

unknown information. Note that SAM are – more than any other methodology – able to

handle gaps which are interpreted as indel operations (section 7.2.2). Given the above

constraints and the strategic dispersion of nodes across the study area (Figure 7.2), it is

probable that visitors remain near to the node of their last observation during gaps. As the

interpretation of gaps and V episodes may depend on neighbouring characters, sequences

consisting for more than 50% of gaps or V episodes have been excluded.


Figure 7.6 – Extract of transcoded Bluetooth sequences.

7.3.3 Sequence alignment

The area covered by a node’s radio range contains multiple fair stands which hampers the

analysis of visiting patterns at the stand-level. Therefore, we will rely on the thematic

grouping of stands within the exhibition halls (see section 7.3.1) to define the mutual

similarity of sequence characters. Node character episodes of nodes within the same hall can

be considered more similar than those of nodes in different halls. Figure 7.7 displays the

considered scoring matrix. An exact character match (identity) is assigned a similarity score

of 10 (maximal similarity). A mismatch (substitution) is given a similarity score of 7 in the

case of characters of nodes in the same hall, and 0 (maximal dissimilarity) otherwise. An

exception has been made for the substitutions A-K, A-M, J-M, B-L, B-P, and L-P which have

been allotted lower similarity scores due to the greater distances between the

corresponding nodes. Also, alternative scores apply for the identity and substitution of V

characters in order to lower the priority of matching V episodes in the alignment process. To

this end, the identity value for V characters is set to 3 and the substitution value with respect

to all other characters to 1 (not to 0 as V characters are related to at least three different

nodes, see section 7.3.2). Finally, separate indel penalties have been considered for gap

openings and for gap extensions; respectively -5 and -3.

510 sequences were found to validate the restrictions imposed by the data preparation

(section 7.3.2). Using the yet specified similarity scores and penalties, a multiple alignment

of these sequences has been generated within the ClustalTXY software package (Wilson

2008) by means of a progressive alignment procedure which consists of (i) a pairwise

alignment of all sequence pairs (i.e. 129 795 pairs) using a local alignment algorithm (Smith

& Waterman 1981), (ii) a neighbour-joining process (Saitou & Nei. 1987), and (iii) a multiple

alignment using a global alignment algorithm (Needleman & Wunsch 1970). The neighbour-

joining process aims to structure the sequence data by joining similar sequences on the basis

136 Chapter 7

of their pairwise alignment score such that a guide tree is derived which determines the

optimal order for adding sequences to the multiple alignment by proceeding from the leaves

to the root of the tree.

A B C D E F G I J K L M N O P Q R S T V

A 10 0 0 0 0 0 0 0 7 5 0 3 0 0 0 0 0 0 0 1

B 0 10 0 0 0 0 0 0 0 0 5 0 0 0 5 0 0 0 0 1

C 0 0 10 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 1

D 0 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 1

E 0 0 0 0 10 0 0 0 0 0 0 0 0 0 0 7 0 0 0 1

F 0 0 0 0 0 10 0 0 0 0 0 0 7 0 0 0 0 0 0 1

G 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0 1

I 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 0 0 7 1

J 7 0 0 0 0 0 0 0 10 5 0 0 0 0 0 0 0 0 0 1

K 5 0 0 0 0 0 0 0 5 10 0 7 0 0 0 0 0 0 0 1

L 0 5 0 0 0 0 0 0 0 0 10 0 0 0 5 0 0 0 0 1

M 3 0 0 0 0 0 0 0 0 7 0 10 0 0 0 0 0 0 0 1

N 0 0 0 0 0 7 0 0 0 0 0 0 10 0 0 0 0 0 0 1

O 0 0 7 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 1

P 0 5 0 0 0 0 0 0 0 0 5 0 0 0 10 0 0 0 0 1

Q 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 10 0 0 0 1

R 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 0 1

S 0 0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 1

T 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 10 1

V 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3

Figure 7.7 – Sequence alignment scoring matrix.

7.3.4 Results

Three results are obtained from the threefold sequence alignment process described in

section 7.3.3: (i) a square matrix with pairwise alignment scores, (ii) a neighbour-joining

guide tree, and (iii) a multiple alignment. The alignment matrix is the most raw and low-level

result which will not be further considered as the information it contains is also captured by

the other results.

The guide tree obtained from the neighbour-joining process (section 7.3.3) is shown in

Figure 7.8. It totals 509 hierarchical clusters of similar sequences. The clusters observed in

this guide tree may assist in the determination of a typology of different visitor behavioural

patterns. The number of members in a cluster can thus be considered an indicator for the

importance of the corresponding behavioural pattern. Sequences in smaller clusters,

however, tend to have more elements in common. In SAM literature regarding activity

patterns, it is usually considered up to the analyst to determine the number and

interpretation of clusters in the guide tree. This can be facilitated by means of the multiple


Figure 7.8 – Multiple alignment guide tree with clusters and subclusters labeled at their root node.

alignment. To enable a visual exploration of patterns in the multiple alignment, we have

sorted the aligned sequences according to the leave order of the guide tree. In addition, the

node characters in the multiple alignment have been colour coded according to the

exhibition hall where they are located. A fragment of this representation is displayed in

Figure 7.8. It illustrates a clear pattern of related sequences with predominant episodes at

the exhibition halls 8, 7 and 1 (see further cluster 1.1).

Within the guide tree, three major clusters (Figure 7.8, 1-3) can be observed at the top of the

hierarchy. At this level, the aligned sequences hardly share common characteristics, if at all.

On the basis of visual supervision of the sorted and colour coded multiple alignment (Figure

7.9) an exhaustive subdivision has been made into 21 non-overlapping subclusters (Figure

138 Chapter 7

7.8, 1.1-3.8). For each subcluster the number of members and the shared pattern has been

summarised in Table 7.1. In addition, the subcluster median and average sequences have

been listed in Table 7.2. The median and average sequences are representative sequences of

a cluster (Wilson 2008). In analogy to the homonymous descriptive statistics, these

sequences respectively minimise the sum Levenshtein distances and the sum of squared

Levenshtein distances to all other members of the cluster.

Figure 7.9 – Extract of the sorted and colour coded multiple alignment (colour legend: hall 1,

hall 2, hall 3, hall 4, hall 5, hall 6, hall 7, hall 8).

The results in Table 7.1 and Table 7.2 reveal some interesting aspects about the behaviour of

Horeca Expo visitors. First of all, they reflect a large heterogeneity of visiting patterns in

terms of visit duration, the number of visited locations, and in particular the order of visiting

these. Notwithstanding that the fair can be entered and left from only two locations, the

variety of tracking sequences emphasizes the lack of one or a few predominant

spatiotemporal behavioural patterns of Horeca Expo visitors. Inferences can be made

concerning the attractiveness of locations, although these might be misleading given that

not all exhibition halls have been equally covered by Bluetooth nodes (e.g. hall 6). The

abundant hall 1 episodes reflect that the main hall is also the most important one in terms of

visits, as could be expected given its size and central location. More than that, it can be

observed that most sequences visit the main hall more than once, whereas other halls are

usually visited once at most. 12 of the 21 common cluster patterns in Table 7.1 feature two

disjoint episodes at hall 1, whereas none of them features repetitive visits of other halls

(except for hall 7 in cluster 2.1). Thus, people most often tend to benefit maximally from

their visit by passing as much locations as possible, thereby avoiding revisiting halls, which is

inevitable for the main hall. Merely one cluster (2.2) seems to represent an exhaustive visit

to the fair, i.e. calling at all exhibition halls. However, given that only shared episodes have


been listed in Table 7.1, many other clusters may encompass such visits as well (e.g. see

Table 7.2, Figure 7.9).

Cluster Members Common pattern Legend

1.1 47

1.2 17 predominant episode

1.3 17 frequent episode

1.4 18 occasional episode

1.5 29 disjunction of episodes

1.6 19 1 – 8 exhibition halls

1.7 49 A – T Bluetooth nodes

1.8 17

2.1 38

2.2 15

2.3 44

2.4 14

2.5 34

3.1 26

3.2 26

3.3 5

3.4 22

3.5 19

3.6 7

3.7 38

3.8 9

Table 7.1 – Number of members and common patterns per cluster. Pattern episodes are colour

coded to hall location and annotated with hall numbers or node characters. Hollow episode

symbols represent episodes at one of the eight exhibition halls.

Other inferences can be made regarding the chronology of hall visits. Most sequences

consist to a considerable extent of logically structured chains of subsequent episodes at

neighbouring locations. The common patterns of clusters 1.1, 1.3, 1.7, 2.2-3.3, and 3.4-3.8

consist entirely of such chains. The most frequently combined exhibition halls are halls 1-2,

2-4, and 1-7 (in both directions). When considering the Flanders Expo map, the first two

combinations seem straightforward for visitors entering the fair at node R (Figure 7.2). The

third combination, on the other hand, is particularly reasonable for visitors who have

reached the end of the main hall (and its adjacent halls) and want to make the bridge to hall

8. When looking into more detail, such combinations may give insights into the importance

of different connections. The concatenation of D and Q episodes, for instance, underlines

the significance of the direct passage which connects both halls (Figure 7.2). Finally,

8 7 1 2 4

1 8 1

4 1

1 5 3 7 1

7 3 8 A

A J A J 7

3 2 8 1 1 4

7 1 6 4 2 1

4 6 2 1 1

6 1 7 3

2 7 4 6 M 3 5

5 1 4 2 8 1

B 1 7 1 7

M 2 4 6 8 1

8 5 7 4

T 1 1

K 5 3

1 2 4 6 1 7 5 3

7 J 4 2

2 3 J 4

2 4 6 1 7 8 3 5 1

M

140 Chapter 7

concerning the time passed beyond visiting exhibition halls, it can be observed that visitors

tend to spend more time at the entrance than at the exit (e.g. see Table 7.2, Figure 7.6,

Figure 7.9). This can be explained by typical entrance activities such as registering, informing

and depositing luggage in a cloakroom, which do not or to a lesser temporal extent apply for

visitors leaving the fair.

Median and average sequence

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

2.1

2.2

2.3

2.4

2.5

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

Table 7.2 – Median (top) and average (bottom) sequence per cluster (colour legend: hall 1, hall

2, hall 3, hall 4, hall 5, hall 6, hall 7, hall 8).

7.4 Conclusions

In this chapter, we have explored the potential of sequence alignment methods to analyse

data obtained from tracking individuals by means of Bluetooth. After a brief introduction on

Bluetooth tracking and sequence alignment methods (SAM), an experimental case study has

been presented on the sequence alignment analysis of spatiotemporal patterns of visitors

tracked by Bluetooth nodes at the Horeca Expo fair in Belgium. The contribution of this work

is original since, until present, SAM have not been applied to analyse Bluetooth tracking

data. This study is also important in light of the growing attention to Bluetooth as a novel

technology to track people at mass events. We have shown that, provided that the

necessary steps have been taken to filter raw Bluetooth tracking data, SAM can be

successfully adopted to analyse Bluetooth tracking sequences. The results of the case study


have revealed some important and plausible insights about the behaviour of visitors at the

Horeca Expo. In particular, the study has disclosed the existence of a large variety of visiting

patterns especially with respect the number of and order of visited locations.

Notwithstanding this considerable heterogeneity, we have demonstrated the ability of SAM

to detect and extract the sequential structures hidden in the tracking data. The vast majority

of tracking sequences respects a reasonable chronological concatenation of visited locations,

which in turn confirms the ability of, in essence, simple Bluetooth tracking systems to

capture the spatiotemporal behaviour of large crowds of individuals at a mass event. The

results of our study may be insightful to the planners and organisers of such events in

keeping track of and exploring the behaviour of participants over the course of an event.

Despite the above contributions, some aspects still limit the potential of sequence alignment

methods for the analysis of tracking data. Unlike the structure of nucleotides in a strand of

DNA, spatiotemporal sequences within tracking data might differ very much amongst

tracked individuals, both with respect to sequence composition as with respect to the

number of elements (duration). In sequence alignment, the latter aspect may cause a large

number of gaps, for which there is yet no consensus on their interpretation (Wilson 2006).

Shoval and Isaacson (2007) recognize the lack of a solid method to assess the reliability of

alignments, as well as the lack of knowledge on the impact of the spatial and temporal scale

on the results. Other issues relate to the shortcoming of SAM as an exact science, or to

quote Morrison (2010, p. 363): “The basic problem with sequence alignment is that it seems

to be more an art than a science”. For example, there is no consensus method or standard

calibration procedure for the setting of sequence alignment parameters such as indel

penalties. Regarding tracking data, even common practices are lacking in this respect. Future

progress on these issues will enable more refined analysis configurations and support

stronger and more detailed interpretations of alignment results.

References

Abbott, A. (1995) Sequence analysis: new methods for old ideas. Annual Review of Sociology, 21, 1,

93-113.

Abbott, A. & Tsay, A. (2000) Sequence analysis and optimal matching methods in sociology.

Sociological Methods & Research, 29, 1, 3-33.

Bargeman, B., Joh, C.-H. & Timmermans, H. (2002) Vacation behavior using a sequence alignment

method. Annals of Tourism Research, 29, 2, 320-337.

Bullock, D. M., Haseman, R., Wasson, J. S. & Spitler, R. (2010) Anonymous Bluetooth probes for

measuring airport security screening passage time: the Indianapolis pilot deployment. In

Transportation Research Board Annual Meeting 2010, Paper #10-1438.

Choujaa, D. & Dulay, N. (2009a) Activity inference through sequence alignment. In Location and

Context Awareness, eds. T. Choudhury, A. Quigley, T. Strang & K. Suginuma, Springer Berlin /

Heidelberg, 19-36.

142 Chapter 7

Choujaa, D. & Dulay, N. (2009b) Aligning activity sequences for continuous tracking of cellphone

users. In Proceedings of the IEEE International Conference on Pervasive Computing and

Communications (PerCom 2009), I, 1-6.

Delafontaine, M., Chavoshi, S. H., Cohn, A. G. & Van de Weghe, N. (2010) A Qualitative Trajectory


Representation and Reasoning: Trends and Future Directions, ed. S. M. Hazarika, IGI Global.



Dodge, S., Weibel, R. & Forootan, E. (2009) Revealing the physics of movement: Comparing the

similarity of movement characteristics of different types of moving objects. Computers,

Environment and Urban Systems, 33, 6, 419-434.

Dodge, S., Weibel, R. & Lautenschutz, A. (2008) Towards a taxonomy of movement patterns.

Information Visualization, 7, 3-4, 240-252.

Fallast, K., Scholz, A. & Ekam, H. W. (2008) Sichere basis für verkehrsplanung: Erfassung von

fahrgastströmen via Bluetooth. Der Nahverkehr, 9/2008, 72-75.

Furbach, U., Maron, M. & Read, K. (2008) Information systems for spatial metro. In Street-level

desires. Discovering the city on foot., eds. F. D. van der Hoeven, M. G. J. Smit & S. C. van der

Spek, Delft, The Netherlands: Delft University of Technology, Department of Urbanism, 74-

79.

Gottfried, B. & Aghajan, H. (2009) Behaviour Monitoring and Interpretation - BMI: Smart

Environments, Volume 3 Ambient Intelligence and Smart Environments. IOS Press, 368.



Hermersdorf, M., Nyholm, H., Perkiö, J., Tuulos, V., Salminen, J. & Tirri, H. (2006) Sensing in rich

Bluetooth environments. In World-Sensor-Web’06 at SenSys'06, 5, Boulder, Colorado, USA:

ACM.

Joh, C.-H., Arentze, T., Hofman, F. & Timmermans, H. (2002) Activity pattern similarity: a

multidimensional sequence alignment method. Transportation Research Part B:

Methodological, 36, 5, 385-403.

Joh, C.-H., Arentze, T. & Timmermans, H. (2007) Identifying skeletal information of activity patterns

by multidimensional sequence alignment. Transportation Research Record: Journal of the

Transportation Research Board, 2021, 1, 81-88.

Joh, C.-H., Arentze, T. A. & Timmermans, H. J. P. (2001a) Multidimensional sequence alignment

methods for activity-travel pattern analysis: A comparison of dynamic programming and

genetic algorithms. Geographical Analysis, 33, 3, 247-270.

Joh, C. H., Arentze, T. A. & Timmermans, H. J. P. (2001b) A position-sensitive sequence-alignment

method illustrated for space-time activity-diary data. Environment and Planning A, 33, 2, 313-

338.


point objects. International Journal of Geographical Information Science, 19, 6, 639 - 668.

Laube, P., van Kreveld, M. & Imfeld, S. (2005) Finding REMO - Detecting relative motion patterns in

geospatial lifelines. In Developments in Spatial Data Handling, ed. P. Fisher, Berlin: Springer-

Verlag Berlin, 201-215.


Laube, P., Wolle, T. & Gudmundsson, J. (2007) Movement patterns in spatio-temporal data. In

Encyclopedia of GIS, eds. S. Shekhar & H. Xiong, Springer, 1377.

Levenshtein, V. (1966) Binary codes capable of correcting deletions, insertions and reversals. Soviet

Physics Doklady, 6, 707 -710.

Miller, H. J. & Han, J. (2008) Geographic Data Mining and Knowledge Discovery. Blackwell Publishing,

352-366.

Morrison, D. A. (2010) Sequence alignment: Methods, models, concepts, and strategies. Systematic

Biology, 59, 3, 363-365.

Needleman, S. B. & Wunsch, C. D. (1970) A general method applicable to the search for similarities in

the amino acid sequence of two proteins. Journal of Molecular Biology, 48, 3, 443-453.

O’Neill, E., Kostakos, V., Kindberg, T., Schiek, A., Penn, A., Fraser, D. & Jones, T. (2006) Instrumenting

the city: Developing methods for observing and understanding the digital cityscape. In

Proceedings of the 8th International Conference on Ubiquitous Computing (UbiComp 2006),

315-332.

Saitou, N. & Nei., M. (1987) The neighbour-joining method: A new method for reconstructing

phylogenetic trees. Molecular Biology and Evolution, 4, 4, 406-425.

Schlich, R. (2003) Homogenous groups of travellers. In 10th International Conference on Travel

Behaviour Research, Lucerne, 29.

Shoval, N., Auslander, G. K., Freytag, T., Landau, R., Oswald, F., Seidl, U., Wahl, H.-W., Werner, S. &

Heinik, J. (2008) The use of advanced tracking technologies for the analysis of mobility in

Alzheimer's disease and related cognitive diseases. BMC Geriatrics, 8, 7.

Shoval, N. & Isaacson, M. (2007) Sequence alignment as a method for human activity analysis in


Smith, T. F. & Waterman, M. S. (1981) Identification of common molecular subsequences. Journal of

Molecular Biology, 147, 1, 195-197.

Van Londersele, B., Delafontaine, M. & Van de Weghe, N. (2009) Bluetooth tracking - a spy in your

pocket. In GIM International, Geomares Publishing, 23-25.

Wasson, J. S., Sturdevant, J. R. & Bullock, D. M. (2008) Real-time travel time estimates using media

access control address matching. ITE Journal, June 2008, 20-23.

Wilson, C. (2001) Activity patterns of Canadian women: Application of ClustalG sequence alignment

software. Transportation Research Record: Journal of the Transportation Research Board,

1777, 1, 55-67.

Wilson, C. (2006) Reliability of sequence-alignment analysis of social processes: Monte Carlo tests of

ClustalG software. Environment and Planning A, 38, 1, 187-204.

Wilson, C. (2008) Activity patterns in space and time: calculating representative Hägerstrand

trajectories. Transportation, 35, 4, 485-499.

Wilson, W. C. (1998) Activity pattern analysis by means of sequence-alignment methods.

Environment and Planning A, 30, 6, 1017-1038.

Modelling potential movement using rough obstacle-constrained space-time prisms 145

8 Modelling potential movement in constrained travel

environments using rough space–time prisms

Delafontaine M., Neutens T., Van de Weghe N.

in International Journal of Geographical Information Science, forthcoming

Copyright © Taylor & Francis

Abstract. The widespread adoption of location-aware technologies (LATs) has

afforded analysts new opportunities for efficiently collecting trajectory data of

moving individuals. These technologies enable measuring trajectories as a finite

sample set of time-stamped locations. The uncertainty related to both finite sampling

and measurement errors makes it often difficult to reconstruct and represent a

trajectory followed by an individual in space–time. Time geography offers an

interesting framework to deal with the potential path of an individual in-between

two sample locations. Although this potential path may be easily delineated for

travels along networks, this will be less straightforward for more non-network-

constrained environments. Current models, however, have mostly concentrated on

network environments on the one hand and do not account for the spatiotemporal

uncertainties of input data on the other hand. This chapter simultaneously addresses

both issues by developing a novel methodology to capture potential movement

between uncertain space–time points in obstacle-constrained travel environments.

Keywords. Qualitative calculus – Moving point objects – Implementation

8.1 Introduction

Recent years have seen the development of a range of widely and readily available tracking

technologies, such as location-aware technologies (LATs) (Schiller & Voisard 2004) and

geosensor networks (Stefanidis & Nittel 2003). These technologies are revolutionising the

ways in which data about spatial behaviour is acquired by enabling researchers to collect

massive volumes of trajectory data of mobile objects and individuals in real-time. Tracking

data, however, are affected by at least two important sources of spatiotemporal uncertainty.

First, trajectories are typically approximated by a sequence of locations pinpointed at

discrete timestamps. Due to finite sampling, the uncertain positions of an individual have to

be interpolated between successive sample points. While uncertainty about an individual’s

trajectory increases if sampling intervals are larger, higher sampling frequencies result in

finer granularity and more spatiotemporal detail (Hornsby & Egenhofer 2002). The sampling

146 Chapter 8

frequency may be inherent to the tracking device at hand or may result from an incomplete

spatial coverage of a geosensor network (i.e. the position of an individual is not recorded in

areas outside the radio range of the sensors). In addition, sampling frequency can be

influenced by system failures. For example, the sampling rate of GPS measurements may

decrease in urban locales if the signal is blocked by obstructions (e.g. buildings). A second

source of uncertainty arises from the fact that sample points themselves are prone to

measurement inaccuracy depending on the spatial resolution of the tracking technique used.

While individuals may be traced with an acceptable accuracy using GPS, the accuracy of

short-range, wireless radio-communication technologies is often much lower and may

depend upon the radio range and power class of the sensors and the amount of overlap

between their radio ranges. Both finite sampling and measurement errors often hamper a

straightforward reconstruction of individual trajectories on the basis of tracking data.

To cope with the problem of finite sampling in moving object databases (MODs), several

researchers, among them Sistla et al. (1998), Moreira et al. (1999), Trajcevski et al. (2004),

and Pfoser et al. (2005) have sought to delineate and query the unknown path between two

observed locations given a presupposed maximum travel velocity in an unconstrained

isotropic travel environment. In line with the advances in MODs, time geographers have also

studied the sampling problem extensively using time geography’s key concept, i.e. the

space-time prism (Hägerstrand 1970, Yu & Shaw 2008, Miller 1991, Kwan & Hong 1998).

However, while the sampling problem is well-studied in time geography, the equally

important problem of how this sampling problem interferes with the imperfect observation

of sample points has received far less attention (Miller 2005). A notable exception is Neutens

et al. (2007) who, relying on the basic principles of rough set theory (Pawlak 1982), provide a

conceptual framework to analyse how spatial and temporal uncertainty about the sample

points propagates through a space-time prism by specifying lower and upper approximations

of the prism dimensions. While conceptually appealing, their model has limited applicability

since it assumes that travel occurs in an environment without any obstacles. The aim of the

present chapter is to enhance the applicability of this conceptual model to constrained travel

environments and put it into practice by proposing and implementing a formal theoretical

framework for defining and constructing rough space-time prisms in planar space with

obstacles. The framework is particularly useful for modelling non-network-constrained

phenomena (e.g. pedestrian movement in urban and built environments) and accounts for

both finite sampling and measurement errors.

The remainder of this chapter is organised as follows. Since our approach relies on time

geography, the next section introduces the key concepts of time geography and documents

the geocomputational models that have been developed in recent years for analysing an

object’s uncertain position between two fixed sample points. Section 8.3 discusses the

formal definition and representation of a traditional space-time prism. This definition is

extended in section 8.4 toward the case of uncertain travelling constraints, i.e. uncertainty


about an individual’s departure time, arrival time, and potential travel speed. In section 8.5,

this case is further extended toward travel environments populated with obstacles. Then in

section 8.6, both approaches are combined, and an algorithm to derive obstacle-constrained

space-time prisms with uncertain constraints is presented. An example case within a simple

environment is used throughout the chapter to clarify the methodology. Finally, in section

8.7, we draw conclusions and outline avenues for future research.

8.2 Background

Time geography

Back in the 1960s, Torsten Hägerstrand (1970) and his associates at the University of Lund

(Sweden) developed a worldview for understanding the interdependencies between human

beings, nature and technology, known as time geography. Time geography provides a

conceptual perspective to analyse spatiotemporal patterns of human movement. In

particular, the time-geographical approach articulates the scarcity of space and time, and

emphasizes the importance of the constraints an individual is faced with when moving

through geographical space (Lenntorp 1978, Pred 1977). Three types of constraints are

distinguished: (i) Capability constraints refer to an individual’s cognitive limitations and

physiological necessities such as eating or sleeping; (ii) Coupling constraints restrict travel

and activity participation by dictating where, when, and for how long individuals have to join

other people, tools, or material artefacts in space and time; (iii) Authority constraints refer to

the institutional and societal context including laws, rules, norms and other regulations

implying that specific areas are only accessible at specific times for specific persons. These

three constraints are interrelated and manifest themselves by dictating the time budget

during which activities can be undertaken to achieve a project (i.e. a series of sequential

tasks necessary to the completion of any intention-inspired or goal-oriented behaviour), as

well as the individual’s travelling restrictions (e.g. travel velocity) (Carlstein, Parkes & Thrift

1978, Pred 1981).

The basic tenet of time geography is the space-time path which represents the

uninterrupted string of movements of an individual in space-time. The course of a space-

time path results from the interaction between constraints and projects and is typically

visualised in a three-dimensional framework in which time is integrated orthogonally to a

flattened topography. In this representation, an individual’s travel speed is inversely

proportional to the slope of its space-time path, where more horizontal paths represent

moves at higher speed, whereas vertical paths (infinite slope) express stationarities (zero

speed). Another key concept is the space-time prism which demarcates the envelope of all

space-time paths an individual might have drawn during the time budget between two

successive timestamps. It is important to note that while a space-time path represents

revealed spatial behaviour, space-time prisms capture potential spatial behaviour.

148 Chapter 8

Implementations of time-geographical concepts

In the past two decades, the time-geographical approach has regained attention in

geographical information science and transportation geography. Technological advances in

geographical information systems (GISs) as well as the increased availability of

georeferenced trajectory data have opened up new opportunities to enhance the realism of

the time-geographical entities and to apply these in empirical studies regarding individual

accessibility (Schwanen & de Jong 2008, Miller 1991, Yu & Shaw 2007, Kwan & Hong 1998).

Renewed interest in time geography also dovetails with the paradigm shift in transportation

policy towards travel demand management and the activity-based approach to travel

forecasting that has increasingly gained momentum since the mid-70s (Axhausen & Gärling

1992, Timmermans, Arentze & Joh 2002, Dong et al. 2006).

Modelling heterogeneous travel environments

In recent years, there has been a flurry of geocomputational methods to model the unknown

position of an individual during the time budget between two time-stamped positions. These

methods have sought to improve the classical representation of the space-time prism to deal

with the complexities of real-world travel environments. An important accomplishment is

the calculation of potential path areas within transportation networks. Following the seminal

work of Miller (1991), a number of authors have specified GIS-based algorithms to derive the

paths that an individual could have taken between two discrete locations within a road

network (e.g. Kwan & Hong 1998, Miller & Wu 2000, Wu & Miller 2001, Weber & Kwan

2002, Kim & Kwan 2003). These network-based approaches offer only a static synopsis of an

individual’s travel possibilities but do not account for the spatial variation in travel

possibilities during a time budget. Therefore, some authors have proposed algorithms to

derive the full three-dimensional, network-based space-time prism based on shortest path

algorithms within road networks (Neutens et al. 2007, Kuijpers & Othman 2009). Despite the

proliferation of methods to delineate travel possibilities within transportation networks,

only few studies have been concerned with modelling non-motorised, non-network yet

spatially constrained movements through space-time prisms. A recent example is given by

Miller and Bridwell (2009). They introduced an analytical theory to derive field-based space-

time paths and prisms using velocity fields. A velocity field is a smooth differential function

that assigns a velocity to each location in continuous space (Puu & Beckmann 1999).

Although this method allows examining theoretical conjectures about accessibility in

continuous space, a spatial decomposition into a lattice is required to use the approach in

empirical research. A drawback of this decomposition is that it introduces errors that cannot

be resolved by increasing the lattice density (see Miller & Bridwell 2009, Goodchild 1977).

Modelling travel constraint uncertainty

Another line of scientific inquiry concerns the implications of spatiotemporal uncertainty

about the prism properties (i.e. maximum travel velocity, origin and destination point) for


the prism dimensions. For example, several researchers have examined the ways in which

prism-based accessibility is affected by uncertainty in travel time caused by unreliable

transportation or systematically recurring congestion (e.g. Schwanen & de Jong 2008, Hall

1983, Ettema & Timmermans 2007). Hendricks et al. (2003), for their part, have proposed a

sequential partitioning method to model a wayfinder’s indiscernibility between future travel

possibilities. Neutens et al. (2007) have furthered this approach and sought to calculate and

represent the three-dimensional prism if its origin and destination points are not known

exactly. They introduced the concept of a rough space-time prism to model the potential

movement between two uncertain sample points through the prism’s lower and upper

approximation. Although a conceptually elegant solution to deal with both finite sampling

and measurement errors, the application of the approach is currently limited to

unconstrained travel environments. Furthermore, it does not explicitly address how

measurement uncertainty about sample points intertwines with uncertainty about the

maximum travel velocity.

The present chapter contributes to these lines of inquiry in at least two ways. First, we

complement existing network-based methods with a novel approach to model non-network-

constrained phenomena, including pedestrian movements in urban and built environments.

Drawing on research in computational geometry (e.g. Inkulu & Kapoor 2009, Kapoor,

Maheshwari & Mitchell 1997, Hershberger & Suri 1999), we propose a methodology to

construct space-time prisms in planar space with obstacles. Our approach does not require a

discretisation of space and time. Rather than approximating space-time prisms as a set of

contours at discrete moments in time using a field-based lattice, space-time prisms are

modelled and implemented as solid objects in continuous space. This eliminates errors

resulting from discretisation and avoids the storage and processing of large amounts of voxel

data. Second, the approach allows gaining insights into how combinations of uncertainty

about the maximum travel velocities and the spatiotemporal uncertainty about sample

points affect an individual’s travel possibilities.

8.3 A space-time prism in an unconstrained travel environment

A space-time prism measures the ability to reach locations in space and time in between two

locations separated in time, respectively denoted as origin and destination. Origins and

destinations may be derived from the locations of fixed activities reported in travel diaries

(e.g. Cullen & Godson 1975, Weber & Kwan 2003), or they can be estimated using stochastic

frontier modelling (e.g. Kitamura et al. 2006, Pendyala, Yamamoto & Kitamura 2002). As in

(Shoval & Isaacson 2007, Miller 2005), this chapter will take the viewpoint of origins and

destinations sampled through a tracking system, although our method can be applied to

spatiotemporal data obtained from other observation or estimation techniques as well. In

classical time geography, a space-time prism is determined by its origin, destination, and a

finite maximum velocity in an unconstrained isotropic travel environment (Miller 2005).

150 Chapter 8

Given these constraints, a space-time prism is obtained from the intersection of two cones

(Figure 8.1). The forward cone encloses all space-time points that can be reached from the

origin, while the backward cone captures all space-time points where an individual could

have come from when (s)he is to arrive at the destination. In the remainder we will refer to

these cones as reachability cones. The height of the reachability cones corresponds to the

time budget that results from the origin and destination temporal coupling constraints. Their

side slopes and aperture correspond to the maximum travel velocity that an individual may

attain.

Figure 8.1 – Space-time prism obtained from the intersection of a forward cone and a backward

cone.

More formally, a space-time prism in an unconstrained isotropic travel environment can be

defined as follows. Let be the set of real numbers, the set of positive real numbers,

and the two-dimensional real plane with metric being the Euclidean distance. Though

any metric space with metric would be possible, we will consider travel in the -

plane and represent this movement in -space , where represents time.

Let denote the origin, the destination,

the time budget, and the maximum velocity.

Definition 8. 1. The forward cone with origin , time budget , and

maximum velocity is the set of all space-time points that satisfy:

The forward cone has its apex at the origin and is oriented forward in time.


Definition 8.2. The backward cone with destination , time budget , and

maximum velocity is the set of all space-time points that satisfy:

The backward cone has its apex at the destination and is oriented backward in time.

A space-time prism can now be defined as the intersection of a forward and a backward

cone:

Definition 8. 3. The space-time prism with origin , destination , and

maximum velocity is given by:

Figure 8.1 shows how for is

obtained from the intersection of reachability cones. In the remainder, we will extend the

space-time prism to cope with uncertain origins, destinations, and maximum velocities, and

with obstacle-constrained travel environments.

8.4 A rough space-time prism in an unconstrained travel environment

In order to model the uncertainty of an individual’s travelling constraints, each space-time

prism will be represented as a rough set through its lower and upper (approximation)

prism. The upper prism includes all space-time locations that are potentially reachable.

is delimited by the least restricted space-time paths in terms of accessibility, i.e. what is

reachable in the best case. Suppose that there is uncertainty about the departure time

(temporal coupling constraint) of an individual. Then will be bounded by space-time

paths that assume the earliest possible departure time. Analogously, the lower prism

represents the space-time points that are reachable in all cases. It consists of all feasible

space-time paths in the potentially most constrained situation (e.g. assuming the latest

possible departure time). The uncertain part of a rough space-time prism is the boundary

body , which equals . Hence, three parts can be distinguished: what is certainly

reachable ( ), what may be reachable ( , and what is certainly not reachable ( .

Though this distinction has to be kept in mind, we will not explicitly consider any

further, due to its dependency on and . In the remainder of this chapter, we will use

the term rough to refer to the dual representation of a lower and upper approximation.

Rough space-time prisms can deal with three types of uncertainty, i.e. spatial, temporal and

velocity uncertainty (Neutens et al. 2007). In the context of tracking systems, there is spatial

and temporal uncertainty stemming from the measurement inaccuracy of the tracking

technology. Wireless tracking technologies such as Bluetooth and WiFi employ a certain

spatial radio range and temporal scanning interval. Although uncertainty may differ in space

and time, for many tracking data it makes sense to presume a constant spatial and temporal

152 Chapter 8

uncertainty related to the accuracy of the technology at hand. The maximum velocity, on the

other hand, cannot be directly related to measurement accuracy and is often approximated

by means of a lower and an upper estimate (e.g. maximum velocity on a road during

respectively peak and off-peak hours).

Consider origin , destination , time budget , spatial accuracy , temporal accuracy ,

maximum velocity , lower maximum velocity , and upper maximum velocity , with

, and .

Definition 8.4. The lower forward cone is the set of all space-time

points that satisfy:

Definition 8.5. The upper forward cone is the set of all space-time


Definition 8.6. The lower backward cone is the set of all space-time


Definition 8.7. The upper backward cone is the set of all space-time


In analogy to Definition 8.3, lower and upper space-time prisms can be determined from the

intersection of respectively the lower and upper forward and backward cones:

Definition 8.8. The lower space-time prism is given by:

Definition 8.9. The upper space-time prism is given by:

The following property expresses the relationship between a classical space-time prism

(Definition 8.3) and its corresponding rough approximations (Definitions 8.8-8.9):

Property 8.1.


That is, for each space-time prism and for each set of valid rough maximum velocities,

spatial accuracy, and temporal accuracy, there exist a lower space-time prism and an

upper space-time prism , such that contains , and contains . Note that might

be the empty set independent of the uncertainty parameters, whereas can never be an

empty set whenever one of these parameters is strictly positive. The model of rough space-

time prisms also generalises the classical model, which is obtained from the special case

where accuracies are negligible ( and rough maximum velocities are considered

equal ( . Therefore, the boundary body dissolves and, according to Definition 8.9,

the attained upper and lower prisms both equal the classic prism. In addition, note that,

according to the first equation of Definition 8.5, the upper forward cone has its apex at time

. However, due to the second equation, only time stamps higher than

or equal to are valid. Analogous reasoning applies for the upper backward cone, and

therefore, upper reachability cones are flattened at the top over a circular area with radius

which reflects the underlying spatial uncertainty.

The example approximation prisms and

are illustrated in Figure 8.2 (with , as in Figure 8.1).

Figure 8.2 – An uncertain space-time prism modelled by its lower (grey), and upper (black outlines)

approximation.

8.5 A space-time prism in an obstacle-constrained travel environment

Until now, movement has been considered to happen in an unconstrained travel

environment. Though this assumption underlies traditional time geography, it is hardly

tenable and most often highly unrealistic for true geographical spaces. This assumption has

been abandoned in later work, as discussed in section 8.2. In addition to these approaches,

we present an alternative considering an isotropic travel space populated with obstacles.

Obstacles can be any kind of inaccessible areas, as are building blocks, water bodies and

highways to pedestrians. The space in between the obstacles is assumed to be

154 Chapter 8

unconstrained and isotropic, which enables us to preserve the maximum velocity constraint

and thereby support the well-studied time-geographical entities introduced earlier.

We will clarify our approach using a simple example case. Figure 8.3 shows a map of three

buildings , , and at university campus ‘De Sterre’ in Ghent (Belgium). The area

surrounding the buildings can be assumed open and accessible to pedestrians. Two positions

are located at building entrances, for which we assume they are a student’s origin and

destination in between two subsequent lectures. Let us consider a time budget of two

minutes for the student to walk from to , with a maximum walking velocity of 2m.s-1 as

an educated guess. Our aim is now to construct the student’s space-time prism according to

these constraints, taking account of the obstacles blocking his/her passage.

Figure 8.3 – Travel environment constrained by university buildings A, B, and C.

As follows from section 8.3, reachability cones provide an answer to two fundamental

questions: (i) which locations are reachable for the individual within the given time budget if

(s)he starts at the origin; (ii) from which locations is the destination reachable within the

given time budget. Assessing the accessibility from (to) a certain location requires knowledge

about all shortest paths from (to) this place. In an unconstrained isotropic space, all

reachable locations lie within a certain radius from the origin or destination, as all shortest

paths are simply the straight beeline connectors. To construct space-time prisms in obstacle-

constrained environments, however, shortest paths are to be calculated that avoid the

obstacles.

In computational geometry and geographical information systems, obstacles such as

buildings and impassable areas are generally modelled as regions using a polygonal

geometry. Research in computational geometry has offered efficient algorithms to compute

the shortest paths in a Euclidean plane in the presence of such polygonal obstacles. To this

end, there have been two fundamentally different approaches. The visibility graph method


(Kapoor & Maheshwari 1988, Kapoor, Maheshwari & Mitchell 1997), on the one hand, and

the wavefront method (Mitchell 1993, Hershberger & Suri 1999) on the other hand. Some

(e.g. Inkulu & Kapoor 2009) have also considered combinations thereof. For exact algorithms

and computational details, we refer to the specialised literature. We may employ such an

algorithm in order to determine all necessary shortest paths within an obstacle-constrained

travel environment in case of obstacles modelled as polygons, as we will further assume

according to its generality in GIS. It is important to note that only the shortest paths to

polygon vertices have to be calculated, due to the following reasoning. Whenever an

obstacle blocks the straight connection from to any other point, the corresponding

shortest path(s) from will pass along an extreme (i.e. a tangential point) of when

observed from . This extreme will always be a vertex in the case of a polygonal obstacle.

Let be a set of obstacles, and be the set of

vertices of obstacle . Let denote the shortest path from to avoiding the

obstacles in . Let denote the parent, i.e. the preceding vertex, of vertex along

.

Definition 8.10. The shortest path tree from with respect to the obstacles in

is given by:

An is a tree in which each vertex is a node that is associated with its parent along the

shortest path from the root parent to . Given a shortest path tree , the shortest

path can be easily determined as the ordered sequence of parent vertices

starting from the root parent to the destination vertex Figure 8.4 and Figure 8.5

respectively show a map of and for the example case.

Each vertex can be associated with a shortest path distance. Let denote the distance

to vertex along shortest path . A vertex is reachable if its shortest path distance is smaller

than or equal to the distance budget, i.e. the product of time budget and maximum velocity.

Based on the shortest path distance and the time budget, we may define the set of

reachable vertices:

Definition 8.11. The reachable set is the set of all vertices of obstacles in

that lie within distance budget from origin along a shortest path avoiding the

obstacles in :

156 Chapter 8

Figure 8.4 – Shortest paths (black lines) from the origin (big dot) to all obstacle vertices (small

dots).

Figure 8.5 – Shortest paths (black lines) from the destination (big dot) to all obstacle vertices (small

dots).

All parent vertices in the reachable set act as wavefront propagators that induce separate

reachability cones according to the time budget that remains at the time they are reached.

Given a set of obstacles , a time budget , and a maximum velocity , the forward

cone at parent vertex is denoted as with

. Analogous reasoning applies for the backward cone and

.

Not all parts of the yet obtained cones are reachable within the remaining time budget

. Only the directly reachable parts, i.e. parts accessible by a straight path from the


parent concerned, are to be selected, as the other parts will either be directly reachable

from other parent vertices, or they will not be accessible within . Hence, the non-

directly reachable parts are to be subtracted from the cone. The spatial footprint of these

parts belongs to either areas that overlap with an obstacle (i), or to areas that are obscured

by one or more obstacles (ii). The directly reachable parts of a parent’s reachability cone can

be obtained by extruding the spatial zones (i) and (ii) vertically along the time axis, and

subtracting these volumes from the cone. As thereafter, the resulting body is no longer a

true cone, we will term it a reachability body, i.e. forward body and backward body. The

respective reachability bodies for a parent vertex can be defined as follows:

Let denote the straight spatial connection line segment from to .

Definition 8.12. The parent forward body for a parent with respect

to origin , obstacle set , time budget , and maximum velocity is given by:

Definition 8.13. The parent backward body for a parent with

respect to destination , obstacle set , time budget , and maximum velocity is

given by:

Figure 8.6 and Figure 8.7 illustrate the reachability bodies for a parent vertex of building ,

according to origin, destination and time budget specified earlier. The figures also indicate

the footprint of the obstructed zones to be extruded ((i) and (ii)). Note that the reachability

bodies are situated at different time intervals, due to their different temporal orientation as

well as to the temporal difference corresponding to the respective shortest path distances

from to and from to .

A parent reachability body delimits the potential path space at a parent vertex, according to

the remaining time budget at that vertex. The overall reachability bodies are now obtained

from the union of all reachability bodies, either the forward or the backward bodies, over all

parents in the reachable set.

Definition 8.14. The forward body with origin , obstacle set , time

budget , and maximum velocity is given by:

158 Chapter 8

Definition 8.15. The backward body with destination , obstacle set ,

time budget , and maximum velocity is given by:

In analogy to Definition 8.3, the obstacle-constrained space-time prism is obtained from the

intersection of the forward and backward bodies (Figure 8.8):

Definition 8.16. The obstacle-constrained space-time prism with origin ,

destination , obstacle set , and maximum velocity is given by:

The yet obtained obstacle-constrained space-time prism demarcates the potential path

space for an individual travelling from origin to destination, respecting a given maximum

velocity, and avoiding the obstacles in his/her enviroment.

Figure 8.6 – Parent forward reachability body (grey) with indication of the parent vertex (black dot)

and the spatial extrusion zones (black outlines).


Figure 8.7 – Parent backward reachability body (grey) with indication of the parent vertex (black

dot) and the spatial extrusion zones (black outlines).

8.6 A rough space-time prism in an obstacle-constrained travel environment

8.6.1 Combination of approaches

This section concerns the integration of the approaches of sections 8.4 and 8.5. Whereas in a

classical unconstrained environment, space-time prisms follow from the intersection of two

reachability cones (Definitions 8.1-8.3), two sets of parent reachability bodies are to be

intersected, when accounting for obstacles (Definitions 8.14-8.16). These reachability bodies

are geometrically equivalent to cones with subtracted vertical extrusions (section 8.5). The

constraints that determine these underlying cones, however, are not affected by the further

subtraction of parts (Definitions 8.13-8.14), and subsequent union with other bodies

(Definitions 8.15-8.16). Therefore, we may preserve the methodology of section 8.5 and

adopt Definitions 8.13 and 8.14, in order to obtain rough parent reachability bodies.

Subsequently, the Definitions 8.15-8.17 can be adapted analogously in order to construct the

rough reachability bodies and space-time prisms for an environment constrained by

obstacles. Hence, for a given origin , destination , obstacle set , time budget , spatial

160 Chapter 8

accuracy , temporal accuracy , lower maximum velocity , and upper maximum

velocity , we obtain:

Figure 8.8 – Obstacle-constrained space-time prism (grey) with indication of obstacles (black).

Definition 8.17. The lower parent forward body for a parent is

given by:

Definition 8.18. The upper parent forward body for a parent

given by:

Definition 8.19. The lower parent backward body for a parent

is given by:


Definition 8.20. The upper parent backward body for a parent

is given by:

Definition 8.21. The lower forward body is given by:

Definition 8.22. The upper forward body is given by:

Definition 8.23. The lower backward body is given by:

Definition 8.24. The upper backward body is given by:

Definition 8.25. The lower obstacle-constrained space-time prism is

given by:

Definition 8.26. The upper obstacle-constrained space-time prism

is given by:

8.6.2 Algorithm

Based on the methodology of section 8.5 and the Definitions 8.17-8.26, we have

implemented an application program that takes an origin, a destination, a set of obstacles, a

spatial accuracy, a temporal accuracy, a lower maximum velocity, and an upper maximum

velocity as input parameters, and returns the corresponding rough obstacle-constrained

space-time prisms. The resulting prisms are then visualised as 3D solids by means of a CAD

162 Chapter 8

system. A description of the application’s main algorithm is given in pseudo-code in

Algorithm 8.1.

Input:

Output:

Algorithm:

01: [shortest paths from o]

02: [shortest paths from d]

03: [time budget]

04: [lower forward reachability set]

05: [lower backward reachability set]

06: [upper forward reachability set]

07: [upper backward reachability set]

08: for each parent in

09: [lower parent forward cone]

10: [extrusions]

11: [lower parent forward body]

12: [lower forward body]

13: next


15: [lower parent backward cone]

16: [extrusions]

17: [lower parent backward body]

18: [lower backward body]

19: next


21: [upper parent forward cone]

22: [extrusions]

23: [upper parent forward body]

24: [upper forward body]

25: next


27: [upper parent backward cone]

28: [extrusions]

29: [upper parent backward body]

30: [upper backward body]

31: next

32: [lower obstacle-constrained prism]

33: [upper obstacle-constrained prism]

34: return

Algorithm 8.1 – Main algorithm for computation of rough obstacle-constrained space-time prisms.


The algorithm first computes the shortest paths from the origin ( and from the

destination , relying on an existing algorithm as discussed in section 8.5. Next, these

shortest path sets are used to compute the reachable sets of obstacle vertices according to

the time budget and maximum velocity for the lower and upper

approximations. Then, the reachability bodies

corresponding to the four reachable sets are calculated. According to Definitions 8.21-8.24,

this is achieved as the union of the respective parent bodies over all parents in the reachable

set. As follows from Definitions 8.17-8.20, these parent bodies are obtained as cones

subtracted with extrusions of obstructed areas. Finally, forward and backward bodies are

intersected to achieve the overall lower and upper space-time prisms .

From an application point of view, the algorithm will have to be reasonably efficient when

dealing with massive datasets consisting of numerous origins, destinations, time budgets,

and obstacles. The efficiency of Algorithm 8.1 highly depends on the following subroutines:

The calculation of shortest paths avoiding polygonal obstacles (Algorithm 8.1, lines 1-2).

According to Inkulu et al. (2009), the known lower bound on time complexity for finding

such a path is , with the number of obstacles, and the number of

vertices of all obstacles together. Given this complete dependency on the amount of

vertices and obstacles, we note that for large datasets these amounts may be reduced in

preprocessing, by means of shape approximation algorithms.

The subtraction of a body from another body (Algorithm 8.1, lines 11, 17, 23, 29).

The union of two bodies (Algorithm 8.1, lines 12, 18, 24, 30).

The intersection of two bodies (Algorithm 8.1, lines 32, 33).

For the latter three subroutines, the computational efficiency will further depend on

whether or not the resulting bodies are to be represented visually, such as with the 3D solids

returned in our CAD implementation.

8.6.3 Example

To illustrate our methodology, we will reconsider the university campus example with a

student having two minutes to travel from to (Figure 8.3). Suppose that (s)he was

tracked at and with a spatial accuracy of 10m and a temporal accuracy of 5s.

According to Bohannon (1997), reliable estimates for an adult’s maximum gait speed range

from 1.749m.s-1 to 2.533m.s-1 when considering differences in sex and age class. Let us take

this as lower and upper approximation maximum velocity respectively. The lower and

upper prisms corresponding to these constraints are presented in Figure 8.9 and Figure 8.10.

A cross section through both prisms along the origin-destination axis is shown in Figure 8.11.

Note that, according to the definitions and properties of section 8.4, the temporal extremes

of the prism lie strictly within the time budget for the lower approximation, whereas they

164 Chapter 8

exceed the time budget in the upper approximation. Also, the upper prism is flattened out at

its origin and destination, due to the spatial uncertainty.

It appears that there is a large difference between the lower and upper prisms in this case:

whereas the student might have easily passed along all sides of all buildings in the upper

prism, (s)he is restricted to an almost linear course passing north of the buildings in the

lower approximation scenario. Hence, it would have been a harmful limitation not to

consider the given spatial and temporal accuracy for this case. However, beyond this

example, this reasoning may apply for many real-world applications, as similar or even lower

accuracies may be obtained from existing tracking technologies. Further, we note that only a

limited part of the lower prism intersects with the beeline connector from to (Figure

8.11), which contrasts sharply with the case of an unconstrained environment emphasizing

the impact of accounting for intermediate obstacles.

The resulting lower and upper prisms can be considered a basis for further analysis. The

volume of a space-time prism, for instance, may be used as a measure of general

accessibility (Lenntorp 1978, Villoria 1989, Burns 1979). Let us apply this measure in order to

illustrate the impact of our approach. Table 8.1 presents the resulting volumes for all four

scenarios that arise from taking into account or otherwise neglect the uncertainty and/or

the obstacles. We obtain significantly smaller volumes when accounting for the uncertainty

and for the obstacles. Ignoring uncertainty, we find a restriction to 68% when taking account

of the obstacles. Analogously, when considering uncertainty, we achieve restrictions to 13%

and 82% for lower and upper approximations respectively. Hence, with respect to the prism

volume, we may conclude that, for this case, considerable overestimates are to be made

whenever we neglect either the uncertain constraints, or the obstacles.

Without uncertainty* With uncertainty

Unconstrained 1 908 020 (lower) 185 383

(upper) 5 423 407 Unconstrained with removal of obstacle extrusions

1 675 617 (lower) 144 206

(upper) 5 032 327

Obstacle-constrained 1 297 306 (lower) 24 125

(upper) 4 432 806

* taking

Table 8.1 – Space-time prism volumes in m².s according to four different scenarios.

To isolate the effect of travel restrictions induced by the obstacles in their surrounding

environment from the obstacles themselves being inaccessible, Table 8.1 additionally

specifies the volumes of the unconstrained prisms after removal of the obstacle extrusions.

For the case without uncertainty, we observe that 62% of the total volume reduction is due

to this effect, whereas only 38% is caused by the inaccessible obstacles themselves. For the

lower and upper prisms, we find respective shares of 74% and 60%. These findings


Figure 8.9 – Obstacle-constrained lower space-time prism (grey) with indication of obstacles

(black).

Figure 8.10 – Obstacle-constrained upper space-time prism (grey) with indication of obstacles

(black).

166 Chapter 8

demonstrate that merely removing the obstacles from unconstrained prisms causes

considerable overestimation of an individual’s travel possibilities in obstacle-constrained

environments.

Figure 8.11 – Cross section through time of lower (dark grey) and upper (light grey) prisms along

the axis origin (o) – destination (d), with indication of vertical obstacle extrusions (white

rectangles).

8.7 Conclusions

Taking the viewpoint of nowadays tracking technologies, our contribution to time geography

is twofold. First, it was shown how classical time-geographical concepts can be redefined in

order to model the uncertainty associated with their underlying constraints (section 8.3).

Typically with tracking data, uncertainties will arise from inaccuracies, errors and noise

associated with the technology at hand. Relying on the basic principles of rough set theory,

we have formally elaborated how space-time prisms under uncertainty can be described as

rough sets with lower and upper approximations. Not only are these approximations

conceptually appealing, they are also robust as they allow an easy integration of different

sorts of uncertainty. In addition, rough approximations are efficient when it comes to

computation and interpretation, as they abstract from a mass of numerical details that may

otherwise increase the computational load and blur the complex results in alternative

approaches.

Secondly, we have proposed an alternative to the assumption of unconstrained travel

environment by assuming an isotropic space studded with impassable obstacles (section

8.4). A comprehensible methodology for the construction of space-time prisms according to

this alternative assumption was elaborated. We may find many kinds of environments, both

indoors and outdoors, that might be acceptably abstracted to isotropic spaces with

impassable obstacles. Pedestrian precincts in urban environments, among others, are usually

open, freely accessible and populated with discrete obstacles such as buildings, monuments,

fenced or hedged areas, etc. Our approach complements earlier studies that have modelled

space-time prisms within transportation networks. It also adds to the recent work by Miller


and Bridwell (2009) who propose a field-based representation implemented as a lattice

approximation. Although their approach allows for a complete relaxation of the uniform

velocity assumption, it will be a less efficient solution, in terms of both storage and

computation, in case of isotropic environments with obstacles. Our approach avoids the

elongation and deviation errors related to a lattice approximation, and offers a valuable

alternative if the necessary data is lacking to build a reliable and fully covering velocity field.

Both contributions, when integrated (section 8.5), offer a framework for time geography to

represent and analyse uncertain spatiotemporal data in an environment constrained by

obstacles. The yet obtained rough and obstacle-constrained space-time prisms allow for the

assessment of the impact of different spatial and temporal uncertainty factors as well as

various configurations of obstructs on accessibility. Rough obstacle-constrained prisms, and

by extension the chains (or necklaces) of chronologically successive prisms, are powerful

tools for accessibility analysis. The approach presented will be particularly effective for

micro-scale applications because the smaller the travel environment and time budgets, the

more impact spatiotemporal uncertainty will have and the less acceptable will be the

ignorance of obstacles. While it may be acceptable to neglect uncertainty and abstract entire

cities or urban districts as network-constrained spaces at a macro or meso scale (e.g. Kwan &

Lee 2004, Kwan 1999, Weber 2003, Weber & Kwan 2002), this reasoning may not apply

when focusing on city centres and urban neighbourhoods at a micro scale. Therefore, we

believe that our approach may provide increased insights into various micro-scale

applications, including monitoring tourists or mass event visitors, crowd management, crime

scene analysis, disaster management and evacuation planning.

Several extensions and refinements of our model should be addressed in future work. From

a computational perspective, as reported in section 8.6.2, challenges lie in a more detailed

elaboration, and eventually optimization of the complete approach in terms of

computational complexity. Further, since the concept of a space-time prism has now gained

an acceptable degree of realism in order to analyse common tracking data in obstacle-

constrained environments, we are planning to validate our methodology by means of

extensive data sets. Particular emphasis will be placed on how to employ the proposed

concepts to infer additional knowledge about trajectories and to measure the accessibility in

space and time (Dijst, de Jong & van Eck 2002, Shoval & Isaacson 2007, Schwanen & de Jong

2008, Neutens et al. 2008, Berger et al. 2009). Furthermore, we could consider alternatives

to modelling uncertainty. Detailed and abundant numerical uncertainty data, if available,

may validate the calculation of presence probabilities or membership functions. These

functions, however, may significantly complicate the proposed methodology, especially

when it comes to the combination of different sorts of uncertainty. Concerning the

environmental constraints, an appealing extension could be to consider time-varying

constraints. Instead of permanent obstacles, this would allow for handling temporary objects

such as those associated to temporary events (e.g. stages, tents, and stands during a

168 Chapter 8

festival). Another challenge is the relaxation of the assumption of an isotropic travel

environment in between obstacles, and the associated maximum speed. For example, it may

well be that another maximum travel speed applies in the direct neighbourhood of an

obstacle. Also, we might consider obstacles with passable interiors for which then different

constraints apply. Lawn and bushes patches in a park, for example, could, instead of

isotropic space, be considered permeable obstacles with a deviant maximum velocity with

respect to pedestrian visitors.

References

Axhausen, K. W. & Gärling, T. (1992) Activity-based approaches to travel analysis: conceptual

frameworks, models, and research problems. Transport Reviews: A Transnational

Transdisciplinary Journal, 12, 4, 323-341.

Berger, F., Klein, R., Nussbaum, D., Sack, J.-R. & Yi, J. (2009) A meeting scheduling problem respecting

time and space. Geoinformatica, 13, 4, 453-481.

Bohannon, R. W. (1997) Comfortable and maximum walking speed of adults aged 20-79 years:

reference values and determinants. Age Ageing, 26, 1, 15-19.

Burns, L. D. (1979) Transportation, Temporal, and Spatial Components of Accessibility. Lexington,

Massachusetts: Lexington Books.

Carlstein, T., Parkes, D. & Thrift, N. (1978) Timing Space and Spacing Time. London: Edward Arnold.

Cullen, I. & Godson, V. (1975) Urban networks: the structure of activity patterns. Progress in

Planning, 4, 1-96.

Dijst, M., de Jong, T. & van Eck, J. R. (2002) Opportunities for transport mode change: an exploration

of a disaggregated approach. Environment and Planning B: Planning and Design, 29, 3, 413-

430.

Dong, X. J., Ben-Akiva, M. E., Bowman, J. L. & Walker, J. L. (2006) Moving from trip-based to activity-

based measures of accessibility. Transportation Research Part A: Policy and Practice, 40, 2,

163-180.

Ettema, D. & Timmermans, H. (2007) Space-time accessibility under conditions of uncertain travel

times: Theory and numerical simulations. Geographical Analysis, 39, 2, 217-240.

Goodchild, M. F. (1977) An evaluation of lattice solutions to the problem of corridor location.



21.

Hall, R. W. (1983) Travel outcome and performance: The effect of uncertainty on accessibility.

Transportation Research Part B: Methodological, 17, 4, 275-290.

Hendricks, M. D., Egenhofer, M. J. & Hornsby, K. (2003) Structuring a wayfinder's dynamic space-time

environment. In Spatial Information Theory, LNCS 2825, 75-92.

Hershberger, J. & Suri, S. (1999) An optimal algorithm for Euclidean shortest paths in the plane. SIAM

Journal on Computing, 28, 6, 2215-2256.



Inkulu, R. & Kapoor, S. (2009) Planar rectilinear shortest path computation using corridors.

Computational Geometry, 42, 9, 873-884.


Kapoor, S. & Maheshwari, S. N. (1988) Efficient algorithms for Euclidean shortest path and visibility

problems with polygonal obstacles. In Proceedings of the 4th Annual Symposium on

Computational Geometry, Urbana-Champaign, Illinois, United States: ACM.

Kapoor, S., Maheshwari, S. N. & Mitchell, J. S. B. (1997) An efficient algorithm for Euclidean shortest

paths among polygonal obstacles in the plane. Discrete and Computational Geometry, 18, 4,

377-383.

Kim, H.-M. & Kwan, M.-P. (2003) Space-time accessibility measures: A geocomputational algorithm

with a focus on the feasible opportunity set and possible activity duration. Journal of

Geographical Systems, 5, 1, 71-91.

Kitamura, R., Yamamoto, T., Susilo, Y. O. & Axhausen, K. W. (2006) How routine is a routine? An

analysis of the day-to-day variability in prism vertex location. Transportation Research Part A:

Policy and Practice, 40, 3, 259-279.


space–time prisms. International Journal of Geographical Information Science, 23, 9, 1095-

1117.

Kwan, M.-P. (1999) Gender and individual access to urban opportunities: A study using space-time

measures. The Professional Geographer, 51, 2, 211-227.

Kwan, M.-P. & Hong, X. D. (1998) Network-based constraint-oriented choice set formation using GIS.

Journal of Geographical Systems, 5, 139-162.

Kwan, M. & Lee, J. (2004) Geovisualization of human activity patterns using 3D GIS: A time-

geographic approach. In Spatially Integrated Social Science, eds. M. F. Goodchild & D. G.

Janelle, New York: Oxford University Press, 48-66.

Lenntorp, B. (1978) A time-geographical simulation of activity programs. In Timing Space and Spacing

Time, Human Activity and Time Geography, eds. T. Carlstein, D. Parkes & N. Thrift, London:

Edward Arnold, 162-180.

Miller, H. J. (1991) Modelling accessibility using space-time prism concepts within geographical

information systems. International Journal of Geographical Information Systems, 5, 3, 287-

301.

Miller, H. J. (2005) A measurement theory for time geography. Geographical Analysis, 37, 1, 17-45.



Miller, H. J. & Wu, Y.-H. (2000) GIS software for measuring space-time accessibility in transportation

planning and analysis. Geoinformatica, 4, 2, 141-159.

Mitchell, J. S. B. (1993) Shortest paths among obstacles in the plane. In Proceedings of the 9th Annual

Symposium on Computational Geometry. San Diego, California, United States: ACM.

Moreira, J., Ribeiro, C. & Saglio, J.-M. (1999) Representation and manipulation of moving points: An

extended data model for location estimation. Cartography and Geographic Information

Science, 26, 109-124.

Neutens, T., Schwanen, T., Witlox, F. & De Maeyer, P. (2008) My space or your space? Towards a

measure of joint accessibility. Computers, Environment and Urban Systems, 32, 5, 331-342.

Neutens, T., Witlox, F., Van de Weghe, N. & De Maeyer, P. (2007) Human interaction spaces under

uncertainty. Transportation Research Record, 2021, 28-35.

170 Chapter 8

Pawlak, Z. (1982) Rough sets. International Journal of Information and Computer Science, 11, 5, 341-

356.

Pendyala, R. M., Yamamoto, T. & Kitamura, R. (2002) On the formulation of time-space prisms to

model constraints on personal activity-travel engagement. Transportation, 29, 1, 73-94.

Pfoser, D., Tryfona, N. & Jensen, C. (2005) Indeterminacy and spatiotemporal data: Basic definitions

and case study. Geoinformatica, 9, 3, 211-236.

Pred, A. (1977) The choreography of existence: Comments on Hägerstrand's time-geography and its

usefulness. Economic Geography, 53, 2, 207-221.

Pred, A. (1981) Social reproduction and the time-geography of everyday life. Geografiska Annaler.

Series B, Human Geography, 63, 1, 5-22.

Puu, T. & Beckmann, M. (1999) Continuous space modelling. In Handbook of Transportation Science,

ed. R. W. Hall, Kluwer Academic Publishers, Amsterdam, 269-310.

Schiller, J. & Voisard, A. (2004) Location-Based Services. San Francisco, CA: Morgan Kaufmann.

Schwanen, T. & de Jong, T. (2008) Exploring the juggling of responsibilities with space-time

accessibility analysis. Urban Geography, 29, 6, 556-580.



Sistla, P. A., Wolfson, O., Chamberlain, S. & Dao, S. (1998) Querying the uncertain position of moving

objects. In Temporal Databases: Research and Practice, eds. O. Etzion, S. Jajodia & S. Sripada,

Berlin: Springer, 310-337.

Stefanidis, A. & Nittel, S. (2003) GeoSensor Networks. Boca Raton, FL: CRC.

Timmermans, H., Arentze, T. & Joh, C. H. (2002) Analysing space-time behaviour: new approaches to

old problems. Progress in Human Geography, 26, 2, 175-190.

Trajcevski, G., Wolfson, O., Hinrichs, K. & Chamberlain, S. (2004) Managing uncertainty in moving

objects databases. ACM Transactions on Database Systems, 29, 3, 463-507.

Villoria, O. G. (1989) An operational measure of individual accessibility for use in the study of travel-

activity patterns. In Department of Civil Engineering. Columbus, Ohio: Ohio State University.

Weber, J. (2003) Individual accessibility and distance from major employment centers: An

examination using space-time measures. Journal of Geographical Systems, 5, 1, 51-70.

Weber, J. & Kwan, M.-P. (2002) Bringing time back in: A study on the influence of travel time

variations and facility opening hours on individual accessibility. The Professional Geographer,

54, 2, 226-240.

Weber, J. & Kwan, M. P. (2003) Evaluating the effects of geographic contexts on individual

accessibility: A multilevel approach. Urban Geography, 24, 8, 647-671.

Wu, Y. H. & Miller, H. J. (2001) Computational tools for measuring space-time accessibility within

dynamic flow transportation networks. Journal of Transportation and Statistics, 4, 2-3, 1-14.

Yu, H. & Shaw, S.-L. (2007) Revisiting Hägerstrand’s time-geographic framework for individual

activities in the age of instant access. In Societies and Cities in the Age of Instant Access, ed.

H. J. Miller, Springer, 103-118.

Yu, H. & Shaw, S. L. (2008) Exploring potential human activities in physical and virtual spaces: a

spatio-temporal GIS approach. International Journal of Geographical Information Science, 22,

4-5, 409-430.

Reconciling place-based and person-based accessibility: a GIS toolkit 171

9 Reconciling place-based and person-based accessibility: a

GIS toolkit

Delafontaine M., Neutens T., Van de Weghe N.

in International Journal of Geographical Information Science, submitted for

publication

Abstract. This chapter introduces a novel GIS toolkit for measuring and mapping the

accessibility of individuals to services. The toolkit contributes to earlier

implementations by combining the benefits of both place-based and person-based

accessibility measures. To this end, place-based accessibility measures are derived

from a person-based framework by considering space-time prisms which are centred

at service facilities rather than individual anchor points. The implementation is also

innovative by explicitly accounting for the opening hours of service delivery in its

accessibility measurement. In addition, the toolkit is aimed to be user-friendly and to

generate insightful and comprehensible results for non-technically-oriented users,

which is illustrated in a brief case study.

Keywords. Accessibility – Place-based measures – Person-based measures – GIS

9.1 Introduction

Accessibility is a fundamental concept in transport geography and urban planning. It refers

to individuals’ ability to travel and participate in activities given the available transport and

land use system (Pirie 1979). To assess accessibility, researchers have relied on various

accessibility measures. Roughly, these can be divided into place-based and person-based

measures (Miller 2007). Place-based measures associate a level of accessibility to a location

or spatial unit of analysis (e.g. census tract, ward, traffic analysis zone, etc.). They express

accessibility as the proximity to desired activity locations from key locations in an individual's

daily life, such as the residence or workplace. The family of place-based measures includes

such well-known and commonly applied accessibility measures as the travel time or distance

to the nearest opportunity and the number of opportunities within a particular area or

within a specific cut-off distance from a given location. While rigid, easily implementable and

insightful, place-based measures have often been criticised as they tend to reduce individual

travel behaviour to a (set of) key location(s), while ignoring important temporal constraints

on activity behaviour such as the opening hours of urban opportunities and the limited

availability of discretionary time on the part of an individual (Neutens et al. 2010a). This

172 Chapter 9

criticism has called a foundation for the development of person-based accessibility

measures.

Person-based measures are specified at the lowest level amenable to the social sciences, i.e.

the individual. Drawing on concepts of time geography (Hägerstrand 1970), these measures

express accessibility on the basis of detailed observations of the spatiotemporal constraints

individuals are faced with. Hence, person-based measures allow accessibility to fluctuate

during the course of the day as well as across persons, as has been shown by, among others,

Kwan (1998, 1999), Kim and Kwan (2003), Miller (2007), Casas (2007), Schwanen en de Jong

(2008), Yu and Shaw (2008), Neutens et al. (2010a, 2010b), and Páez et al. (2010). Whilst

more subtle and detailed, they are also more complex to calculate than place-based

measures – although this difficulty has been increasingly overcome by the growing

capabilities of geographical information systems (GIS) in recent years. In addition, the

assessment of person-based accessibility requires dedicated and representative information

about the activities (e.g. travel diaries) of sampled individuals, which is in many cases

unavailable or at least difficult to collect.

From a cartographical point of view, person-based measures have an important

disadvantage over place-based measures, since they cannot simply be summarised into a

single map. This is because a person-based accessibility value should be seen as an attribute

of a travelling individual who may visit multiple activity locations over the course of a day,

and therefore cannot be simply mapped onto a single location such as an individual’s

residence. Maps can be drawn representing the accessibility of locations according to a

person-based measure (e.g. potential path areas). Such maps, however, only express the

accessibility of one or ultimately a few individuals, instead of providing an area-

representative map. Place-based measures, on the other hand, can easily be represented

synoptically in conventional maps as they directly capture the physical proximity of urban

opportunities at a particular location (e.g. see some recently published maps El-Geneidy &

Levinson 2007, Nettleton et al. 2007, Drew & Rowe 2010, Colclough & Owens 2010,

Achuthan, Titheridge & Mackett 2010, Lei & Church 2010).

This chapter attempts to make the link between place-based and person-based tools by

introducing PrismMapper, a GIS toolkit for measuring and mapping accessibility to service

facilities. To this end, we will consider place-based measures that implement person-based

concepts building on time geography. In addition, the toolkit is intended to be simple, robust

and comprehensible such that it is directly appealing to all kinds of end-users. The toolkit is

available from (http://users.ugent.be/~mdlafont/PrismMapper). The remainder of the

chapter is structured as follows. The next section discusses related tools to measure

accessibility and provides a motivation for the current contribution. Section 9.3 presents the

toolkit and the accessibility measures it implements. An example case is illustrated in section

9.4, followed by conclusions in section 9.5.


9.2 Related tools

Many existing information systems and services implement accessibility measures in various

ways. GPS devices and routing systems, for instance, are able to calculate travel times and

distances, i.e. simple place-based accessibility measures. These implementations, however,

are usually a black box to the user. Web services, such as the OpenRouteService

(http://openrouteservice.org) (Neis, Dietze & Zipf 2007), the National Accessibility Map of

the Netherlands (http://www.bereikbaarheidskaart.nl), and the recently released

Mapnificent (http://www.mapnificent.net), offer explicit tools to map accessibility

measures. While useful, such services are often limited on two aspects: (i) meta-information

on the data sources and exact methods they use to assess the implemented accessibility

measures, and by consequence (ii) the freedom they offer the user to manipulate or

configure these data and methods.

On the other hand, dedicated GIS packages or extensions, most of which implement place-

based measures, can cope with the above shortcomings. Travel times and distances, are

supported in many GIS packages either by the calculation of beeline distances in

unconstrained space or shortest paths within a geographic network. A noteworthy toolkit

going beyond these simple measures is Flowmap (http://flowmap.geog.uu.nl), developed at

the University of Utrecht and released in 1990. Flowmap has been specifically designed to

handle spatial flow patterns, but also supports computing travel costs along a network, and

modelling the market areas of existing or planned facilities. In 1998, the Environment

Systems Research Institute (ESRI®) introduced the Network Analyst extension of its

ArcView™ software (nowaydays ArcGIS™). The Network Analyst allows calculating and

mapping shortest paths, nearest facilities, and service areas over a given network (N. N.

1998). O’Sullivan et al. (2000) have described a desktop GIS application to map isochrones

for accessing facilities trough public transport. In 2004, Liu and Zhu (2004) have presented

their own ArcGIS accessibility extension. Although their implementation includes tools that

are currently also covered by the Network Analyst extensions, such as origin-destination

travel cost matrices, it additionally supports more complicated place-based measures such

as gravity- and utility-based measures and catchment profiles. Despite the authors’

argumentation that the extension is available to a wide range of users, any further reference

on how to obtain and use their toolkit is regretfully missing. The same is true for the recent

Urban.Access tool (Benenson, Martens & Rosenthal 2010) which allows for the mapping of

place-based measures based on detailed car and bus travel times.

Regarding person-based accessibility, especially in the field of exploratory spatiotemporal

data analysis and visualisation, several implementations exist which may assist the

assessment of person-based accessibility measures without explicitly operationalizing these

(e.g. Andrienko & Andrienko 1998, Yu 2006, Andrienko et al. 2009, Andrienko et al. 2010,

Kraak 2003). In addition, there have been early operationalizations of fundamental time-

geographical concepts such as (Kitamura, Kostyniuk & Uyeno 1981, Lenntorp 1976, Villoria

174 Chapter 9

1989, Nishii & Kondo 1992, Kondo & Kitamura 1987, Landau, Prashker & Alpern 1982). These

have been characterised by an unrealistic modelling of the travel environment as they ignore

the transportation network (Kwan & Hong 1998). This shortcoming has been addressed later

in both theoretical (Neutens et al. 2007, Kuijpers et al. 2010, Miller & Bridwell 2009) and

empirical work (Kim & Kwan 2003, Kwan & Weber 2003, Kwan & Hong 1998, Kwan 1998,

Neutens et al. 2010a, Neutens et al. 2010b).

In 2000, Miller and Wu (2000) introduced the first true person-based toolbox which allows

mapping three different benefit measures for an individual to participate at discretionary

activities in space and time. This prototype is a user-friendly front-end / back-end application

for measuring an individual’s accessibility. Recently, Neutens, Versichele and Schwanen

(2010) presented a stand-alone person-based accessibility toolkit for assessing the

opportunities for joint activity participation. Their toolkit provides a dynamic and animated

view of the activity locations that are accessible to a person or group during the course of

the day. Both toolkits are characterised by a sincere demand for detailed input data about

the individual activity schedules. Not only is such information merely occasionally available

for a sample of individuals, it is also questionable whether this sample data is representative

in all its dimensions for the associated population. This delicate issue has never been

profoundly addressed in studies on person-based accessibility, which questions the extent to

which the results of the related tools may be extrapolated. More than that, given that the

necessary information would be available, these toolkits are unable to generate maps of the

accessibility of an entire population - let alone area covering maps - thereby passing over the

synoptic power of maps. This could be considered a significant inadequacy in the eyes of

decision makers or urban planners dissuading them from using these tools. In addition, both

toolkits implement comparable benefit measures which are obtained from complex utility

functions. The complexity of these functions obscures the interpretation for end-users who

do not have prior knowledge about time geography and accessibility modelling. Finally, a last

and perhaps most poignant point of critique is that the toolkits nullify the added value of

person-based measures since they only account for the spatiotemporal constraints on the

part of the individual while neglecting the time constraints on the part of the urban facilities

(e.g. opening hours, waiting times).

The PrismMapper tool introduced in this chapter aims to contribute to the set of existing

implementations in at least three ways. First, it tends to support a comprehensible set of

simple and rigid place-based accessibility measures. That is to say, the measures should be

meaningful, interpretable and self-evident, even for end-users who are not acquainted with

the accessibility literature. Second, while taking advantage of the mapping opportunities of

place-base measures, it implements key properties of person-based measures by considering

reverse space-time prisms (see section 9.3). This enables making true accessibility maps

representative for an entire region or population instead of a single (or a few) predefined


individual(s). Third, PrismMapper accounts for the space-time constraints of service delivery

by explicitly considering the opening hours of service facilities.

9.3 PrismMapper

This section will first describe the person-based accessibility measures implemented in

PrismMapper and then give an overview of the system.

9.3.1 Accessibility measures

Most person-based measures rely on the well-known time geographical framework

originated in the 70’s by Hägerstrand (1970). The basic unit of analysis in time geography is

the space-time path, i.e. an individual’s daily trajectory in space and time. Space-time paths

comply with three types of constraints: (i) an individual’s physiological capabilities (capacity

constraints), (ii) an individual’s commitments that bind him/her to specific locations and

time budgets (coupling constraints), and (iii) rules stemming from norms and laws (authority

constraints). These constraints delineate a set of space-time points accessible, i.e. physically

reachable, by the individual. The subset of this set which corresponds to an individual’s

space-time budget that is available between an origin and a destination is referred to as a

space-time prism (STP). The origin and destination are denoted as the anchor points of the

STP. STPs are typically represented in a 3D space-time cube where a vertical time axis is

integrated with a flattened topography (Figure 9.1, Figure 9.2a). The STP of an individual

with a time budget from to between an origin and a destination can be formally

described as:

– (9.1)

with the travel time from to , the travel time from to . In the case of

an isotropic travel environment with a constant finite maximum velocity – as has been

understood in Figure 9.1 and Figure 9.2 – a STP is obtained from the intersection of two

cones (Miller 2005). While the STP is a powerful concept to model a global level of an

individual’s physical accessibility, many studies have used it to assess, specifically, individual

accessibility to services by simply considering a service accessible on the basis of the

presence of its location within the space-time prism. Hence, they overlook the time

constraints of services, which are however only delivered and thus accessible within well-

defined opening hours. Therefore, in addition to STPs, PrismMapper will account for the

opening hour regimes of facilities in order to decide on their accessibility (see equation (9.2)

further on in this section).

The cartographical equivalent of a space-time prism, i.e. its spatial footprint, is called a

potential path area (PPA) (Figure 9.1). Since one individual may have more than two anchor

points in the course of a day and thus multiple STPs, the mapping of PPAs across multiple

individuals soon becomes cluttered. To overcome this cartographical problem, PrismMapper

176 Chapter 9

considers ‘reverse’ STPs which are centred at service facilities instead of anchor points, and

which we will refer to as reverse space-time prisms (RSTPs). The RSTP for a facility and its

opening hour time slot from to with respect to a time budget from to is given by:

(9.2)

Figure 9.1 – Space-time prism and related concepts.

The RSTP comprises all space-time points from which an individual may travel to a facility in

order to visit it at some time point during the given opening hour such that the individual

may return back to his/her origin within the given time budget. The difference between a

STP and a RSTP is illustrated in two cross sections through space-time shown in Figure 9.2.

Instead of looking at the accessible locations in between two anchor points, the PPAs of

RSTPs capture all anchor points that may be interpreted as valid pairs of a coinciding origin

and destination, such that an individual can travel from the origin to visit the facility and

return to the destination within the time budget at hand. The interpretation of such back-

and-forth trips is straightforward, since they are common in daily life, especially with respect

to residential locations, i.e. home-facility-home trips.

RSTPs have an essential property:

(9.3)

Thus, for each space-time point of a RSTP, all coinciding earlier space-time points within the

time budget belong to the RSTP as well. In other words, from each anchor location within a

RSTP, an individual may always leave earlier within the time budget. Hence, the space-time

points will determine the PPA of the RSTP, with the earliest possible departure

time.


Figure 9.2 – Cross section through space-time of a STP (left) and a RSTP (right).

RSTPs differ significantly from traditional STPs in being independent from individual anchor

points. This is advantageous in several respects. First, it takes away the requirement of high-

level individual activity/travel data. Second, this is also desirable from a computational point

of view, since RSTPs have only to be calculated once in total, instead of once for each

individual. Finally, yet most importantly, given a set of facilities with their opening hours and

a presumed time budget, RSTPs are representative for all anchor locations. Thus, area-

covering maps may be produced to represent the PPAs of RSTPs, which will be

PrismMapper’s core functionality. In addition to calculating and mapping the PPAs of RSTPs,

the toolkit implements three optional user-defined cut-off criteria to further refine the set of

valid anchor locations: (i) a maximum travel time , (ii) a minimum activity duration , and

(iii) a minimum number of accessible facilities . Hence, whether a facility with opening

hours is accessible to an individual at location with a time budget from to within a

total travel time of at most for a duration of at least can be expressed by a function

:

(9.4)

with

(9.5)

Given a set of facilities and the cut-off criteria , and , PrismMapper implements six

accessibility measures (equations (9.6-9.11)) with respect to an individual at a location

with a time budget from to . Building on equations (9.4) and (9.5), these measures are

defined as follows:

(9.6)

(9.7)

178 Chapter 9

(9.8)

(9.9)

(9.10)

(9.11)

In other words, for an individual with a time budget from at location :

returns a boolean value which expresses whether (true) or not (false) there

exists a facility in s(he) can visit respecting and ;

returns an integer value which represents the number of facilities s(he) can visit

respecting and ;

returns a ratio value which indicates the minimum total travel time that is

required for visiting a facility , respecting and , and returning to ;

returns the facility which corresponds to the minimum travel time specified by

;

returns a ratio value which indicates the maximum feasible duration for visiting a

facility in respecting and ;

returns the facility which corresponds to the maximum feasible duration

specified by .

The parameter expressing the minimum number of accessible facilities has been absent in

the accessibility measures’ formulas, but it can be easily implemented by considering in

equations (9.6-9.11) only these for which is true for at least

facilities.

Unlike the implicit assumption of an isotropic travel environment and a constant maximum

travelling velocity underlying Figure 9.1 and Figure 9.2, PrismMapper implements all above

accessibility measures within a much more realistic network-based travel environment with

maximum travelling velocity varying all across the network (see Computational module,

section 9.3.2).


9.3.2 System

An overview of the system architecture of PrismMapper is presented in Figure 9.3. It has

three main components: (i) a GIS component, (ii) a computational module (CM) and (iii) a

graphical user interface (GUI).

Figure 9.3 – PrismMapper system architecture.

PrismMapper is embedded in ESRI’s ArcGIS Desktop GIS software as an ArcMap project

template. The choice for ArcGIS Desktop is due to several reasons. To begin with, ESRI has

been considered the global market leader in GIS software, ever since it was established in

1969 (Scott & Janikas 2010, Qingquan et al. 2010). Moreover, ESRI’s GIS products have been

especially developed to serve spatial planners, decision makers, and (local) government

officials (e.g. see Greene 2000, O'Looney 2000, Huxhold, Fowler & Parr 2004, Thomas &

Humenik-Sappington 2009, Scott & Janikas 2010), which is the target group of PrismMapper.

ArcGIS Desktop is ESRI’s most important desktop GIS product, offering a comprehensive set

of tools to manipulate, analyse, visualise and store geospatial data in general and network-

based data, including some place-based accessibility measures (see section 9.2), in

particular. Embedding PrismMapper as a project template thus enables the integration of its

functionality with the yet extended set of ArcGIS tools. This allows PrismMapper to be

incorporated with one’s yet existing ArcGIS projects on the one hand, and to further

manipulate, analyse, store or export PrismMapper results in a rich and well-known GIS

environment on the other hand. The form of a project template ensures an easy distribution

of the toolkit, as well as no installation requirements.

For more information about the GIS component of PrismMapper, the reader is referred to

the official ArcGIS documentation (http://www.esri.com/products/index.html#desktop_gis).

GIS

• database

• visualisation

• analysis

CM

• ACCESS

• CUMF

• MINT

• MINTF

• MAXD

• MAXDF

GUI

• load network

• load facility locations

• add/edit opening hours

• set individual parameters

• set accessibility measure

• solve

ArcGIS Desktop

PrismMapper ArcMap project template

180 Chapter 9

The remainder of this section will respectively discuss the computational module and

graphical user interface components, respectively.

Computational module

The core of the PrismMapper toolkit is the computational module (CM). It consists of several

code modules written in Visual Basic using the ArcObjects object model (Burke 2003). CM is

responsible for the calculation and mapping of the accessibility measures presented in

section 9.3.1. To this end, CM relies on the following input data:

Network dataset ;

Travel time attribute ;

Set of facilities ;

Time budget ;

Maximum travel time ;

Minimum activity duration ;

Minimum number of accessible facilities ;

Accessibility measure .

The network dataset represents a transportation network which delineates the

considered travel environment and thus the area of potential anchor locations. Networks are

supported by ArcGIS through the Network Dataset data type. Network Datasets may be

created from all kinds of data sources that participate in a transportation network such as

road segments, junctions and turns. The data type implements an advanced connectivity

model to handle complex issues such as multimodality. Also, it may carry a number of

attributes in order to model travelling impedances, restrictions, and hierarchy within the

network. These attributes are accounted for within PrismMapper, which requires at least

one travel time attribute to enable the calculation of travel times.

A facility dataset consists at least of the location and the opening hours for a set of service

facilities. Facility locations are obtained from a point data source and they should be covered

by the study area delimited by the . The opening hours are represented by their weekly

schedules given that this is the most general manner to express the opening hours of service

facilities.

The individual parameters time budget , maximum travel time , minimum activity

duration , minimum number of accessible facilities , and the accessibility measure

are all obtained from manual user input. The computation of proceeds as follows. First,

the set is filtered to which includes only those facilities of which the opening hours have

a temporal overlap with the time budget . Second, for each facility in , the module

calculates all shortest paths within the threshold time according to the attribute .

This is done once for all paths towards and once for all paths from in order to obtain all

necessary travel costs and required in equations (9.2) and (9.5). For each


location which is on at least of such shortest path pairs, the module proceeds with

assessing using one of the equations (9.6-9.11). The final accessibility results are

spatially summarised to the level of network segments and stored as a polyline shapefile.

After the computation of the accessibility results, these are mapped within the ArcGIS map

environment. Map type and symbolisation are chosen according to the data type of (see

section 9.3.1):

The network locations for which is true are represented through a single-value

map by means of a simple solid bright green line symbol;

, , and are mapped onto a chloropleth map with in between five

and seven equal interval classes. These classes are symbolised through solid line

symbols with colours ranging from bright green for the network locations in the most

accessible class to bright red for the locations in the least accessible class;

and are expressed by a chorochromatic map using a random color

ramp to associate each facility with a unique color.

Graphical user interface

According to the underlying objective, the PrismMapper’s GUI is kept particularly simple. The

associated workflow for using the toolkit is depicted in Figure 9.4. After opening the

PrismMapper project template, the user can launch the application by clicking a command

button which opens up the toolkit’s main window (Figure 9.5). From this window, the user

proceeds with three tasks, in arbitrary order, to load the necessary data sources and set the

required parameters for the accessibility computations (see Computational module).

First, a network dataset should be loaded. This is done by clicking the associated button

(Figure 9.5) and selecting an appropriate data source within a file system browser window.

After loading a network dataset, the user may choose the desired travel time attribute from

a drop-down list (the application automatically restricts this list to impedance attributes

expressed in temporal units). In addition, some network analysis settings can be configured.

These include a threshold distance for matching facility locations to the network, and

restrictions to account for when calculating shortest paths (e.g. one-way traversable

network segments). Second, the user can specify a facility dataset, which can be done by

either loading a point dataset from a physical source as for the network dataset, or by

manually picking facility locations on screen. In the latter case, the main window disappears

and the user is subsequently prompted to click a facility location within the ArcGIS map view

and specify a name for this facility. Once facility locations are loaded or picked, the user can

add or modify their weekly opening hours within a separate window. Opening hours can be

manually added or deleted per facility, copied from one facility to others, or they can be

loaded from a text file. Finally, the user should set the remaining parameters, i.e. the

individual time budget, maximum travel time, minimal activity duration, and minimum

number of facilities.

182 Chapter 9

Figure 9.4 – PrismMapper workflow.

Having configured all required input settings, the user can pick one of the six accessibility

measures and start the solving process by clicking the ‘Solve’ button (Figure 9.5). A small

status window informs the user about the major steps within the calculation process (see

Computational module). After a successful calculation, the accessibility results are stored in a

shapefile and a map of the requested accessibility measure is drawn in the ArcGIS map view.

Load

network

dataset

Solve

Set travel

time attribute

Set time budget

Set maximum travel

time

Set minimum activity

duration

Accessibility map

Results

shapefile

Open project template

Launch

Set accessibility

measure

Load facility

locations

Pick facility

locations

Set minimum number

of accessible facilities

Add opening hour

Delete opening

hour

Copy opening

hours

Load opening

hours

Edit network

analysis

settings


Figure 9.5 – PrismMapper main application window.

9.4 Example case

In this section, we will elaborate a brief case study to illustrate the application of the

PrismMapper toolkit. In this study, we will examine the daily variability in individual

accessibility to the public libraries in Ghent (Belgium). A transportation network for Ghent

has been compiled from TeleAtlas MultiNet® road network data. Car travel times can be

estimated from this network using the shortest travel time attribute. The locations,

presented in Figure 9.6, and weekly opening hours of Ghent’s municipal libraries have been

obtained from the official city website (http://www.gent.be). Ghent has one central main

library and fifteen smaller branch libraries dispersed across the city.

In order to configure the individual settings, we will consider persons who would like to

make an evening library visit of at least half an hour in between 6:20 PM and 8:00 PM, and

who do not want to travel by car for more than 15 minutes in total. We will compare the

accessibility results for these settings on Monday to those obtained on Tuesday. The latter

configuration is also shown in Figure 9.5. The resulting accessibility maps are shown in

Figures 9.7-9.16. The maps for MAXDF have been left out in this case, since these maps are

of the same type as the MINTF maps.

184 Chapter 9

Figure 9.6 – Public libraries in Ghent (Belgium).

The ACCESS maps, which show the anchor locations from which individuals may access one

or more facilities respecting the specified constraints, indicate considerable difference

between the situation on Monday and Tuesday. On Monday, individuals may pay an evening

visit to a library from practically everywhere in Ghent, whereas on Tuesday this is not

feasible in the more peripheral parts of the city, especially in the northern area. Note that, in

spite of their proximity to accessible libraries, some network locations offer no library access

in both maps because they are located within a tangle of one-way streets, or they are

prohibited for cars (e.g. the pedestrian precinct in downtown Ghent).

The CUMF maps show that on a Monday evening, more than nine libraries can be visited in

downtown Ghent – even over a dozen within some areas. In peripheral areas this reduces to

less than three. On Tuesday evening, merely two libraries can be visited from the city centre

and at most three libraries within two zones south and west of the city centre.

The MINT maps clearly illustrate the decay of travel times near accessible facilities. It follows

that, on Monday the minimum total travel times to the nearest accessible facility are fairly

limited (below 9 minutes on most locations), given the number of accessible facilities and

their spatial dispersion across the city. On Tuesday, many of the locations outside the city

centre feature travel durations of at least 12 minutes. Note that MINT maps reflect physical


Figure 9.7 – Map of ACCESS on Monday.

Figure 9.8 – Map of ACCESS on Tuesday.

186 Chapter 9

Figure 9.9 – Map of CUMF on Monday.

Figure 9.10 – Map of CUMF on Tuesday.


Figure 9.11 – Map of MINT on Monday.

Figure 9.12 – Map of MINT on Tuesday.

188 Chapter 9

Figure 9.13 – Map of MINTF on Monday.

Figure 9.14 – Map of MINTF on Tuesday.


Figure 9.15 – Map of MAXD on Monday.

Figure 9.16 – Map of MAXD on Tuesday.

190 Chapter 9

proximity in a nuanced manner as they neatly articulate the discordance between network-

based proximity, captured by back-and-forth shortest paths, and beeline proximity read

from the map. Especially the directional nature of network segments may cause higher

travel times than expected. Many locations in the vicinity of the main library, for instance,

have rather high travel times due to the predominance of one-way streets in that area.

The MINTF maps complement the MINT maps in indicating by colour which facility is

accessible in the least travel time from which anchor location. Each thus obtained connected

zone can be considered a facility’s catchment area in terms of minimum travel time. On

Monday, catchment areas are unequally distributed both in terms of size and road density.

In this respect, it is remarkable that – notwithstanding its high road density – by far the

smallest catchment area accrues to the main library. Since fewer libraries are accessible on

Tuesday evening, their catchment areas are significantly larger than on Monday and of

comparable size.

Finally, the MAXD maps depict the maximum feasible activity duration at each possible

anchor location. These durations depend on the time budget, the travel time and the facility

opening hours. Since all libraries that are accessible on Monday and Tuesday have the same

evening closing hour, the maps in this case capture the effects of minimum travel time on

potential activity duration and therefore mirror the patterns observed in Figure 9.11 and

Figure 9.12 in this case.

9.5 Conclusion

This chapter has introduced a novel toolkit, named PrismMapper, for measuring and

mapping the accessibility of individuals to services. The toolkit aims to combine the benefits

of both place-based and person-based accessibility measures basing on the time

geographical concept of a space-time prism. Through the consideration of reverse space-

time prisms, potential path areas can be derived that are representative for individual

anchor locations in general rather than for one individual in particular. Thus, a foundation

for deriving place-based measures has been obtained on the basis of person-based

constraints including individual time budget, maximum travel time, and minimum activity

duration. The toolkit is also innovative in explicitly accounting for the opening hours of

service delivery in its assessment of accessibility.

Beyond the original integration of place-based and person-based aspects and the

incorporation of opening hours, PrismMapper has been developed with the eye on two main

objectives which have hitherto often been ignored in existing related tools. First, the toolkit

should be simple and user-friendly. This has been achieved through an undemanding user

interface and an easy workflow which consists, in essence, of three steps: launching the

application, configuring the input data and parameters, and processing the results. In

addition, the embedding of the toolkit within an ArcGIS project template allows an easy


distribution and takes away any installation requirements. A second objective has been that

the results generated by the toolkit should be useful and in as much as possible

comprehensible for end-users who are not acquainted with the accessibility literature. We

believe to have demonstrated this through the case study presented in section 9.4, although

a genuine user study may support a further evaluation of this objective.

References

Achuthan, K., Titheridge, H. & Mackett, R. L. (2010) Published map. In Mapping accessibility

differences for the whole journey and for socially excluded groups of people, Journal of Maps,

eds. K. Achuthan, H. Titheridge & R. L. Mackett, 220-229.

Andrienko, G., Andrienko, N., Bremm, S., Schreck, T., von Landesberger, T., Bak, P. & Keim, D. (2010)

Space-in-time and time-in-space self-organizing maps for exploring spatiotemporal patterns.

Computer Graphics Forum, 29, 3, 913-922.

Andrienko, G., Andrienko, N., Rinzivillo, S., Nanni, M. & Pedreschi, D. (2009) A visual analytics toolkit

for cluster-based classification of mobility data. Advances in Spatial and Temporal Databases,

5644, 432-435.

Andrienko, G. L. & Andrienko, N. V. (1998) IRIS: Intelligent visualization for data exploration support

in GIS. In Proceedings of the 6th International Conference in Central Europa on Computer

Graphics and Visualization (WSCG '98), 1, 19-26.

Benenson, I., Martens, K. & Rosenthal, A. (2010) Urban.Access: High-resolution estimation of urban

accessibility. In Proceedings of the 6th International Conference on Geographic Information

Science ( GIScience 2010), Extended Abstracts Volume, eds. R. S. Purves & R. Weibel, Zürich,

Switzerland, 5.

Burke, R. (2003) Getting to know ArcObjects. Programming ArcGIS with VBA. Redlands, CA:

Environmental Systems Research Institute, 436.

Casas, I. (2007) Social exclusion and the disabled: An accessibility approach*. The Professional

Geographer, 59, 4, 463-477.

Colclough, J. G. & Owens, E. (2010) Published map. In Mapping Pedestrian Journey Times using a

Network-based GIS Model, Journal of Maps, eds. J. G. Colclough & E. Owens, 230-239.

Drew, K. & Rowe, M. (2010) Published map. In Applying accessibility measures to assess a transport

intervention strategy: A Case Study of Bromsgrove, eds. K. Drew & M. Rowe, 181-191.

El-Geneidy, A. & Levinson, D. M. (2007) Published map. In Mapping Accessibility Over Time, Journal of

Maps, eds. A. El-Geneidy & D. M. Levinson, 76-87.

Greene, R. W. (2000) GIS in Public Policy. Using Geographic Information for More Effective

Government. Redlands, CA: Environmental Systems Research Institute, 100.


21.

Huxhold, W. E., Fowler, E. M. & Parr, B. (2004) ArcGIS and the Digital City. A hands-on approach for

local goverment. Redlands, CA: Environmental Systems Research Institute, 303.




192 Chapter 9

Kitamura, R., Kostyniuk, L. P. & Uyeno, M. J. (1981) Basic properties of urban time-space paths:

empirical tests. Transportation Research Record, 794, 8-19.

Kondo, K. & Kitamura, R. (1987) Time-space constraints and the formation of trip chains. Regional

Science and Urban Economics, 17, 1, 49-65.

Kraak, M. J. (2003) The space-time cube revisited from a geovisualization perspective. In Proceedings

of the 21st International Cartographic Conference (ICC), Durban, South Africa, 1988-1996.


on road networks. International Journal of Geographical Information Science, 24, 8, 1223-

1248.

Kwan, M.-P. & Hong, X. D. (1998) Network-based constraint-oriented choice set formation using GIS.

Journal of Geographical Systems, 5, 139-162.

Kwan, M. P. (1998) Space-time and integral measures of individual accessibility: A comparative

analysis using a point-based framework. Geographical Analysis, 30, 3, 191-216.

Kwan, M. P. (1999) Gender and individual access to urban opportunities: A study using space-time

measures. Professional Geographer, 51, 2, 210-227.

Kwan, M. P. & Weber, J. (2003) Individual accessibility revisited: Implications for geographical

analysis in the twenty-first century. Geographical Analysis, 35, 4, 341-353.

Landau, U., Prashker, J. N. & Alpern, B. (1982) Evaluation of activity constrained choice sets to

shopping destination choice modelling. Transportation Research A, 16A, 3, 199-207.

Lei, T. L. & Church, R. L. (2010) Mapping transit-based access: integrating GIS, routes and schedules.


Lenntorp, B. (1976) Paths in time-space environments: A time geographic study of movement

possibilities of individuals. In Lund studies in geography, Lund, Sweden: Royal University of

Lund, 961-972.

Liu, S. X. & Zhu, X. A. (2004) Accessibility Analyst: an integrated GIS tool for accessibility analysis in

urban transportation planning. Environment and Planning B: Planning and Design, 31, 1, 105-

124.


Compass, 1, 3, 503-535.






N. N. (1998) ArcView Network Analyst. ESRI White Paper, Redlands, CA: Environmental Systems

Research Institute, 12.

Neis, P., Dietze, L. & Zipf, A. (2007) A web accessibility analysis service based on the OpenLS Route

Service. In Proceedings of the 10th AGILE International Conference on Geographic

Information Science, Aalborg University, Denmark.

Nettleton, M., Pass, D. J., Walters, G. W. & White, R. C. (2007) Published map. In Public Transport

Accessibility Map of access to General Practitioners Surgeries in Longbridge, Birmingham, UK,

Journal of Maps, eds. M. Nettleton, D. J. Pass, G. W. Walters & R. C. White, 64-75.


Neutens, T., Schwanen, T., Witlox, F. & De Maeyer, P. (2010a) Equity of urban service delivery: A


1635.

Neutens, T., Schwanen, T., Witlox, F. & De Maeyer, P. (2010b) Evaluating the temporal organization

of public service provision using space-time accessibility analysis. Urban Geography, 31, 8,

1039-1064.

Neutens, T., Versichele, M. & Schwanen, T. (2010) Arranging place and time: A GIS toolkit to assess

person-based accessibility of urban opportunities. Applied Geography, 30, 4, 561-575.

Neutens, T., Witlox, F., Van de Weghe, N. & De Maeyer, P. (2007) Space-time opportunities for

multiple agents: a constraint-based approach. International Journal of Geographical

Information Science, 21, 10, 1061-1076.

Nishii, K. & Kondo, K. (1992) Trip linkages of urban railway commuters under time-space constraints:

some empirical observations. Transportation Research B, 26B, 1, 33-44.

O'Looney, J. (2000) Beyond Maps: GIS and Decision Making in Local Government. Redlands, CA:

Environmental Systems Research Institute, 239.

O'Sullivan, D., Morrison, A. & Shearer, J. (2000) Using desktop GIS for the investigation of accessibility

by public transport: an isochrone approach. International Journal of Geographical

Information Science, 14, 1, 85-104.

Páez, A., Gertes Mercado, R., Farber, S., Morency, C. & Roorda, M. (2010) Relative accessibility

deprivation indicators for urban settings: Definitions and application to food deserts in

Montreal. Urban Studies, 47, 7, 1415-1438.

Pirie, G. H. (1979) Measuring accessibility – Review and proposal. Environment and Planning A, 11, 3,

299-312.

Qingquan, T., Yongjun, Q., Zhanying, W. & Qun, L. (2010) Implementation on Google Maps-style

WebGIS based on ArcGIS. In Proceedings of the 2nd International Conference on Advanced

Computer Control (ICACC), 60-64.



Scott, L. M. & Janikas, M. V. (2010) Spatial statistics in ArcGIS. In Handbook of Applied Spatial

Analysis, eds. M. M. Fischer & A. Getis, Springer Berlin / Heidelberg, 27-41.

Thomas, C. & Humenik-Sappington, N. (2009) GIS for Decision Support and Public Policy Making.

Redlands, CA: Environmental Systems Research Institute, 204.

Villoria, O. G. (1989) An Operational Measure of Individual Accessibility for Use in the Study of Travel-

Activity Patterns, Doctoral Dissertation, Columbus, Ohio: Department of Civil Engineering,

Ohio State University.

Yu, H. (2006) Spatio-temporal GIS design for exploring interactions of human activities. Cartography

and Geographic Information Science, 33, 3-19.

Yu, H. & Shaw, S. L. (2008) Exploring potential human activities in physical and virtual spaces: a

spatio-temporal GIS approach. International Journal of Geographical Information Science, 22,

4-5, 409-430.

The relationship between opening hours and accessibility of public service delivery 195

10 The relationship between opening hours and accessibility

of public service delivery

Neutens T., Delafontaine M., Schwanen T., Van de Weghe N.

in Journal of Transport Geography, forthcoming


Abstract. In the past two decades urban time policies have been proposed and

implemented in many European cities as a complement to traditional spatial planning

methods. Such policies seek to provide an answer to the growing number of people

facing time problems as a result of an erosion of collective time rhythms and a

desynchronisation of different time structures of urban life. Particular emphasis is

being placed on the reconciliation of opening hours of public service facilities with

the travel and activity patterns of citizens in order to increase individual accessibility

to urban services. In spite of the increasing relevance of time policies, only limited

quantitative research has been conducted about the relationships between opening

hours and accessibility. This chapter seeks to extend this line of inquiry by exploring if

and to what extent the accessibility of public facilities can be ameliorated by

redesigning the timetables of service delivery. A method is proposed to optimise the

temporal regime of public service delivery in terms of accessibility. The method is

illustrated in a case study of accessibility of government offices within the city of

Ghent (Belgium). Our findings suggest that by rescheduling the opening hours of

public service facilities individual accessibility to service delivery can be improved

significantly. Our study may support urban service deliverers, policymakers and urban

planners in assessing timetables for a better ‘accessible’ service provision.

Keywords. Accessibility – Opening hours – Public services – Time geography

10.1 Introduction

In recent years there has been increasing awareness about the impact of urban time policies

on people’s quality of life. Especially in Europe, several projects have been launched, seeking

to improve the temporal organization of public service provision (Mückenberger & Boulin

2002, Boulin 2006). These temporal policies concentrate on the ways in which the opening

hours of urban service delivery can be better attuned to the activities and travel patterns of

citizens. Due to the erosion of collectively maintained time rhythms and the fragmentation

of activities in space and time, people’s time use patterns are becoming increasingly

individualized and intensified (Breedveld 1998, Couclelis 2004, Glorieux, Mestdag and

196 Chapter 10

Minnen 2008). Public service administrations try to respond to these trends by rescheduling

the opening hours of public service facilities in order to increase the accessibility of services

to particular constituencies and to improve the quality of urban life. As such, temporal

planning is increasingly becoming a critical aspect of city government (Boulin 2005).

Micro-economists have extensively studied the strategic aspects of opening hour decisions,

but have primarily focused on the provision of private services with price competition. A

number of authors have concentrated on the implications of changes to temporal

regulations and the liberalization of service hours (e.g. Clemenz 1994, Thum and

Weighenrieder 1997, Rouwendal & Rietveld 1999, Jacobsen & Kooreman 2005). Others have

sought to derive the socially optimal service hours by specifying utility-theoretic models that

maximise both consumer surplus and industry profits (Shy & Stenbacka 2006, 2008). While

insightful, these studies fail to address the heterogeneity of consumers’ space-time activity

patterns and travel behaviour. This is to be considered a critical inadequacy in the context of

public service provision because, in the absence of price competition, consumer surplus

primarily relates to consumers’ accessibility benefits at public service locations and thus

indirectly to their space-time behaviour (Miller 1999). Transport geographers have long since

stressed the importance of individual-specific space-time constraints on activity participation

when evaluating individual accessibility to urban services. In particular, a large number of

researchers have shown that individual accessibility is shaped by inter alia an individual’s

mandatory activity schedule, trip chaining behaviour and transport mode availability (see

e.g. Weber & Kwan 2002; Kim & Kwan 2003; Kwan & Weber 2008; Schwanen & De Jong,

2008, Neutens et al. 2010a, 2010b, Neutens, Versichele & Schwanen 2010).

The present chapter examines how such individualized aspects of accessibility can be

considered in the determination of optimal opening hours of public services in terms of

accessibility. Rather than to look for the most cost-efficient regime of opening hours, we

want to examine the ways in which opening hours can be amended to improve individual

accessibility. More specifically, a novel, sample-based geocomputational procedure is

developed that determines the collectively optimal regime of opening hours of a network of

service facilities by maximising the overall accessibility of citizens. The proposed procedure

can aid urban service deliverers, policymakers and urban planners in defining optimally

accessible timetables of service provision. It is applied in a case study of government offices

in the city of Ghent, Belgium. These government offices take care of the administration

concerning marriage, cohabitation, birth, death, residential moves, elections, and so on. The

case study is particularly timely because local authorities are currently seeking to reschedule

and curtail the historically emerged opening hours of the government offices and to tailor

these to the daily activity patterns of the citizens.

The chapter is organized as follows. The next section reviews prior research on the

relationships between space-time demands, opening hours and accessibility, and identifies


relevant research gaps. Section 10.3 presents a measure of the space-time accessibility of

public services based on the concept of locational benefits, and discusses a method to

optimise service opening hours in terms of accessibility. The methodology is illustrated in a

case study. Data and data preparation are described in section 10.4.1 and 10.4.2. Results are

reported in section 10.4.3. Finally, we conclude with the major findings and outline some

avenues for future work.

10.2 Space-time demands, opening hours and accessibility

In the past two decades, lack of time has become an important social issue that is felt in

virtually all strata of society (Glorieux, Mestdag & Minnen 2008). More and more people

seem to have become caught up in a ‘temporal treadmill’ (Law & Wolch 1993, Jarvis 2005,

Szollos 2009), experiencing competing claims on their time-space resources by different

responsibilities. Negative effects of continued time shortage on well-being can be profound

and can include work-life imbalance, lower family satisfaction and such health issues as

stress, over-fatigue and burn-out (Pelfrene et al. 2001, Ritsema van Eck, Burghouwt & Dijst

2005). People’s experience of time shortage seems to be exacerbated by malfunctioning

urban infrastructures, exemplified by road congestion and delays in public transport

systems. Further, transport and communication technologies, which are often believed to

accelerate activity patterns and make them more efficient (e.g. by reducing travel time),

seem to have complex and contradictory effects in practice. While technologies such as the

Internet and mobile phone imply that people can be reached more easily anywhere, anytime

and that home-work boundaries become more blurred for many (Schwanen & Kwan 2008),

transport infrastructures intended to speed up daily travel are often used to travel longer

distances rather than shorter times (Harris et al. 2004, Metz 2008). As a result, individual

activity patterns are frequently stretched out across multiple geographical scales, exceeding

the administrative boundaries of cities and regions.

Activity patterns have also become more fragmented over time. Recent years in particular

have witnessed a tendency towards a desynchronisation of social times, and more diverse

and complex activity schedules due to the increase of temporal constraints imposed by daily

obligations (e.g. paid labor, childcare, etc.) and limited mobility resources. Given the large

and growing number of women entering the European labour market and the concomitant

decay of the traditional male breadwinner model, scheduling incompatibilities are emerging

most strongly within dual-earner families – families with young children in particular – who

are juggling employment, housework, care-giving and leisure activities (e.g. Kwan 1999,

Jarvis 2005, McDowell et al. 2006, Schwanen 2007).

The above and related developments imply that the demand for urban services fluctuates

and shows irregular patterns over time and that individual accessibility can no longer be

measured straightforwardly in terms of physical proximity to the residence or workplace

(Weber & Kwan 2003). Rather, accessibility has become a matter of connectivity, which

198 Chapter 10

implies that access to places and services not only depends on spatial proximity but also on

the tense interface between individual daily time schedules and the temporal rhythms of the

city.

The increasing importance of connectivity in relation to time problems is currently

challenging the efficiency of traditional planning methods such as zonal land-use plans which

are largely focused on improving accessibility on the basis of stationary populations within

administrative boundaries (Zandvliet et al. 2008). Recently, however, a number of scholars

have expressed their concern about the a-temporal nature of spatial planning policies and

have called for more attention to the distributional effects of temporal practices (see e.g.

Moccia 2000, Hajer & Zonneveld 2000, Nuvolati 2003, Healey 2004, Deffner 2005, Zandvliet

& Dijst 2005). Their concern develops in tandem with a growing number of initiatives in

European cities for harmonizing the time structures of urban environments with the needs

and the desires of the inhabitants (for overviews see e.g. Mückenberger & Boulin 2002,

Boulin 2006).

While interest in temporal planning is starting to grow, only few studies have been carried

out about the ways in which opening hours can be amended to enhance individual

accessibility to services and to foster the quality of life in cities. Research that has made ex-

ante and ex-post evaluations of temporal regimes of opening hours by means of accessibility

measures is virtually non-existent. This may in part be attributed to the paucity of

accessibility measures that can adequately capture the temporal dimension of individuals’

mobility patterns. The majority of accessibility measures proposed to date does not explicitly

consider the potential temporal mismatch between individuals’ mandatory activity schedule

and the opening hours of services.

An exception to the neglect of temporal connections in accessibility research lies in the

strand of literature that has evolved around time geography. Time geography (Hägerstrand

1970) is a conceptual framework for analyzing spatiotemporal activity patterns and

individual accessibility on the basis of a set of space-time constraints. The nature of these

constraints is threefold: (i) capability constraints are linked with physiological capabilities

such as the need or wish to sleep and eat, (ii) coupling constraints refer to the need to join

other people or material artefacts in space-time, and (iii) authority constraints are imposed

by laws, norms and regulations such as the opening hours of public services and the

timetables of public transport. A key concept within time geography is the space-time prism

which delineates all possible space-time points that an individual can reach within a given

time budget (i.e. the time available for travel and discretionary activity participation

between two mandatory activities). The spatial footprint of the space-time prism is called

the potential path area.

Relying on these time-geographical concepts, various so-called space-time accessibility

measures (STAMs) have been proposed that incorporate the performance of the transport


network (Miller 1991, Kwan 1998, Neutens et al. 2008b, Miller & Bridwell 2009, Kuijpers et

al. 2010). Spurred on by the developments in geographical information systems (GIS) and

the availability of disaggregate travel data, the use of network-based STAMs has developed

rapidly in the past decade. Within the STAM tradition, at least three studies are important

for evaluation of accessibility along the temporal dimension. Weber and Kwan (2002) have

calculated various STAMs for 200 individuals in Portland (OR, USA) such as the number of

accessible opportunities and the total length of accessible road segments and shown that

ignoring the effects of traffic congestion and opening hours of opportunities may produce

spatially uneven reductions in individual accessibility. Their work has been continued in the

ethnographic space-time accessibility analysis by Schwanen & De Jong (2008) who have

demonstrated that extending the opening hours of childcare centres can help to improve the

work-life balance of dual-earner families. Finally, Neutens et al. (2010a) have shown that

individuals with certain personal and household attributes are affected differently by

changes to the temporal regime of public service facilities.

While previous research has clearly foregrounded the ramifications of opening hours for

individual accessibility, no attempt has been made thus far to explore the ways in which

opening hours can be amended to achieve a higher accessibility of urban services. In what

follows, we will extend accessibility research in this direction.

10.3 Method

10.3.1 Measuring accessibility

The point of departure of our method is an accessibility measure that takes into account the

spatial and temporal dimensions of people’s daily activity paths. The measure presented

here is based on Burns’ (1979) utility-theoretic framework that assesses accessibility in terms

of the benefits accruing to individuals at particular activity locations – henceforth termed

locational benefits. Burns’ framework has been extended to transport networks and

reconciled with consumer surplus approaches by Miller (1999). Ever since, the approach has

received increased attention in the transport modelling field, which is exemplified by the

various extensions to the framework that have been proposed in recent years, including

Ashiru, Polak and Noland (2003), Hsu and Hsieh (2004), Ettema and Timmermans (2007),

Neutens et al. (2008a), and Neutens, Schwanen & Miller (2010).

A central assumption of the Burns/Miller framework is that, when seeking to perform a

discretionary activity, individuals are both spatially and temporally constrained by a set of

fixed activities that bind them to particular places at specific times of the day (Cullen &

Godson 1975, Schwanen, Kwan & Ren 2008). Fixed activities are mandatory commitments

that are difficult to reschedule in the short run and include such activities as paid labour and

fetching children.

200 Chapter 10

For an individual , let denote the chronologically ordered set of fixed

activities, where each activity has a location and a time span from to .

Between each pair of subsequent fixed activities and , there is an amount of space

and time available for discretionary activities, denoted as . Each is constrained by the

compulsory trip from at to at . In line with time geography, we will

refer to this space-time volume as a space-time prism (Miller 2005) (Figure 10.1). Let

denote the chronologically ordered set of opening hour intervals

of a service facility . Then, the potential activity window (PAW) for individual

to participate in a discretionary activity at a facility between two fixed activities and

and during the opening interval is given by (Figure 10.1):

– (10.1)

with the travel time from to ;

the travel time from to .

Figure 10.1 – Cross section through space (horizontal axis) and time (vertical axis) of the space-time

prism (grey) between fixed activities xj and xj+1 of an individual i, with the indication of the PAW

with respect to the opening hour interval hk of service facility f.

A is located between two fixed activities of and within the opening hours of

. Each PAW can be assigned a utility value expressing the benefit an individual enjoys from

participating in an activity at a service facility over the time span of the PAW. For a given

, this utility value, henceforth termed locational benefit, can be

specified as:


(10.2)

with attractiveness of service facility ;

benefit resulting from attractiveness ;

benefit resulting from the activity duration ;

travel cost to facility ;

disutility resulting from travel cost .

A locational benefit measures the benefit that an individual derives from participating in an

activity at a certain facility as a function of the facility’s attractiveness, the duration of the

activity and the physical separation to/from this facility. To determine the different

components in equation (10.2), we follow earlier specifications by Burns (1979). For the

attractiveness and activity duration components, we use a simple linear function to express

that benefits increase proportionately to the attractiveness of and the activity duration at a

service facility. The advantage over other functional forms (e.g. a positive power function) is

that the linear function does not require complex parameter estimation procedures and

dedicated data collection methods. For generality, a minimum required activity duration

threshold will be left unspecified; this and other refinements (such as delay times) should be

accommodated in future work. The multiplicative functional form of equation (10.2) ensures

that an individual will not derive any utility if a service facility is not attractive or if an

individual cannot spend time at the service facility. For the disutility component associated

with the travel costs, we adopt a negative exponential function with parameter . This

function implies that the willingness to travel to services decays most rapidly at low travel

costs. Since the negative exponential form declines more gradually relative to power

functions, it is better suited to express travel impedance for shorter trips such as those to

the government offices considered in our case study (Ianoco et al., 2010). Incorporating the

above assumptions in equation (10.2) yields:

(10.3)

The travel cost in equation (10.3) can be calculated as the detour travel costs

for to travel to in between the first and the second fixed activity instead of travelling

directly in between both fixed activities:

(10.4)

The locational benefit for an individual over an arbitrary time window (ATW) can

then be expressed as:

(10.5)

Based on equation (10.5), we can specify the locational benefit of a network of service

facilities to an individual over a given time interval. When considering public facilities that

202 Chapter 10

offer highly comparable services – as is the case for the government offices (see section

10.4.1) – an individual may not benefit from having a larger set of facilities to choose from.

In other words, it is assumed that an individual is a rational decision maker who patronizes

the service facility that yields the largest locational benefit. Therefore, when calculating an

individual’s accessibility to a network of facilities, we will assume that an individual

maximises the locational benefits over the available facilities during the considered ATW.

More formally, the accessibility of a network of service facilities to individual over an ATW

is specified as:

(10.6)

For clarification, a simple example of how a locational benefit is calculated over a time

interval is given in Table 10.1.

Example

Consider a person , for whom we would like to assess his/her locational benefit

over the time interval from 8.00 AM to 9.00 AM with respect to the

facility . Suppose that is opened over a time interval from 8.00 AM to 12.00 AM,

and that has two fixed activities and with ending at 8.10 AM and

starting at 10.10 AM. Also, it is given that it takes 25 minutes to travel from to ,

15 minutes to travel from to , and 20 minutes to travel from to . Then, from

equation (10.1) it follows that , of which 35

minutes are within . We then calculate the locational benefit of to

over using equations (10.3-10.5) as .

Table 10.1 – Locational benefit calculation example

10.3.2 Optimising opening hours in terms of accessibility

Having introduced a measure for evaluating the accessibility of a network of service facilities

to a population of individuals over a time interval, we now propose a method for identifying

the opening hours that would generate the highest total accessibility for a given population.

It should be noted that we will only seek to optimise along the temporal dimension of

service delivery; spatial relocations of service facilities will not be considered in this chapter

(i.e. facility locations will be assumed fixed during the optimisation procedure).

In our approach, the study period at hand (e.g. one week) is subdivided into a discrete

sequence of non-overlapping time intervals (e.g. hours). These minimum time intervals

(MTIs) are the basic temporal units of analysis. We will refer to an MTI during which a service

facility is open as a minimum opening interval (MOI) and denote it as a pair (facility, MTI).

The complete schedule of opening hours of a set of service facilities can be represented as a

set of MOIs, henceforth termed a regime. Starting from an empty regime (zero MOIs),

then, of all possible MOIs not in , the MOI returning the highest additional benefit for the


entire population with respect to the benefit of , can be iteratively assessed using equation

(10.6) and added to . This best-first selection procedure is presented in Algorithm 10.1.

Input:

set of individuals

set of service facilities , with denoting the set of MOIs allocated to facilities in

set of all possible MOIs of facilities in covering the study period

number of MOIs

Output:

-MOI regime (ordered set of MOIs) with maximal total locational benefit

total benefit associated with

Algorithm:

01: set to ,

02: for to

03: set to

04: set to ,

05: for each in subtract from

06:

07: add to

08: for each in

09:

10: end for

11: if then

12:

13: set to

14: end if

15: subtract from

16: end for

17: add to

18:

19: end for

20: return

Algorithm 10.1 – Computational procedure to determine the optimal n-MOI regime.

The algorithm takes as input a population of individuals with their fixed activities, a set

of service facilities , a set of all possible MOIs of facilities in over the entire study

period, and the number of requested MOIs in the resulting regime. Obviously, is limited

to the number of MOIs in . The output is the -MOI regime (i.e. regime consisting of

MOIs) that yields the maximal total locational benefit, which is returned as well. The

algorithm consists of two major nested iterations. The inner iteration (lines 5-16) runs

through all remaining MOIs in the study period that are not yet included in the optimal

204 Chapter 10

regime so far. Each of these MOIs is alternately added to the set of facility opening hours in

the regime in order to assess the total locational benefit of its addition by cumulating all

individual benefits using equation (10.6) at line 9. From this inner iteration, the algorithm

holds back the MOI whose addition returns the highest total benefit and adds it to the

regime in the outer iteration (lines 2-19). The latter is done until the regime contains the

requested number of MOIs.

At this stage we are able to derive the optimal -MOI regime in terms of total accessibility.

However, since no conditions have been specified concerning the internal consistency of a

regime, it may well be that a regime consists of combinations of non-contiguous MOIs

scattered across the study period, which may be impracticable and undesirable to

implement by local authorities. In an attempt to derive the -MOI regime that accounts for

continuity of service delivery, we propose a second algorithm using a penalty and a reward

parameter, denoted and respectively. The idea is that the locational benefits for an

added MOI have to be valued higher (multiplied by ) when an MOI connects with one of the

previously selected MOIs of the same facility, whereas they have to be devaluated

(multiplied by ) if the MOI is not temporally adjacent with a yet included MOI. This

extended approach has been pseudo-coded in Algorithm 10.2.

Although it would be straightforward to choose symmetric (i.e. inverse) values for and ,

i.e. , we have intentionally introduced them as two different parameters, because

they have different effects on the allocation of MOIs across facilities. On the one hand,

rewarding contiguous opening hours ( ) will favour a regime consisting of

contiguous opening hours for a limited set facilities. Penalising ( ), on the other

hand, will favour a regime with contiguous opening hours for multiple facilities.

Both parameters can be adjusted by policymakers at will in order to derive meaningful

regimes. It should be noted, however, that temporal contiguity may come at the expense of

accessibility: the more contiguity is aimed for (i.e. the more and deviate from 1), the less

optimal in terms of the number of people who can access the evaluated facility or facilities a

resulting regime may be.


Input:

see Algorithm 10.1

penalty factor

reward factor

Output:

connected -MOI regime (ordered set of MOIs) with (sub)optimal total locational

benefit

total benefit associated with

Algorithm:

01: set to

02: for 1 to n

03: set to

04: set to

05: for each in subtract from

06:

07: add to

08: if adjacent then

09: q = r

10: else

11:

12: end if

13: for each in

14:

15:

16: end for

17: if then

18:

19:

20: set to

21: end if

22: subtract from

23: end for

24: add to

25:

26: end for

27: return

*The Boolean function returns true if the MOI is temporally adjacent

with an existing MOI of facility in regime ; otherwise false is returned

Algorithm 10.2 – Computational procedure to determine the (sub)optimal connected n-MOI

regime.

206 Chapter 10

10.4 Case study

In order to illustrate the applicability of the method described in section 10.3, we will now

elaborate a case study. In this case study we will try to find the optimal regime of opening

hours for the government offices in the city of Ghent (Belgium). The input data, data

preparation and results will be discussed below.

10.4.1 Data

The study area is the city of Ghent, which is the third largest city in Belgium and capital of

the province of East-Flanders. Ghent has a population of approximately 240 000 inhabitants

and an area of almost 160 km² (Figure 10.2). The northern part of the study area is sparsely

populated and known for its flourishing industrial and harbour activities.

For this case study, we rely on the following data sources:

Individuals

The first data source is an activity/travel data set consisting of a two-day consecutive diary of

out-of-home activities of persons aged five or more living in the Ghent region. The data set

was collected in 2000 within the framework of the SAMBA project (Spatial Analysis and

Modelling Based on Activities) (see Tindemans et al. 2005). Reported activity locations were

geocoded at the street level. Individuals sampled at the same day of the week are grouped

and their fixed activities are considered representative for the type of activities that they

usually undertake on this day of the week. Since no fixity levels are available for the reported

activities, fixed activities were determined on the basis of the activity purpose. The

categories “work”, “school”, “pick up/drop off” and categories closely related to these were

considered fixed, given that it is generally difficult to conduct them at other places and

times. In total 3 047 person-days were selected, ranging from Monday to Saturday. Sunday

openings will not be considered in this case study as they relate to different societal

constraints and are not considered by the local authorities. Given that households were

randomly sampled within the SAMBA project, we will assume that the spatial distribution of

the home locations of the selected individuals mirrors the general distribution of the actual

population (Figure 2).

Service facilities

The second source of data comprises information about the government offices in Ghent.

The addresses, opening hours and services offered are obtained for each government office

from the official city website (http://www.gent.be). Two types of government offices are

distinguished: head and branch offices (Figure 10.3). The centrally located head office forms

the core of the municipal service delivery network. In addition to the conventional

administrative services delivered at all branch offices, the head office offers few additional

though rather exceptional formalities. Furthermore, this office is generally able to process

administrative documents (e.g. identity cards) quicker than the branch offices.


Figure 10.2 – Study area and sampled households.

Figure 10.3 – Spatial distribution of government offices.

208 Chapter 10

The current regime of opening hours is given in Table 10.2 (opening hours are grey-

coloured). The opening hours of government offices 4-15 exhibit a lot of overlap, while the

opening hours of offices 1-3 in the northern part of the city are very limited.

Monday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 8 AM- 9 AM

9 AM-10 AM 10 AM-11 AM 11 AM-12 AM 12 AM- 1 PM 1 PM- 2 PM 2 PM- 3 PM 3 PM- 4 PM 4 PM- 5 PM 5 PM- 6 PM

Tuesday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 8 AM- 9 AM


Wednesday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 8 AM- 9 AM

9 AM-10 AM 10 AM-11 AM 11 AM-12 AM 12 AM- 1 PM 1 PM- 2 PM 2 PM- 3 PM 3 PM- 4 PM 4 PM- 5 PM 5 PM- 6 PM Table 10.2 – Current regime of opening hours for the government offices in Ghent (1-15).


Thursday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 8 AM- 9 AM


Friday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 8 AM- 9 AM


Saturday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 8 AM- 9 AM

9 AM-10 AM 10 AM-11 AM 11 AM-12 AM 12 AM- 1 PM 1 PM- 2 PM 2 PM- 3 PM 3 PM- 4 PM 4 PM- 5 PM 5 PM- 6 PM Table 10.2 (continued)

Transport system

The third data source is TeleAtlas® MultiNetTM (version 2007.10) road network data for

Belgium. Based on this data set, travel times were estimated using ESRI®’s Network Analyst

(ArcGIS 9.3.1). Two predominant transport modes in Ghent will be considered in this case

study: car and bicycle. Local public transportation is not addressed in this study because it

would significantly increase the computational intensity and requires among others

information about the location of stops and the time tables for each of the different public

transportation alternatives (i.e. trains, trams and buses) in Ghent, which were not available

to us.

210 Chapter 10

To compute travel times by car, we have manipulated our data set in order to account for

congestion. Therefore, we relied on a recent report prepared for the Federal Government

Service for Mobility and Transport (Maerivoet and Yperman, 2008), where average travel

times are reported for Ghent and its conurbation for three different road classes at four

different times of the day for both weekdays and weekends. A factor for each of these

categories has been determined (Table 10.3). As expected, the highest congestion (i.e.

highest factor) is found during weekday mornings and weekday evening peaks, while the

lowest congestion (i.e. lowest factor) occurs during weekend middays and nights. These

Road type Morning

6 AM – 9 AM Midday

9 AM – 4 PM Evening

4 – 7 PM Night

7 PM – 6 AM

Weekday Highways and ring roads 1.062 1.057 1.065 1.029

Regional and main connection roads 1.202 1.117 1.249 1.117

Other paved roads 1.118 1.094 1.196 1.094

Weekend Highways and ring roads 1.013 1.000 1.026 1.007

Regional and main connection roads 1.000 1.025 1.037 1.025

Other paved roads 1.060 1.000 1.036 1.000

Table 10.3 – Congestion factor according to day type, day time and road class.

congestion factors allow us to estimate time-varying travel times by car as the weighted

product of the uncongested travel time (based on TeleAtlas® MultiNetTM) with the

corresponding factors in Table 2. If the uncongested travel time covers different congestion

periods, factors are weighted accordingly.

Specific information about specialized bicycle facilities (e.g. dedicated bicycle paths) was not

readily available for the city of Gent. Hence, in order to compute travel times by bicycle, we

had to adopt a compromise solution following Ianoco, Krizek & El-Geneidy (2010). This

compromise solution consisted of excluding highways and other exclusive motorways from

the transport network and allowing travel directions for non-motorized travelers – one-way

streets for motorized vehicles passable in both directions for bicyclists are common in

Ghent. Travel times by bicycle were estimated as the product of the shortest path distance

and a mean travel speed of 15 km/h (El-Geneidy, Krizek & Iacono 2007). Note that these

estimates are rather coarse; they could have been refined given that recent empirical studies

about pedestrian and bicycle travel have shown travel times and speeds to vary with micro-

level characteristics of the built environment (Krizek & Roland 2005; Krizek, Handy & Forsyth

2009) and according to age and gender (Wendel-Vos et al. 2004; Gomez et al. 2005).

However, we believe that the current estimations are accurate enough for testing our

method and leave such refinements for future work.


10.4.2 Data preparation

Prior to the optimisation, the input data needs to be adapted. The following issues have

been dealt with. First, all necessary detour travel costs have been calculated as described in

section 10.4.1. To account for mobility resources, we have assumed that car-owners with a

driving license are able to travel by car, whereas others are assumed to travel by bicycle.

Second, the attractiveness value af (see equation (10.3)) was determined for each

government office. On the basis of the number of extra services provided at the head office

and in consultation with the local authorities, we have specified the attractiveness difference

between the head office and the branch offices at the proportion of 1 for the central office

to 0.8 for the other offices. Third, the decay parameter α of the negative exponential

deterrence function (see equation (10.3)) was estimated for car and bicycle separately, using

the observed cumulative distribution of service trips according to travel time (Figure 10.4).

Similar decay parameters were found across both travel modes: = 0.081 ( = 0.97) and

= 0.092 ( = 0.98).

Figure 10.4 – Estimation of distance decay parameters.

Finally, the Algorithms 10.1 and 10.2 presented in section 10.3.2 have been implemented in

a Visual Basic module.

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60

Trip

like

liho

od

(%

)

Travel time (min)

Observed (car)

Observed (bicycle)

Exponential decay (car)

Exponential decay (bicycle)

y = e-0.081x

y = e-0.092x

212 Chapter 10

10.4.3 Results

Optimal temporal regimes by number of opening hours

We start our analysis by examining if and to what extent the accessibility of Ghent’s

government offices can be improved by rescheduling the current opening hours using

Algorithm 10.1. We will consider MTIs of one hour, which reflect the minimal time span for a

government office to be open as can be found in the current regime (office 3 on Wednesday,

Table 10.2). Given that people generally have less time constraints resulting from fixed

activities on Sundays and in the evening (Neutens et al. 2010a), it is rather self-evident that

citizens’ accessibility will be improved significantly by shifting the current opening hours

towards these time periods. Therefore, we will restrict our analysis to the accessibility gains

that can be made by applying the optimisation algorithm within the current range of

opening hours (i.e. 8 AM to 6 PM and Monday to Saturday). Within this range, the fifteen

government offices can maximally cover 900 possible opening hours (MOIs) – each office can

be open for ten hours between 8 AM to 6 PM for six days a week (Monday to Saturday).

Currently, the government offices cover 405 of these 900 possible opening hours.

Using Algorithm 10.1, we have assessed the 900 optimal regimes ranging from one to all 900

opening hours in the study period. Figure 10.5 shows that the accessibility increases with the

number of opening hours at a decreasing rate. The accessibility values on the vertical axis of

this diagram have been calculated as a trade-off between attractiveness, possible activity

duration and travel costs (equation (10.7)) and express how well the complete set of

individuals is able to access the network of government offices during a given regime of

opening hours. Figure 10.5 offers a yardstick regarding the number of opening hours to be

included in a temporal regime. One can see that accessibility increases quite rapidly for the

first, say, 150 opening hours. Hence, a curtailment of these hours would considerably harm

the overall accessibility of government offices. Beyond this value the marginal utility of

adding extra opening hours declines until 820 opening hours. From that point on, expanding

the opening hours does not increase the total accessibility anymore because none of the

added opening hours is able to attract (i.e. offer higher benefits to) individuals from

government offices with concurrent opening hours that were already included in the optimal

regime. In other words, for the remaining 80 opening hours – covered only by the peripheral

government offices no. 1 and 2 – people are better off, if they go to surrounding offices.

Evaluating the current temporal regime

We have also calculated the total accessibility of the current regime of 405 opening hours

and have positioned this regime into the diagram depicted in Figure 10.5. Vertical

movements in the diagram represent gains or losses in accessibility caused by rescheduling

the current number of opening hours; horizontal movements represent curtailing or

expanding the opening hours. Clearly, the current regime is suboptimal in terms of

accessibility since the same level of accessibility can be achieved with merely 98 opening


hours if the optimal regime is adopted. In other words, Figure 10.5 indicates that significant

improvements in the total accessibility can be made by simply reconfiguring the existing

opening hours without expanding them.

Figure 10.5 – Total accessibility for all 900 optimal regimes with indication of the current regime.

Improving accessibility by rescheduling opening hours

To improve the accessibility of the government offices, a suitable strategy would be to

reschedule the current 405 opening hours within the current range of opening hours. The

regime that yields the maximum total accessibility with 405 opening hours has been

calculated using Algorithm 10.1 and is depicted in Table 10.4. At least two characteristics of

this optimal regime can be identified. First, a relatively large share of government offices

have been allocated opening hours between 4 PM and 6 PM on weekdays, reflecting that

many individuals in the sample have time available for accessing a government office upon

completing (mandatory) paid work activities. Second, opening hours tend to be allocated to

government offices that are located centrally within the city – offices 5, 8 and 15 in

particular. This can be explained by the high concentration of residences and employment

(or other fixed activity) locations within this area from which people tend to access the

government offices. The optimal regime of 405 opening hours also implies that the small

demand for branch offices 1 and 2 can easily be taken over by the other offices. Also, it

appears that in the optimal regime the head office (no. 15) is continuously open on each day

of the study period. This could have been expected since this office was assigned a larger

attractiveness and is located centrally.

214 Chapter 10

Monday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 8 AM- 9 AM

9 AM-10 AM 10 AM-11 AM 11 AM-12 AM 12 AM- 1 PM 1 PM- 2 PM 2 PM- 3 PM 3 PM- 4 PM 4 PM- 5 PM 5 PM- 6 PM Tuesday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

8 AM- 9 AM 9 AM-10 AM 10 AM-11 AM 11 AM-12 AM 12 AM- 1 PM 1 PM- 2 PM 2 PM- 3 PM 3 PM- 4 PM 4 PM- 5 PM 5 PM- 6 PM Wednesday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

8 AM- 9 AM 9 AM-10 AM 10 AM-11 AM 11 AM-12 AM 12 AM- 1 PM 1 PM- 2 PM 2 PM- 3 PM 3 PM- 4 PM 4 PM- 5 PM 5 PM- 6 PM Thursday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

8 AM- 9 AM 9 AM-10 AM 10 AM-11 AM 11 AM-12 AM 12 AM- 1 PM 1 PM- 2 PM 2 PM- 3 PM 3 PM- 4 PM 4 PM- 5 PM 5 PM- 6 PM Table 10.4 – Optimal 405-hour regime.


Friday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 8 AM- 9 AM

9 AM-10 AM 10 AM-11 AM 11 AM-12 AM 12 AM- 1 PM 1 PM- 2 PM 2 PM- 3 PM 3 PM- 4 PM 4 PM- 5 PM 5 PM- 6 PM Saturday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

8 AM- 9 AM 9 AM-10 AM 10 AM-11 AM 11 AM-12 AM 12 AM- 1 PM 1 PM- 2 PM 2 PM- 3 PM 3 PM- 4 PM 4 PM- 5 PM 5 PM- 6 PM Table 10.4 – (continued)

While, compared to the current regime, the total accessibility can be increased by 70%

without expanding the number of opening hours, the optimal 405-hour regime is rather

impracticable as it contains 13 discontinuities (gaps within an office’s day schedule) with

nine isolated hours (offices opened for only one hour). To overcome this issue, we have

computed the (sub)optimal 405-hour regime using Algorithm 10.2 with symmetric reward

and penalty parameters (i.e. ). In order to limit the impact of connectedness on

the total accessibility, we have gradually increased the impact of both factors simultaneously

(increased and decreased by increments of 0.1 to the same extent), starting from = =

1. We found that for and regimes without any discontinuities are

obtained. The results of the adjusted regime are depicted in Table 10.5. Since 96% of the

opening hours of the optimal regime are preserved in the adjusted contiguous regime, the

total accessibility has diminished by less than 1% compared to the optimal regime with 405

hours. In other words, by adjusting the reward and penalty parameters, we are able to

develop a regime consisting of contiguous blocks of opening hours that offers high levels of

accessibility among the population. This regime may be used by local authorities as a basis

for amending the opening hours of their network of service facilities.

216 Chapter 10

Monday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 8 AM- 9 AM

9 AM-10 AM 10 AM-11 AM 11 AM-12 AM 12 AM- 1 PM 1 PM- 2 PM 2 PM- 3 PM 3 PM- 4 PM 4 PM- 5 PM 5 PM- 6 PM Tuesday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

8 AM- 9 AM 9 AM-10 AM 10 AM-11 AM 11 AM-12 AM 12 AM- 1 PM 1 PM- 2 PM 2 PM- 3 PM 3 PM- 4 PM 4 PM- 5 PM 5 PM- 6 PM Wednesday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

8 AM- 9 AM 9 AM-10 AM 10 AM-11 AM 11 AM-12 AM 12 AM- 1 PM 1 PM- 2 PM 2 PM- 3 PM 3 PM- 4 PM 4 PM- 5 PM 5 PM- 6 PM Thursday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

8 AM- 9 AM 9 AM-10 AM 10 AM-11 AM 11 AM-12 AM 12 AM- 1 PM 1 PM- 2 PM 2 PM- 3 PM 3 PM- 4 PM 4 PM- 5 PM 5 PM- 6 PM Table 10.5 – Contiguous sub-optimal 405-hour regime.


Friday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 8 AM- 9 AM

9 AM-10 AM 10 AM-11 AM 11 AM-12 AM 12 AM- 1 PM 1 PM- 2 PM 2 PM- 3 PM 3 PM- 4 PM 4 PM- 5 PM 5 PM- 6 PM Saturday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

8 AM- 9 AM 9 AM-10 AM 10 AM-11 AM 11 AM-12 AM 12 AM- 1 PM 1 PM- 2 PM 2 PM- 3 PM 3 PM- 4 PM 4 PM- 5 PM 5 PM- 6 PM Table 10.5 – (continued)

10.5 Conclusion and avenues for future work

The purpose of this chapter has been to study the relationship between opening hours and

accessibility in the context of public service delivery. More specifically, a method has been

presented and implemented that allows optimising the opening hours of public service

delivery in terms of the accessibility experienced by a city’s population with heterogeneous

activity and travel patterns. Accessibility has been specified by means of locational benefits

which express the desirability for an individual to participate in an activity at a certain service

facility on the basis of the facility’s attractiveness, the potential activity duration and the

travel costs involved. The proposed method has been illustrated for a case study of public

service delivery in the city of Ghent, Belgium. Our initial findings have shown that substantial

improvements in total accessibility can be made by rescheduling instead of expanding the

existing opening hours of service facilities. We believe that the current study is relevant in

light of the growing attention to time problems and the increasing relevance of urban time

policies. Optimal temporal regimes in terms of accessibility offer policymakers a useful

benchmark to identify the margins within which access to services can be improved by

temporal changes to service delivery.

Although our optimisation method has a sound and generic theoretical basis, a number of

refinements could and should be made in future work. The first and perhaps most important

issue from a policy point of view concerns the absence of equity considerations in our

218 Chapter 10

algorithm. While we were able to identify the regime of opening hours that maximises the

accessibility over the entire (sample of the) population, we did not account for the

inequalities in the distribution of individual accessibility that may ensue from this regime.

One way to promote a more equitable distribution of individual accessibility would be to

weight the individual benefits in the optimisation procedure, such that larger weights are

assigned to the benefits of individuals with less discretionary time available. In this way

policymakers could give priority to the preferences of those persons who are most

vulnerable to a modification of opening hours. For example, local authorities may want to

‘humanize’ the timetables of public service delivery by making these more compatible with

the activity schedules of those constituencies who generally face considerable space-time

demands in their daily lives, such as dual earner households or young women with children.

Policymakers may also want to alter the temporal regime of public service delivery to attract

more visitors from particular socioeconomic groups. Visitor surveys of library use, for

example, have already provided initial support that the opening hours of public libraries

affect the social composition of their visitor populations (Glorieux, Kuppens & Vandebroeck

2007).

Second, the realism of the space-time accessibility measure used in this chapter can be

improved further. Some temporal aspects warrant more attention including the

incorporation of delay times, waiting times, a minimum activity duration and local changes in

travel times due to a rescheduling of opening hours. The valuation of attractiveness and

possible activity duration also deserves more attention. Whereas both components have

currently been assumed directly proportionate to individual accessibility, behaviourally more

appealing functions have been proposed to express this relationship (see e.g. Joh, Arentze &

Timmermans 2001; Ettema, Ashiru & Polak 2004). Increasing the behavioural realism of

space-time accessibility can also be achieved by accounting for dependencies between

household members with respect to car allocation, ride sharing and task re-allocation

strategies (Zhang & Fujiwara 2006, Soo et al. 2009). Since these aspects may impose

additional coupling constraints on activity participation, they should be incorporated in

future work. Finally, given that our approach is sample-based, it is important to point out

that the resulting optimal regime highly depends on the size and the accuracy of the travel

diary data at hand. This is because activities reported in a travel diary on a particular day

may not be representative for the type of activities that an individual is likely to regularly

engage in that day. Ideally, longitudinal data covering multiple days or even weeks should be

used to verify the consistency of activity patterns over a longer time horizon.

Third, at a more general level, rescheduling of the operational hours of public services,

commercial activities and employment may have downsides for family and social life and at

some point begin to reduce social welfare. This is because those services, commercial

activities and firms whose operational hours are to be rescheduled will demand that at least

some of their employees will have to come to work at the rescheduled hours. These hours


may well coincide with times that children, spouses, friends and others will experience fewer

space-time constraints and are available for social and leisure activity participation. This

situation of rescheduled employment hours is most likely to occur for people with low levels

of sovereignty over their employment hours, many of whom will occupy the lower steps on

the occupational ladder, hold less secure jobs, and will be lowly educated and female

(Breedveld 1998, Hildebrandt 2006). Hence, the disadvantages that a large-scale

rescheduling of opening hours would have for family and social life will be distributed

unevenly across socio-economic groups in society (Mills & Taht 2010). There are at least two

ways to account at least to some extent for the negative effects of a rescheduling of

operational hours on family and social life. One, which has also been adopted here, is to a

priori determine a time window, during which opening hours can be rescheduled. Certain

periods of time, such as late evenings and Sundays, could in this way be excluded from the

rescheduling process. Second, it would be possible to incorporate people’s time-of-day

preferences regarding when they would like to participate in certain types of activities into

the Burns/Miller accessibility measures (see also Neutens et al. 2010a). Blocks of time during

the week and during which large groups of people would prefer to engage in social activities

with family, friends and others rather than visit a public service or commercial activity would

then have a lower weight in the calculation of the optimal regime of opening hours. The

value of this second approach could be explored in future work.

Despite these refinements to be made, we believe that the proposed method can be a

valuable instrument aiding policymakers, facility managers and others to explore different

configurations of opening hours that maximise potential visitors’ opportunity to pursue

activities at facilities across cities and regions.

References

Ashiru, O., Polak, J. & Noland, R. (2003) Space-time user benefit and utility accessibility measures for

individual activity schedules. Transportation Research Record: Journal of the Transportation

Research Board, 1854, 1, 62-73.

Ashiru, O., Polak, J. & Noland, R. (2004) Utility of schedules: theoretical model of departure-time

choice and activity-time allocation with application to individual activity schedules.

Transportation Research Record: Journal of the Transportation Research Board, 1894, 1, 84-

98.

Bhat, C. R. & Misra, R. (1999) Discretionary activity time allocation of individuals between in-home

and out-of-home and between weekdays and weekends. Transportation, 26, 2, 193-229.

Boulin, J. Y. (2005) Is the societal dialogue at the local level the future of social dialogue? Transfer:

European Review of Labour and Research, 11, 1, 439-448.

Boulin, J. Y. (2006) Local time policies in Europe. In: Gender Divisions And Working Time In The New

Economy: Changing Patterns of Work, Care and Public Policy in Europe and North America,

eds. Perrons. D., Fagan, C., McDowell, L., Ray, K., Ward, K., Edward Elgar, Cheltenham.

Breedveld, K. (1998) The double myth of flexibilization – Trends in scattered work hours, and

differences in time-sovereignty. Time & Society, 7, 1, 129-143.

220 Chapter 10

Burns, L. D. (1979) Transportation, Temporal, and Spatial Components of Accessibility. Lexington, MA:

Lexington Books.

Clemenz, G. (1994) Competition via shopping hours: A case for regulation. Journal of Institutional and

Theoretical Economics – Zeitschrift Fur Die Gesamte Staatswissenschaft, 150, 4, 625-641.

Couclelis, H., 2004. Pizza over the internet: E-commerce, the fragmentation of activity and the

tyranny of the region. Entrepreneurship and Regional Development, 16, 1, 41-54.

Cullen, I. & Godson, V., 1975. Urban networks: The structure of activity patterns. Progress in

Planning, 4, 1, 1-96.

Deffner, A. M., 2005. The combination of cultural and time planning. City, 9, 1, 125-141.

El-Geneidy, A. M., Krizek, K. J. & Iacono, M. (2007) Predicting bicycle travel speeds along different

facilities using GPS data: A proof of concept model. Paper presented at the 86th Annual

Meeting of the Transportation Research Board, Washington D.C., USA.

Ettema, D., Ashiru, O. & Polak, J. W. (2004) Modeling timing and duration of activities and trips in

response to road-pricing policies. Transportation Research Record, 1894, 1-10.



Glorieux, I., Mestdag, I. & Minnen, J. (2008) The coming of the 24-hour economy? Changing work

schedules in Belgium between 1966 and 1999. Time & Society, 17, 1, 63-83.

Glorieux, I., Kuppens, T. & Vandebroeck, D., (2007) Mind the gap: Societal limits to public library

effectiveness. Library and Information Science Research, 29, 2, 188-208.

Gomez, L. F., Sarmiento, O. L., Lucumí, D. I., Espinosa, G., Forero, R. & Bauman A. (2005) Prevalence

and factors associated with walking and bicycling for transport among young adults in two

low-income localities of Bogotá, Colombia. Journal of Physical Activity and Health, 2, 4, 445-

59.

Graham, S. & Marvin, S. (1997) Telecommunications and the City. Electronic Space, Urban Places.

London: Routledge.

Hajer, M. & Zonneveld, W. (2000) Spatial planning in the network society: Rethinking the principles of

planning in The Netherlands. European Planning Studies, 8, 3, 337-355.

Harris, P., Lewis, J. & Adam, B. (2004) Time, sustainable transport and the politics of speed. World

Transport Policy & Practice, 10, 5-11.

Healey, P. (2004) The treatment of space and place in the new strategic spatial planning in Europe.

International Journal of Urban and Regional Research, 28, 1, 45-67.

Hildebrandt, E. (2006) Balance between work and life: New corporate impositions through flexible

working time or opportunity for time sovereignty? European Societies, 8, 2, 251-271.

Hsu, C. I. & Hsieh, Y. P. (2004) Travel and activity choices based on an individual accessibility model.

Papers in Regional Science, 83, 2, 387-406.

Iacono, M., Krizek, K. J. & El-Geneidy, A. (2010) Measuring non-motorized accessibility: issues,

alternatives, and execution. Journal of Transport Geography, 18, 1, 133-140.

Jacobsen, J. P. & Kooreman, P. (2005) Timing constraints and the allocation of time: The effects of

changing shopping hours regulations in The Netherlands. European Economic Review, 49, 1,

9-27.

Jarvis, H. (2005) Moving to London Time: Household co-ordination and the infrastructure of everyday

life. Time & Society, 14, 1, 133-154.


Joh, C. H., Arentze, T. & Timmermans, H. (2001) Activity scheduling and rescheduling behavior.

GeoJournal, 53, 4, 359-372.

Kim, H. M. & Kwan M. P. (2003) Space-time accessibility measures: A geocomputational algorithm



Krizek, K. J. & Roland, R. W. (2005) What is at the end of the road? Understanding discontinuities of

on-street bicycle lanes in urban settings. Transportation Research Part D: Transport and

Environment, 10, 1, 55-68.

Krizek, K. J., Handy & S. L., Forsyth, A. (2009) Explaining changes in walking and bicycling behavior:

challenges for transportation research. Environment and Planning B: Planning and Design,

36, 4, 725-740.



1248.



Kwan, M. P. (1999) Gender, the home-work link and space-time patterns of nonemployment

activities. Economic Geography, 76, 4, 370-394.

Kwan, M. P., Hong, X. D. (1998) Network-based constraint-oriented choice set formation using GIS.

Journal of Geographical Systems, 5, 1, 139-162.

Kwan, M. P. & Weber, J. (2008) Scale and accessibility: Implications for the analysis of land use-travel

interaction. Applied Geography, 28, 2, 110-123.

Law, R. & Wolch, J. (1999) Social reproduction in the city: Restructuring in time and space. In: Knox,

P. (ed.), The Restless Urban Landscape. Prentice Hall, Englewood Cliffs, NJ.

Maerivoet, S. & Yperman, I. (2008) Analyse van de Verkeerscongestie in België: Rapport in Opdracht

van de Federale Overheidsdienst Mobiliteit en Vervoer, Leuven (Belgium): Transport &

Mobility Leuven, 78.

McDowell, L., Ward, K., Fagan, C., Perrons, D. & Ray, K. (2006) Connecting time and space: The

significance of transformations in women's work in the city. International Journal of Urban

and Regional Research, 30, 1, 141-158.

Metz, D. (2008) The myth of travel time saving. Transport Reviews, 28, 3, 321-336.

Miller, H. J. (1991) Modeling accessibility using space-time prisms concepts within geographical

information-systems. International Journal of Geographical Information Systems, 5, 3, 287-

301.

Miller, H. J. (1999) Measuring space-time accessibility benefits within transportation networks: Basic

theory and computational procedures. Geographical Analysis, 31, 2, 187-212.




Mills, M. & Taht, K. (2010) Nonstandard work schedules and partnership quality: Quantitative and

qualitative findings. Journal of Marriage and the Family, 72, 4, 860-875.

Moccia, F. D. (2000) Planning time: An emergent European practice. European Planning Studies, 8, 3,

367-375.

222 Chapter 10

Mückenberger, U. & Boulin, J.-Y. (2002) Times of the city: New ways of involving citizens. Concepts

and Transformation, 7, 1, 73-91.

Neutens, T., Schwanen, T., Witlox, F. & De Maeyer, P. (2008a) My space or your space? Towards a

measure of joint accessibility, Computers, Environment and Urban Systems, 32, 5, 331-342.

Neutens, T., Van de Weghe, N., Witlox, F. & De Maeyer, P. (2008b) A three-dimensional network-

based space-time prism. Journal of Geographical Systems, 10, 1, 89-107.

Neutens, T., Schwanen, T., Witlox, F. & De Maeyer, P. (2010a) Evaluating the temporal organization


1039-1064.

Neutens, T., Schwanen, T., Witlox, F. & De Maeyer, P. (2010b) Equity of urban service delivery: A


1635.

Neutens, T., Versichele, M. & Schwanen, T. (2010c) Arranging place and time: A GIS toolkit to assess

individual and joint accessibility to urban opportunities. Applied Geography 30, 4, 561-575.

Neutens, T., Schwanen, T. & Miller, H. J. (2010) Dealing with timing and synchronization in

opportunities for joint activity participation. Geographical Analysis, 42, 3, 245-266.

Nuvolati, G. (2003) Resident and non-resident populations: Quality of life, mobility and time policies.

Journal of Regional Science Analysis and Policy, 33, 2, 67-83.

Pelfrene, E., Vlerick, P., Mak, R. P., De Smet, P., Kornitzer, M. & De Backer, G. (2001) Scale reliability

and validity of the Karasek 'job demand-control-support' model in the Belstress study. Work

and Stress, 15, 4, 297-313.

Ritsema van Eck, J., Burghouwt, G. & Dijst, M. (2005) Lifestyles, spatial configurations and quality of

life in daily travel: An explorative simulation study. Journal of Transport Geography, 13, 2,

123-134.

Rouwendal, J., Rietveld, P. (1999) Prices and opening hours in the retail sector: Welfare effects of

restrictions on opening hours. Environment and Planning A, 31, 11, 2003-2016.

Schwanen, T. (2007) Gender differences in chauffeuring children among dual-earner families.

Professional Geographer, 59, 4, 447-462.

Schwanen, T. & Kwan, M. P. (2008) The Internet, mobile phone and space-time constraints.

Geoforum, 39, 3, 1362-1377.

Schwanen, T., Kwan, M. P. & Ren, F. (2008) How fixed is fixed? Gendered rigidity of space-time

constraints and geographies of everyday activities, Geoforum, 39, 6, 2109-2121.

Shy, O., Stenbacka, R. (2006) Service hours with asymmetric distributions of ideal service time,

International Journal of Industrial Organization, 24, 4, 763-771.

Soo, J. K. L., Ettema, D. & Ottens, F.L. (2009) Towards a multi-activity multi-person accessibility

measure: concept and first tests. In: Kitamura, R. (Ed.) The expanding sphere of travel

behavior research, UK: Emerald Group Publishing, 745-768.

Szollos, A. (2009) Toward a psychology of chronic time pressure: Conceptual and methodological

review. Time & Society, 18, 2-3, 332-350.

Shy, O., Stenbacka, R. (2008) Price competition, business hours and shopping time flexibility.,

Economic Journal, 118, 531, 1171-1195.

Thum, M. & Weichenrieder, A. (1997) 'Dinkies' and housewives: The regulation of shopping hours.

Kyklos, 50, 4, 539-559.


Tindemans, H., Van Hofstraeten, D., Verhetsel, A. & Witlox, F. (2005) Spatial analysis and modeling

based on activities. A pilot study for Antwerp and Ghent, Belgium. In Spatial Planning, Urban

Form and Sustainable Transport, ed. K. Williams, Aldershot: Ashgate Publishers, 61-82.

Weber, J. & Kwan, M. P. (2002) Bringing time back in: A study on the influence of travel time

variations and facility opening hours on individual accessibility. Professional Geographer, 54,

2, 226-240.

Weber, J. & Kwan, M. P. (2003) Evaluating the effects of geographic contexts on individual

accessibility: A multilevel approach. Urban Geography, 24, 8, 647-671.

Wendel-Vos, G. S. W., Schuit, A. J., De Niet, R., Boshuizen, H. C., Saris, W. H. M & Kromhout, D. (2004)

Factors of the physical environment associated with walking and bicycling. Medicine and

Science in Sports and Exercise, 36, 4, 725-730.

Zandvliet, R. & Dijst, M. (2005) Research note – The EBB and flow of temporary populations: The

dimensions of spatial-temporal distributions of daytime visitors in the Netherlands. Urban

Geography, 26, 353-364.

Zandvliet, R., Bertolini, L. & Dijst, M. (2008) Towards planning for a mobile society: Mobile and

residential populations and the performance of places. European Planning Studies, 16, 1459-

1472.

Zhang, J. Y. & Fujiwara, A. (2006) Representing household time allocation behavior by endogenously

incorporating diverse intra-household interactions: A case study in the context of elderly

couples. Transportation Research Part B: Methodological, 40, 1, 54-74.

The impact of opening hours on the equity of individual space-time accessibility 225

11 The impact of opening hours on the equity of individual

space-time accessibility

Delafontaine M., Neutens T., Schwanen T., Van de Weghe N.

in Computers, Environment and Urban Systems, forthcoming


Abstract. While many studies have concentrated on the effects of the spatial

distribution of services on individual accessibility, only little is known about the ways

in which equity of individual accessibility is affected by the temporal organisation of

service delivery. This chapter seeks to deepen our understanding about the

relationship between accessibility, equity and the opening hours of public service

facilities on the basis of space-time accessibility measures. Three approaches based

on different equity principles are presented to schedule the opening hours of public

service facilities: a utilitarian, an egalitarian and a distributive approach. A case study

of public libraries in Ghent (Belgium) demonstrates the relevance of these

approaches for amending the opening hours of public services to control the equity

of accessibility levels across individuals.

Keywords. Accessibility – Equity – Opening hours – Public services – Time geography

11.1 Introduction

Achieving a higher and more equitable level of access to essential public services has been

an issue of major concern in the urban service delivery and social exclusion literature for at

least three decades (Bigman & ReVelle 1979, Schönfelder & Axhausen 2003, Cass, Shove &

Urry 2005, Hero 1986, Mclafferty 1982, Talen & Anselin 1998, Tsou, Hung & Chang 2005,

Miller 2006). Within this well-developed and active line of research, attention has primarily

been directed toward the variations in service levels between geographic subunits or social

groupings as a consequence of an uneven spatial distribution of public services and

transportation facilities within a city (Scott & Horner 2008). Not only are local authorities

and policymakers concerned with maximising the accessibility of public services, they are

also sensitive to the degree to which the spatial configuration of service allocation favours

particular constituencies over others.

While numerous studies have sought to analyse the distributional effects of the spatial

configuration of public services, far less attention has been paid to the ways in which

accessibility and equity of accessibility is influenced by amending the opening hours of

226 Chapter 11

service facilities. This may in part be a corollary of the fact that accessibility to services has

traditionally been analysed as a static spatial phenomenon and measured through indicators

based on spatial proximity (for reviews about accessibility measures, see e.g. Pirie 1979, Guy

1983, Handy & Niemeier 1997, Kwan et al. 2003, Neutens et al. 2010a).

Recently however, Neutens et al. (2010b) have begun to substantiate empirically the

importance of accounting for opening hours of service delivery in evaluative studies of

accessibility. Relying on earlier empirical contributions in the realm of time geography (Kim

& Kwan 2003, Schwanen & de Jong 2008, Weber & Kwan 2002, Kwan & Weber 2008), they

have shown that, since people differ much in terms of the location, number, duration and

timing of their mandatory activities, changes to opening hours may remediate or exacerbate

individual disparities in accessibility as much as do amendments to the spatial distribution of

public service facilities.

With this in mind, we have developed a method to identify the temporal regime that

maximises person-based accessibility over (a sample of) a population, which has been

documented in Neutens et al. (2011). While this method provides insights into the margins

within which the overall accessibility can be improved by rescheduling the hours of service

delivery, it neglects the equity of accessibility levels across individuals. In other words,

regimes that maximise the overall accessibility may unintentionally favour particular groups

within the population over others.

In this chapter, we will extend our approach by explicitly introducing equity considerations in

the scheduling process. It is however not our intention to derive directly implementable time

schedules for a network of cooperating service facilities. Rather, the aim is to gain insights

into how and to what extent equity of individual accessibility to public services can be

influenced by amendments to the opening hours of service delivery. To this end, we will use

a person-based measure of space-time accessibility since previous research (Neutens et al.

2010a) has shown that such measures are more appropriate (and more conservative) to

assess equity than traditional place-based measures. This is because person-based measures

are premised on multiple reference locations, reveal interpersonal variations in time

budgets, recognize trip-chaining behaviour, and require only a single run to articulate

variations in accessibility across the diurnal cycle.

Three approaches based on different equity principles are presented to schedule the

opening hours of public service facilities: a utilitarian, an egalitarian and a distributive

approach. These scheduling approaches will be illustrated and validated in a case study on

the public libraries in the city of Ghent, Belgium. As with many other public services, public

libraries want to offer a high and equitable level of access to a large and socially diverse

public. Also, prior research (Cole & Gatrell 1986, Grindlay & Morris 2004, Glorieux, Kuppens

& Vandebroeck 2007, Loynes & Proctor 2000) has repeatedly shown that reduced


accessibility through inadequate opening hours is one of the most important causes of a

decline in annual book issues per capita. Furthermore, local authorities are currently re-

examining the regimes of opening hours of public services within the city of Ghent to better

attune these to the activity patterns of the active citizens. These aspects make our case

study particularly relevant and timely to demonstrate our method.

11.2 Method

11.2.1 Scheduling procedure

All approaches to be presented in this chapter rely on the same core scheduling procedure,

which has been generalised from Neutens et al. (2011) and is pseudocoded in Algorithm

11.1. The basic unit of analysis in the procedure is a minimum opening interval (MOI), i.e. a

Input:

set of individuals

set of all candidate MOIs

accessibility function for an individual with respect to a regime

evaluation function for all accessibility values of all individuals in with respect

to a regime

requested number of MOIs

Output:

output regime (ordered set of MOIs)

Additional variables:

, MOIs

, numerical values

Algorithm:

01:

02: for to

03: for each in

04:

05:

06: if then

07:

08:

09: end if

10: end for

11:

12: end for

13: return

Algorithm 11.1 – Iterative scheduling procedure.

228 Chapter 11

time interval with a predefined minimum duration over which a specific facility is opened

(e.g. facility from 9:00 AM to 10:00 AM). The opening hours of a network of service

facilities can be represented through a set of MOIs, which is further referred to as a regime.

The procedure starts with a population of individuals ; a set of all MOIs to be

considered in the scheduling procedure, further referred to as the candidate set; a function

which returns the value of a person-based accessibility measure for an individual with

respect to a regime , such that higher values indicate higher accessibility; a function for

evaluating a regime on the basis of all accessibility values of all individuals in , such that

a more preferable regime yields a higher value; and the number of requested MOIs to be

included in the resulting regime, i.e. the output of the algorithm.

The output regime which consists of MOIs is built iteratively and in a bottom-up manner,

starting with zero MOIs. Each iteration runs through all MOIs in the candidate set which

are not yet included in so far. Each of these MOIs is a potential candidate to be added to

. The addition of each candidate is evaluated through the calculation of for

. The MOI which addition entails the highest value is then selected and added

permanently to , after which the algorithm takes the next iteration until contains

MOIs.

11.2.2 Equity approaches

In Neutens et al. (2011), the above procedure has been implemented to maximise the

accessibility to a set of public service facilities across a population. However, (public) service

providers are unlikely to maximise accessibility, independently from the distribution of

accessibility across individuals of the population. To account for this distribution,

appropriate evaluation functions ( ) will be specified. In the remainder of this section, we

will present three types of such functions, each of which applies to a different distribution

principle.

Utilitarian approach

In the approach of Neutens (2011), accessibility is maximised across the population,

whereas the equity of accessibility among individuals is disregarded. From an equity

perspective, this constitutes a utilitarian approach which means that utility is maximised

regardless of its distribution (Geurs & Ritsema van Eck 2001). The corresponding evaluation

function is given as the sum of individual accessibility values for a particular regime:

(11.1)

Egalitarian approach

While a utilitarian scheduling maximises the sum of individual accessibility across the

population, the approach will not necessarily lead to the most equitable regime as it


implicitly favours those individuals who can obtain higher absolute accessibility levels.

Hence, we present an egalitarian scheduling which maximises the equity of individual

accessibility, as evaluated by a certain (in)equality metric. Various (in)equality metrics may

be adopted, ranging from simple statistical measures, such as quantile ratios, to more

complex and robust indicators such as the various Gini, Theil and Atkinson indices (Hao &

Naiman 2010). Each of these metrics, when expressed as a function in the appropriate

sense1, may be used as an evaluation function. Let denote such a function. Then,

an egalitarian evaluation function can be expressed as:

(11.2)

Distributive approach

Another alternative to the utilitarian approach, which treats all individuals equally

throughout the scheduling procedure, is a distributive scheduling which grants different

(groups of) individuals a different impact on the scheduling procedure. Distributive

evaluation functions can be expressed as a weighted sum of individual accessibility values.

Let denote the weight of an individual . Then, a distributive evaluation function can be

specified as:

(11.3)

Two cases can be distinguished: (i) a case where only positive or negative weights are

considered; and (ii) a case where both positive and negative weights occur. In case (i), the

scheduling procedure will give priority to the regime which maximises the overall

accessibility, allocating different individuals a different impact in the summation. In this way,

opening hours that are beneficial to individuals with larger weights are preferentially chosen

in the eventual regime. In case (ii), a subtraction is made such that the regime is selected

that maximises the difference in accessibility between a group of favoured and a group of

disfavoured individuals. In this way, the accessibility of one group tends to be increased or

decreased proportionally to the other.

11.3 Case study

An empirical case study is elaborated to illustrate and validate the approaches presented in

section 11.2. The study will explore their effects on the equity of individual accessibility

levels to public libraries in the city of Ghent (Belgium). To this end, a full week regime of

opening hours will be considered. The results will be validated against each other and

against the current regime of opening hours. The purpose of this exercise is to examine to

what extent policy makers can exert influence on the distribution of accessibility among the

1 Since evaluation functions are maximised, the functional form of inequality metrics will have to be rewritten

such that their value increases with increasing equality.

230 Chapter 11

population by rescheduling the opening hours of public services. The remainder of this

section will subsequently discuss input data, computation and results.

11.3.1 Input data

Public libraries, opening hours and candidate set

Information on the location and opening hours of Ghent’s municipal network of public

libraries2 is provided by the official city website (http://www.gent.be). The network consists

of one centrally located main library and 15 branch libraries dispersed across the city (Figure

11.1, Table 11.1). The libraries have a well-structured regime of weekly opening hours with

similar schedules for all branch libraries (Table 11.2). 50 (24%) of the total of 209 hours are

allocated to the main library, whereas most branch libraries individually account for merely

11 hours (5%). The common services delivered in each library include the lending of articles

(books, comic strips, DVDs, etc.), the consultation of reference works, magazines and

informative leaflets, and free surfing on the internet. The main library is by far the most

important in terms of service delivery, and it is the sole library with multiple subdivisions.

Figure 11.1 – Public libraries in Ghent.

2 Public archives and documentation centres will not be considered as they usually do not offer lending services

and attract a rather specific kind of visitors.


No Name Collection Attractiveness

1 Zuid 368 907 12.82

2 Bloemekenswijk 7 387 8.91

3 Brugse Poort 7 669 8.94

4 Drongen-Baarle 7 314 8.90

5 Drongen-Centrum 16 543 9.71

6 Gentbrugge 13 791 9.53

7 Ledeberg 16 765 9.73

8 Mariakerke 15 330 9.64

9 Nieuw Gent 5 837 8.67

10 Oostakker 10 372 9.25

11 Sint-Amandsberg 19 228 9.86

12 St-Denijs-Westrem 9 723 9.18

13 Watersportbaan 4 900 8.50

14 Westveld 8 889 9.09

15 Wondelgem 8 057 8.99

16 Zwijnaarde 10 122 9.22

Table 11.1 – Library collection size (2010) and attractiveness estimate.

Library

Monday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

10:00 AM 11:00 AM 12:00 AM 1:00 PM 2:00 PM 3:00 PM 4:00 PM 5:00 PM 6:00 PM Tuesday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

10:00 AM 11:00 AM 12:00 AM 1:00 PM 2:00 PM 3:00 PM 4:00 PM 5:00 PM 6:00 PM Table 11.2 – Opening hours of public libraries in Ghent

232 Chapter 11

Wednesday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

10:00 AM 11:00 AM 12:00 AM 1:00 PM 2:00 PM 3:00 PM 4:00 PM 5:00 PM 6:00 PM Thursday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

10:00 AM 11:00 AM 12:00 AM 1:00 PM 2:00 PM 3:00 PM 4:00 PM 5:00 PM 6:00 PM

Library

Friday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

10:00 AM 11:00 AM 12:00 AM 1:00 PM 2:00 PM 3:00 PM 4:00 PM 5:00 PM

6:00 PM Saturday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

10:00 AM 11:00 AM 12:00 AM 1:00 PM 2:00 PM 3:00 PM 4:00 PM 5:00 PM

6:00 PM Table 11.2 – (continued)

To populate the candidate set , we have considered MOIs of one hour duration. As public

services are usually not offered on Sundays in Belgium (cf. Table 11.2), these will also not be

considered in the rescheduling. Furthermore, we limit our analysis per facility and per day

from Monday to Saturday, to the MOIs within the range from 8:00 AM to 8:00 PM which


reflects the limits within which public facilities tend to offer services in Belgium. Thus, the

candidate set in this example consists of 1 152 MOIs (= 16 facilities x 6 days x 12 MOIs).

Sample population and accessibility measure

The population of library visitors is sampled through an activity/travel data set consisting of

two-day consecutive diaries of out-of-home activities of Ghent citizens aged five or more.

The sampled individuals are considered representative for the target constituency of Ghent’s

municipal libraries. The travel diaries have been collected in 2000 within the scope of the

SAMBA project (Spatial Analysis and Modeling Based on Activities) (Tindemans et al. 2005).

As households have been randomly sampled, the spatial distribution of home locations

reflects the actual population density with a sparsely populated industrial and port area in

the north of Ghent (Figure 11.2). Individuals sampled at the same day of the week have been

grouped under the assumption that their activities are representative for that weekday. In

total, 5 744 person-days have been used, ranging from Monday to Saturday.

The person-based accessibility measure in this case study relies on Burns’ (1979) utility-

theoretic framework for calculating individual accessibility. This framework has attracted

increased attention in recent years because it is theoretically appealing and can nowadays

straightforwardly be operationalized using geographical information systems (GIS) (see e.g.

Miller 1999, Neutens et al. 2008, 2010a, Hsu & Hsieh 2004, Ashiru, Polak & Noland 2003,

Ettema & Timmermans 2007). Also, prior research (Neutens et al. 2010a) has shown that

Burns-Miller measures are more successful in terms of signifying a state of equity than

traditional place-based measures, since they much better articulate inter-personal

differences for the various dimensions of accessibility they capture. Further, it is noted that

less variation in person-based accessibility would have been obtained, should we have used

a Lenntorp accessibility measure which expresses the cardinality of a choice set. This is

because the number of opportunities (i.e. libraries) in our case study is relatively small (see

Neutens et al., 2010a).

The accessibility for an individual to the MOI of service facility from to is specified

as:

(11.4)

With the set of non-overlapping time intervals within over which

can participate in an activity at ; the attractiveness of facility ; the travel

cost required for to participate in an activity at from to ; the calibration parameter

234 Chapter 11

Figure 11.2 – Sampled households and population density in Ghent.

of negative exponential travel cost decay.

The different components in (11.4) have been implemented as follows. The set

is composed of the positive time intervals within that start at the end

time of a fixed activity of plus the travel time to , and that end at the start time of ’s next

fixed activity minus the travel time from . The determination of thus

requires information on both individual fixed activities and travel times. As the fixity level of

activities has not been documented in the travel diaries, we had to extract fixed activities

manually from the diaries. To this end, the activities belonging to the purpose categories

“work”, “education”, “pick up/drop off” and the like have been considered fixed, given the

difficulty to conduct these activities at other places and times (Cullen & Godson 1975,

Schwanen, Kwan & Ren 2008).

The travel times, on the other hand, have been computed as shortest path times within

ESRI’s ArcGIS Network Analyst (9.3.1) based on TeleAtlas® MultiNet™ (2007.10) road network

data. To this end, we have geocoded the reported locations of fixed activities to the street

level. Shortest path times have been calculated according to the two predominant travel

modes in Ghent, i.e. car and bicycle. To account for individual differences in mobility

resources, it has been assumed that adult car owners with a driving license travel by car,


whereas others travel by bicycle. In addition, car travel times have been corrected for

congestion by means of a factor based on road class, weekday, and time of day, following

Neutens et al. (2011). The congestion factor has been derived from average travel times

recently reported by Maerivoet and Yperman (2008) under the authority of the Federal

Government Service for Mobility and Transport. Each car travel time has been calculated as

the sum of the time shares spent along the different road classes within the shortest path,

weighted by their respective congestion factor. For bicycle travel times, a compromise

approach has been adopted due to the lack of information on dedicated bicycle facilities

(e.g. exclusive non-motorised paths) in Ghent. The approach consists of excluding highways

and other exclusive motorways from the road network and allowing travel directions for

non-motorised travellers3. The travel times have been estimated as the division of the

shortest path distance and an average cycling speed of 15 km/h (El-Geneidy, Krizek & Iacono

2007).

All travel costs in (11.4) have been computed as detour travel times for to

travel to in the time window delimited by the fixed activity immediately preceding and

the fixed activity immediately following , instead of travelling directly in between both fixed

activities. The travel times of the different elements in this detour calculation have been

assessed as described above. The decay parameter of the negative exponential deterrence

function in (11.4) has been estimated on the basis of the observed cumulative distribution of

reported travel times of travel diary trips of individuals visiting a service. Details of its

estimation are available in Neutens et al. (2011). Similar estimates for are obtained for car

(0.081) and bicycle travels (0.092).

For the attractiveness factor in (11.4), we have taken for each library the natural

logarithm of its collection size as a proxy (Table 11.1). The natural logarithm ensures that

attractiveness increases with collection size at a decreasing rate and that adheres to the

economic principle of declining marginal benefits. Ideally we would have liked to

operationalize attractiveness in a more holistic way, for instance by also considering the

variety of books/services on offer and the degree to which libraries are specialised in specific

genres. However, the relevant information for this broader operationalization was not

available to us and we leave this issue for future research. More generally, whilst the

measurements of the facilities’ attractiveness, the travel times and the activity participation

time may be refined in future research, we believe that the current procedures are adequate

for this illustrative case study.

To obtain the accessibility of an individual with respect to a complete regime , as required

in the scheduling procedure, we have applied (11.4) using the following maximative

function:

3 One-way streets for motorised vehicles passable in both directions for bicyclists are common in Ghent.

236 Chapter 11

(11.5)

Thus, in the case of concurrent MOIs of different facilities, only the MOI which offers the

highest accessibility to the individual at hand is accumulated. This is in line with the idea that

individuals may not benefit from having a larger choice set of facilities in case they deliver

very similar services, as is the case for the municipal libraries in Ghent. This reasoning also

relies on the potential of each individual to act as a rationale decision maker who is only

concerned with the most beneficial alternative. One advantage of this assumption and of

adopting a maximative formulation for the accessibility measure is that it becomes

consistent with rational utility theory (see Miller 1999 for more information on this), which is

extensively used for modelling choice behaviour in the field of activity-based travel demand

analysis. Note that, since our sample consists of a slightly different number of observations

per weekday, a weighting factor was added, such that each weekday has an equal weight.

The accessibility level for a regime to an individual obtained from (11.5) is a dimensionless

measure on a ratio scale. While the absolute value of this measure may be of limited value,

it is useful to compare the accessibility levels produced by different regimes. It is noted that

equation (11.5) is only one possible instance of an accessibility measure to be applied in the

iterative selection procedure. Future research may examine the effects of more complex

accessibility measures, such as those that account for a minimum activity duration or

interactions among different household members (Fan & Khattak 2009, Pendyala & Goulias

2002).

11.3.2 Evaluation functions and computation

Having specified the candidate set , the population and the accessibility function ,

we may now derive regimes on the basis of evaluation functions that correspond to the

different equity approaches given in section 11.2.2. In this empirical study, a utilitarian,

egalitarian, and distributive function will be illustrated. The utilitarian evaluation function

has been specified in (11.1). For the egalitarian evaluation function we have adopted a

negative form of Theil’s inequality index (Theil 1967):

with (11.6)

The Theil index is an inequality measure based on the concept of entropy, which turns to 0 in

the case of complete equality and to the natural logarithm of the sample size in the case of

complete inequality (i.e. = 8.66 in this case study). The Theil index was chosen in

this case study for various reasons. First, the Theil index is known to be anonymous and

scale-independent with respect to individual values. In addition, it implements the Pigou-

Dalton principle (Pigou 1912) which states that a transfer of value of higher ranked individual

to a lower ranked individual, as long as this does not inverse the ranking of the two, should


result in greater equity. Also, the Theil index is decomposable, such that it can be obtained

from the weighted sum of Theil indices of different subgroups of the population. Finally,

from a computational point of view, the Theil index is preferable as it can be computed in

linear time with respect to the size of the population, whereas, e.g. for calculating a Gini

coefficient, quadratic time would be required. Since the scheduling procedure requires the

inequality measure to be calculated in each iteration for the addition of each remaining

candidate MOI (Algorithm 11.1), this is an important advantage of the Theil index. To obtain

a valid evaluation function that increases with the desirability of a regime, the negative Theil

index has been used for .

To explore the effects of a distributive scheduling approach, we will consider a progressive

evaluation function with balanced weights (i.e. positive and negative weights). A progressive

approach aims to favour disadvantaged individuals over others (Litman 2002). In the context

of our example, disadvantaged in terms of accessibility means having many space-time

constraints on visiting the municipal libraries. To assess the extent to which people

experience these space-time constraints, we will consider the level of accessibility they can

attain within their constraints in a regime consisting of all candidate MOIs. For individual ,

this level can be assessed as his/her total accessibility over all MOIs in the candidate set ,

i.e. . The evaluation function is specified as:

(11.7)

For we take the median value of over the population. Hence, the population is

split into two halves: a lower half consisting of individuals with more space-time constraints,

and an upper half comprised of individuals with fewer space-time constraints. It is important

to note that these halves represent a distinct social mix of persons in terms of socio-

demographics and residential neighbourhoods. One of the more salient differences between

both groups is the employment status of the individuals, since this characteristic determines

to a large degree the number of temporal constraints an individual faces (see also our earlier

findings in Neutens et al. 2010b). Figure 11.3 represents the composition of the upper and

lower half in terms of employment status. It is found that the lower half consists primarily of

full-time employed persons and students who typically experience many temporal

constraints, whereas the upper half includes more part-time employees and those who are

not gainfully employed (i.e. other) such as housewives, senior citizens and unemployed

persons who tend to have more hours per day available for conducting discretionary

activities such as library visits. Since intends to maximise the relative difference in

accessibility between the lower and upper half, it can be expected that the resulting regime

will alleviate the existing accessibility disparities between, among others, persons from

different employment categories.

238 Chapter 11

The ratio

in (11.7) has been introduced in order to express the accessibility of a regime

relative to (i.e. as a value in the range from 0 to 1). This has been done to ensure

that the impact of individuals on the scheduling procedure is independent of the absolute

value of accessibility (cf. utilitarian regime). In this way, we ensure that the lower and upper

halves have equal impact on the evaluation function.

Figure 11.3 – Composition of the lower and upper halves in terms of employment status.

Having specified , , and , we have automatically computed their corresponding

regimes through an implemented module of the iterative scheduling procedure (Algorithm

11.1). For each regime, we have set the requested number of MOIs to 209 in order to be

consistent with the current regime of opening hours (Table 11.2).

11.3.3 Results

The resulting utilitarian, egalitarian, and distributive regimes are presented in Tables 11.3-

11.5, respectively. For each MOI, the order of its allocation to the regime during the iterative

scheduling procedure has been indicated with a number. Additionally, the MOIs have been

gray-scaled into five equal interval classes of allocation order, with darker shading for earlier

allocated MOIs. The ranking provides insights into the relative importance of different

opening hours within each regime. The distributions of opening hours of different regimes

differ to a considerable degree from one another across both days of the week and libraries.

Utilitarian regime

The utilitarian regime (Table 11.3) clearly shows a hierarchy among the libraries. It allocates

opening hours to merely 7 of the 16 libraries. The first 72 hours have been assigned to the

main library covering the entire study period (Monday to Saturday from 8:00 AM to 8:00

PM). This can be explained by the central location of the main library in a well-populated

21%

42%

8%

29%

lower half

student

full-time employee

part-time employee

other

9%

25%

11%

56%

upper half


area of the city and by its significantly higher attractiveness as a service facility relative to

the other libraries. Evening hours (6:00 PM to 8:00 PM) and hours on Saturday are selected

first by the algorithm and thus produce the highest accessibility over the entire population.

This is due to the fact that people have on average fewer space-time constraints resulting

from fixed activities during these periods. Next, branch libraries 2 and 3 are assigned

opening hours. While the collection size of these offices is rather modest, they are located

along the inner ring road around Ghent and are surrounded by major residential areas.

Hence, they can attract a large number of visitors for whom the main library is not the most

beneficial option in terms of accessibility. Again, opening hours outside the common

business hours in Belgium are assigned first. Finally, the algorithm allocates many opening

hours to branch library 11 as well as a few opening hours to branch libraries 5, 7 and 15.

Besides its high attractiveness and its proximity to densely populated areas, the importance

of library 11 can additionally be explained by its potential to attract visitors along their

commute between their home location and the major employment centre in the port area in

the north of Ghent. Furthermore, it is noted that, of all branches, library 11 currently has the

largest number of opening hours (Table 11.2Table 11.2).

In general, the utilitarian approach tends to cover each possible opening hour of the study

period for at least one of the libraries, whereas concurrent opening hours for two or more

libraries tend to be avoided. This is due to the competition effects that are accounted for by

the maximative form of (11.5), which limits the overall gain in accessibility that can be

obtained from the addition of a concurrent opening hour compared to the addition of a yet

uncovered hour of the study period. In other words, the best strategy to maximise the

overall library access in Ghent is to extend the current range of opening hours (cf. Table

11.2) and to reschedule concurrent hours to cover this extended range.

Egalitarian regime

The egalitarian regime (Table 11.4) is radically different from, and in many ways the

opposite, of the utilitarian regime. While the latter respects a strong hierarchy among

facilities, the egalitarian regime can be described as almost facility-independent: all 16

libraries have been allocated 12-17 opening hours. What is more, Table 11.4 shows that

equity of accessibility is almost entirely determined by the timing of opening hours. The

egalitarian regime clearly prioritizes the latest evening hour (7:00 PM – 8:00 PM) which is

allocated to all libraries on all days of the week. It also prioritizes the first morning hour (8:00

AM – 9:00 AM) which is selected in all cases, except on Monday and Saturday. On Saturday,

people appear to benefit in equal measure during noon (12:00 AM – 1:00 PM), since this

period tends to provide a high accessibility to most individuals. This is inter alia because only

few individuals in our sample reported fixed activities during this period (in-home activities

such as eating have not been reported in the travel diaries). The hour from 10:00 AM to

11:00 AM on Monday also enhances the equity of accessibility levels. This may be attributed

240 Chapter 11

Library

Monday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

8:00 AM 41

115

181

9:00 AM 67

129

192

10:00 AM 72

130

194

11:00 AM 70

124

191

12:00 AM 52

110

186

1:00 PM 57

116

185

2:00 PM 61

121

182

3:00 PM 54

119

175

4:00 PM 35

104

163

5:00 PM 15

84

155

6:00 PM 9

80

140

7:00 PM 3

78

136

Tuesday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

8:00 AM 38

137

199

9:00 AM 59

154

10:00 AM 64

159

11:00 AM 62

151

12:00 AM 47

138

1:00 PM 43

145

202

2:00 PM 42

153

197

3:00 PM 40

148

189

4:00 PM 26

123

177

5:00 PM 12

103

173

6:00 PM 7

86

205

167

7:00 PM 1

85

198

162

Wednesday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

8:00 AM 36

114

190

9:00 AM 50

132

10:00 AM 60

133

11:00 AM 55

131

12:00 AM 37

107

196

1:00 PM 34

106

187

2:00 PM 33

105

184

3:00 PM 30

102

183 4:00 PM 19

97

179

5:00 PM 11 83

178

6:00 PM 4 76

172

7:00 PM 2 75

169

Table 11.3 – Utilitarian regime of 209 opening hours, with indication of the allocation order of each

hour in the scheduling procedure. Allocated hours are gray-scaled according to an equal interval

classification into five classes of the allocation order.


Library

Thursday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

8:00 AM 39

108

9:00 AM 63

125

10:00 AM 68

120

11:00 AM 71

122

12:00 AM 53

109

1:00 PM 56

111

2:00 PM 58

117

3:00 PM 45

112

4:00 PM 32

96

188

5:00 PM 13

79

174

6:00 PM 8

74

170

7:00 PM 5

73

168

207

Friday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

8:00 AM 44 113

193

9:00 AM 65 134

200

10:00 AM 69 135

204

11:00 AM 66 139

208

12:00 AM 49 127

201

1:00 PM 48 126

2:00 PM 51 128

3:00 PM 46 118

195

203

4:00 PM 31 95

176

180

5:00 PM 14 82

165

171

6:00 PM 10 81

161

166

7:00 PM 6 77

160

164

Saturday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

8:00 AM 18 88

144

9:00 AM 27 98

158

10:00 AM 28 100

156

11:00 AM 29 101

152

12:00 AM 25 99

141

1:00 PM 22 91

143

2:00 PM 24 93

149

3:00 PM 23 94

150

4:00 PM 21 89

157

5:00 PM 20 90

206

147 6:00 PM 17 92

146

7:00 PM 16 87

209

142

Table 11.3 – (continued)

242 Chapter 11

Library

Monday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

8:00 AM

9:00 AM

10:00 AM 188 167 129 185 182 156 187 159 138 140 179 181 100 112 139 173 11:00 AM

12:00 AM

1:00 PM

2:00 PM

3:00 PM

4:00 PM

2 198

196 201

194 197 199

195

5:00 PM

6:00 PM

7:00 PM 91 22 64 146 86 92 28 40 46 38 16 80 9 48 50 97

Tuesday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

8:00 AM 190 142 172 164 135 153 178 180 117 141 143 166 89 5 116 183 9:00 AM

10:00 AM

11:00 AM

12:00 AM

1:00 PM

2:00 PM

3:00 PM

4:00 PM

5:00 PM

205

207

6:00 PM

7:00 PM 101 21 76 93 45 24 61 56 31 43 54 55 10 95 57 94

Wednesday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

8:00 AM 192 174 130 4 148 128 177 162 118 104 151 165 87 122 115 158 9:00 AM

10:00 AM

11:00 AM

12:00 AM

1:00 PM

2:00 PM

3:00 PM

4:00 PM

5:00 PM

206

209

6:00 PM

7:00 PM 110 18 59 136 65 25 71 74 33 58 49 82 14 8 39 96

Table 11.4 – Egalitarian regime of 209 opening hours, with indication of the allocation order of

each hour in the scheduling procedure. Allocated hours are gray-scaled according to an equal

interval classification into five classes of the allocation order.


Library

Thursday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

8:00 AM 186 169 119 3 161 127 184 107 114 102 176 150 85 149 133 157 9:00 AM

10:00 AM

11:00 AM

12:00 AM

1:00 PM

2:00 PM

3:00 PM

4:00 PM

5:00 PM

200

203

204

6:00 PM

7:00 PM 103 19 44 121 72 20 73 66 34 35 63 78 13 7 41 83

Friday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

8:00 AM 191 171 125 134 170 126 189 105 123 168 154 160 98 23 131 145 9:00 AM

10:00 AM

11:00 AM

12:00 AM

1:00 PM

2:00 PM

3:00 PM

4:00 PM

202

5:00 PM

6:00 PM

7:00 PM 90 29 60 84 32 12 75 6 30 42 68 70 17 120 51 53

Saturday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

8:00 AM

208

9:00 AM

10:00 AM

11:00 AM

12:00 AM 193 99 132 1 62 113 175 144 111 147 152 52 88 106 137 163 1:00 PM

2:00 PM

3:00 PM

4:00 PM

5:00 PM

6:00 PM

7:00 PM 108 11 79 109 155 15 67 47 36 77 27 124 26 69 37 81

Table 11.4 (continued)

244 Chapter 11

Library

Monday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

8:00 AM 65

156

144

155 173 202

9:00 AM

10:00 AM

11:00 AM

12:00 AM

1:00 PM

2:00 PM

3:00 PM

4:00 PM

5:00 PM 12

126 178

88 56 153 76 120 177 104 39 158

6:00 PM 5

179 64 204 53 37 121 34 146 147 93 62 116 194 7:00 PM 2

151 57 201 42 27 160 19 59 166 103 81 91 115

Tuesday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

8:00 AM 18

189

142

186 129

9:00 AM

10:00 AM

11:00 AM

12:00 AM

1:00 PM

2:00 PM

3:00 PM

4:00 PM 167 171

169

172

170 174 168 205

5:00 PM 11 50

54

163

98

152 71 79 52 159

6:00 PM 8 28

165 36

141 122 63

92 72 89 44 143

7:00 PM 1 26

176 21

83 124 67 123 30 60 84 68 85 188

Wednesday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

8:00 AM 17

139

108

130

9:00 AM

10:00 AM

11:00 AM

12:00 AM

1:00 PM

2:00 PM

3:00 PM 4:00 PM

5:00 PM 15

95

80

110 181 164

6:00 PM 10 61

41

55

99 97

7:00 PM 6 48

31

25 208

105 109

Table 11.5 – Distributive regime of 209 opening hours, with indication of the allocation order of

each hour in the scheduling procedure. Allocated hours are gray-scaled according to an equal

interval classification into five classes of the allocation order.


Library

Thursday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

8:00 AM 16

182

149

9:00 AM

10:00 AM

11:00 AM

12:00 AM

1:00 PM

2:00 PM

3:00 PM

4:00 PM 197

199 207

200 198

5:00 PM 13 100

154 69 145 196 150 90 46 157

114

6:00 PM 7 45 180 187 40 138 193 106 87 24 161

96 190

7:00 PM 3 35 162 70 23 119 183 94 102 20 75 195

136 140

Friday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

8:00 AM 32

184 74

9:00 AM

10:00 AM

11:00 AM

12:00 AM

1:00 PM

2:00 PM

3:00 PM

4:00 PM

132

206

134

131

133 135

5:00 PM 14

175

49 117

112 86 38

137

66 111

6:00 PM 9

82

43 113 203 148 77 29

125

51 101

7:00 PM 4 58 185 127 33 107 191 118 73 22 209 128

47 78 192

Saturday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

8:00 AM

9:00 AM

10:00 AM

11:00 AM

12:00 AM

1:00 PM

2:00 PM

3:00 PM 4:00 PM

5:00 PM

6:00 PM

7:00 PM

Table 11.5 – (continued)

246 Chapter 11

to the fact that many people are prohibited from visiting a library within this hour, since they

are constrained by fixed activities reported in their diary. In short, it seems that the best

strategy to improve equity of accessibility among the population is to select simultaneous

opening hours for different facilities at strategic times of the day.

Distributive regime

The distributive regime (Table 11.5) returns another distinct pattern. Whereas in the

utilitarian and egalitarian case, opening hours are well distributed among all days, the

distributive regime has no opening hours on Saturday. This is an artefact of the non-

longitudinal travel diary data consisting of person-days: since most individuals have much

discretionary time on Saturday, it appears to be difficult to advantage individuals with fewer

space-time constraints (lower half) over individuals with more constraints (upper half) on

Saturdays. The same reasoning, albeit to a lesser extent, applies to Wednesdays when most

part-time workers do not work or only work half a day in Belgium. The evening, late

afternoon and early morning hours on other weekdays, on the other hand, are abundantly

covered by all libraries. This pattern mirrors the common timing of discretionary time

budgets of the persons who experience many space-time constraints, including in particular

full-time workers and students (see Figure 11.3).

Accessibility and equity

Beyond the variations in opening hours, we can also evaluate the regimes in terms of their

distribution of accessibility levels4 ( ) across individuals and the equity thereof. To this end,

Figure 11.4 displays a Box-and-Whisker diagram which depicts the spread of accessibility

levels for each regime, and Figure 11.5 presents the inequality of this distribution, measured

by the Theil index. The current regime has been included in these figures as a reference.

Figure 11.4 and Figure 11.5 demonstrate that the distribution of accessibility among

individuals strongly depends on the scheduling approach. The largest increase in accessibility

relative to the current regime can be realised with the utilitarian approach (Figure 11.4),

which confirms its objective. However, the accessibility levels in this regime have a large

spread and are relatively unequally distributed among the population, as is reflected by the

high Theil index (Figure 11.5). The egalitarian approach, on the other hand, offers the lowest

average accessibility level, but produces by far the smallest spread in accessibility levels

(Figure 11.4) and the most equity (i.e. the lowest Theil index) (Figure 11.5). In other words, in

our case study striving for equity among the entire population comes at the expense of the

absolute level of accessibility. This is because, while it is feasible to offer every individual a

comparably low level of accessibility, high accessibility levels cannot be allocated equally

given the substantial differences in the extent of space-time constraints across the

respondents in the sample. Finally, the distributive regime lies somewhere in between the

4 The accessibility levels (A) are calculated for each regime using equation (11.5).


current and egalitarian regime, in terms of the average, the spread and the equity of

accessibility levels. This can be explained by the progressive configuration of the distributive

evaluation function (section 11.3.2): it intends to favour the individuals with more space-

time constraints (lower half) relative to the individuals with fewer space-time constraints

(upper half).

To further validate the distributive approach, we will consider the Box-and-Whisker diagram

of individual accessibility for the lower and upper half of the population separately, as

displayed in Figure 11.6. While for all regimes, the upper half has higher accessibility levels

than the lower half, this difference is smaller for the egalitarian and distributive regimes. In

terms of average accessibility, the distributive regime yields the smallest absolute and

relative difference among both halves (14.9 for the lower half and 19.7 for the upper half).

Also, this regime entails the second highest average accessibility level for the lower half. In

other words, changing the opening hours of public service facilities using a distributive

approach can be a successful strategy to alter the existing disparities in accessibility between

people with different space-time constraints. However, the average accessibility level over

the entire population (17.3) is lower compared to the current (24.2) and utilitarian regime

(38.6). Thus, as for the egalitarian regime, a progressive distribution of accessibility comes at

the expense of the absolute level of accessibility. Nonetheless, given that the decrease in

average accessibility relative to the current regime is smaller than in the egalitarian case, a

progressive distributive approach may be more appropriate if the aim is to improve the

accessibility of those who experience most space-time constraints in their daily life.

Figure 11.4 – Box-and-Whisker diagrams of the accessibility level per regime.

0

20

40

60

80

100

120

Current Utilitarian Egalitarian Distributive

Acc

essi

bili

ty le

vel (

A)

Regime

248 Chapter 11

Figure 11.5 – Theil index of the accessibility level per regime.

Figure 11.6 – Box-and-Whisker diagrams per regime for the lower (left) and upper (right) halves of

the population.

0.33

0.27

0.10

0.30

0,0

0,1

0,2

0,3

0,4


Thei

l In

dex

Regime

0

20

40

60

80

100

120

140


Acc

essi

bili

ty le

vel (

A)

Regime


11.4 Conclusion

In contrast to prior accessibility studies that have focused on the spatial organisation of

public service delivery, this chapter has explored the ways in which equity of individual

accessibility to services within the population can be influenced by adapting the opening

hours of service facilities. To this end, three different scheduling approaches – utilitarian,

egalitarian and distributive – have been elaborated within a generalised iterative scheduling

procedure. While the utilitarian approach aims to compose a regime that offers the highest

overall accessibility, the egalitarian approach seeks to find a regime that maximises the

equity of accessibility levels across individuals. The distributive approach, on the other hand,

uses different weights for different individuals in the scheduling procedure to favour certain

(groups of) individuals and/or disfavour others.

The three scheduling approaches have been implemented and applied in a detailed

empirical case study focusing on the rescheduling of a standard week regime of opening

hours for the municipal libraries in Ghent (Belgium). The resulting time schedules showed

significant differences in terms of the distribution of opening hours among facilities, as well

as across the days of the week and times of the day. We have also demonstrated that

rescheduling according to the various approaches strongly affects the distribution of

individual accessibility and the equity of accessibility. All scheduling approaches have

thereby clearly shown to validate their purpose. Of all scheduling regimes, the utilitarian

regime caused the largest increase in average accessibility, while the egalitarian regime

produced the most equitable regime. However, the improvement in equity realised by the

egalitarian regime was offset by a decrease in the absolute level of accessibility. Finally, we

were able to demonstrate that the distributive approach is effective in redistributing

accessibility among different groups of individuals. The distributive regime combines to a

certain extent the merits of the other two approaches: it offers a higher level of accessibility

than the egalitarian approach and a more compact and equitable distribution of individual

accessibility compared to the utilitarian approach.

This chapter extends the existing literatures about space-time accessibility analysis, urban

service delivery and social exclusion by showing to what extent equity in individual space-

time accessibility can be influenced by changing the opening hours of service delivery. From

a policy point of view, this is an important achievement because it enables ex-ante and ex-

post evaluations of different configurations of opening hours of services and their

consequences in terms of equity. Understanding the relationship between opening hours

and equity of accessibility is also important in view of the growing awareness of the impact

of urban time policies on people’s quality of life (Neutens et al. 2011). In Ghent as well as in

many other European cities, local authorities are currently re-examining the historically

emerged opening hours of their municipal services in order to better attune these to the

temporal needs and desires of the citizens, especially those who have multiple competing

250 Chapter 11

claims on their time (Mareggi 2002, Boulin 2006). This chapter contributes to these lines of

inquiry by providing additional insights into how (equity of) individual accessibility can be

improved by amendments to the temporal structure of urban systems.

The generality of the proposed iterative scheduling procedure and its arbitrary evaluation

function enables to apply the methodology to various aspects linked to the space-time

accessibility of opportunities to individuals. For instance, beyond the equity of accessibility,

the effects of opening hour scheduling on other variables connected to accessibility within

social welfare research and policies (cf. Rouwendal & Rietveld 1999), including indicators of

urban liveability (Pacione 1990) and social capital (Adler & Kwon 2002), can be assessed.

Other possible extensions can be found in urban and transport planning and policy making.

For example, it would be useful to consider evaluation functions which incorporate the

effects of opening hours and space-time accessibility on congestion times in order to control

the flows of traffic by means of rescheduling business hours. The results of such studies

could be compared to the predictions of alternative planning initiatives such as investments

in the spatial transport infrastructure or road pricing systems (Gutiérrez, Condeço-

Melhorado & Martín 2010). It is our aim to continue this line of research about the effects of

opening hour policies in future studies.

References

Adler, P. S. & Kwon, S.-W. (2002) Social capital: Prospects for a new concept. The Academy of

Management Review, 27, 1, 17-40.

Ashiru, O., Polak, J. & Noland, R. (2003) Space-time user benefit and utility accessibility measures for

individual activity schedules. Transportation Research Record: Journal of the Transportation

Research Board, 1854, 1, 62-73.

Bigman, D. & ReVelle, C. (1979) An operational approach to welfare considerations in applied public-

facility-location models. Environment and Planning A, 11, 1, 83-95.

Boulin, J. Y. (2006) Local time policies in Europe. In Gender Divisions and Working Time in the New

Economy: Changing Patterns of Work, Care and Public Policy in Europe and North America,

eds. D. Diane Perrons, C. Fagan, L. McDowell, K. Ray & K. Ward, Northhampton, MA: Edward

Elgar, 459-460.

Burns, L. D. (1979) Transportation, Temporal, and Spatial Components of Accessibility. Lexington,

Massachusetts: Lexington Books.

Cass, N., Shove, E. & Urry, J. (2005) Social exclusion, mobility and access. The Sociological Review, 53,

3, 539-555.

Cole, K. J. & Gatrell, A. C. (1986) Public libraries in Salford: a geographical analysis of provision and

access. Environment and Planning A, 18, 2, 253-268.

Cullen, I. & Godson, V. (1975) Urban networks: the structure of activity patterns. Progress in

Planning, 4, 1-96.

El-Geneidy, A. M., Krizek, K. J. & Iacono, M. J. (2007) Predicting bicycle travel speeds along different

facilities using GPS data: a proof of concept model. In Proceedings of the 86th Annual


Meeting of the Transportation Research Board (TRB), Compendium of Papers. Washington,

DC, USA.



Fan, Y. & Khattak, A. J. (2009) Does urban form matter in solo and joint activity engagement?

Landscape and Urban Planning, 92, 3-4, 199-209.

Geurs, K. T. & Ritsema van Eck, J. R. (2001) Accessibility Measures: Review and Applications, RIVM

Report 408505006, Bilthoven: National Institute for Public Health and the Environment, 265.

Glorieux, I., Kuppens, T. & Vandebroeck, D. (2007) Mind the gap: Societal limits to public library

effectiveness. Library & Information Science Research, 29, 2, 188-208.

Grindlay, D. J. C. & Morris, A. (2004) The decline in adult book lending in UK public libraries and its

possible causes – II. Statistical analysis. Journal of Documentation, 60, 6, 632-657.

Gutiérrez, J., Condeço-Melhorado, A. & Martín, J. C. (2010) Using accessibility indicators and GIS to

assess spatial spillovers of transport infrastructure investment. Journal of Transport

Geography, 18, 1, 141-152.

Guy, C. M. (1983) The assessment of access to local shopping opportunities: A comparison of

accessibility measures. Environment and Planning B: Planning and Design, 10, 2, 219-238.

Handy, S. L. & Niemeier, D. A. (1997) Measuring accessibility: An exploration of issues and

alternatives. Environment and Planning A, 29, 7, 1175-1194.

Hao, L. & Naiman, D. Q. (2010) Assessing Inequality: Quantitative Applications in the Social Sciences,

SAGE Publications, 160.

Hero, R. E. (1986) The urban service delivery literature: Some questions and considerations. Polity,

18, 4, 659-677.

Hsu, C. I. & Hsieh, Y. P. (2004) Travel and activity choices based on an individual accessibility model.

Papers in Regional Science, 83, 2, 387-406.




Kwan, M.-P., Murray, A. T., O'Kelly, M. E. & Tiefelsdorf, M. (2003) Recent advances in accessibility

research: Representation, methodology and applications. Journal of Geographical Systems, 5,

1, 129-138.

Kwan, M. P. & Weber, J. (2008) Scale and accessibility: Implications for the analysis of land use-travel

interaction. Applied Geography, 28, 2, 110-123.

Litman, T. (2002) Evaluating transportation equity. World Transport Policy & Practice, 8, 2, 50-65.

Loynes, R. & Proctor, R. (2000) The effect of reductions in public library opening hours on book

issues: A statistical analysis. Journal of Documentation, 56, 6, 605-623.

Maerivoet, S. & Yperman, I. (2008) Analyse van de Verkeerscongestie in België: Rapport in Opdracht

van de Federale Overheidsdienst Mobiliteit en Vervoer. Leuven (Belgium): Transport &

Mobility Leuven, 78.

Mareggi, M. (2002) Innovation in urban policy: The experience of Italian urban time policies. Planning

Theory & Practice, 3, 2, 173-194.

Mclafferty, S. (1982) Urban structure and geographical access to public services. Annals of the

Association of American Geographers, 72, 3, 347-354.

252 Chapter 11

Miller, H. J. (1999) Measuring space-time accessibility benefits within transportation networks: Basic

theory and computational procedures. Geographical Analysis, 31, 2, 187-212.

Miller, H. J. (2006) Social exclusion in space and time. In Moving through Nets: the Physical and Social

Dimensions of Travel, Selected papers from the 10th International Conference on Travel

Behaviour Research, ed. K. W. Axhausen, Elsevier Science, 380.

Neutens, T., Delafontaine, M., Schwanen, T. & Van de Weghe, N. (2011) The relationship between

opening hours and accessibility of public service delivery. Journal of Transport Geography,

forthcoming.

Neutens, T., Schwanen, T., Witlox, F. & De Maeyer, P. (2008) My space or your space? Towards a


Neutens, T., Schwanen, T., Witlox, F. & De Maeyer, P. (2010a) Equity of urban service delivery: A


1635.

Neutens, T., Schwanen, T., Witlox, F. & De Maeyer, P. (2010b) Evaluating the temporal organization


1039-1064.

Pacione, M. (1990) Urban liveability: a review. Urban Geography, 11, 1, 1-30.

Pendyala, R. M. & Goulias, K. G. (2002) Time use and activity perspectives in travel behavior research.

Transportation, 29, 1, 1-4.

Pigou, A. F. (1912) Wealth and Welfare. London: Macmillan.

Pirie, G. H. (1979) Measuring accessibility: Review and proposal. Environment and Planning A, 11, 3,

299-312.

Rouwendal, J. & Rietveld, P. (1999) Prices and opening hours in the retail sector: welfare effects of

restrictions on opening hours. Environment and Planning A, 31, 11, 2003-2016.

Schönfelder, S. & Axhausen, K. W. (2003) Activity spaces: measures of social exclusion? Transport

Policy, 10, 4, 273-286.




constraints and geographies of everyday activities. Geoforum, 39, 6, 2109-2121.

Scott, D. M. & Horner, M. (2008) The role of urban form in shaping access to opportunities. Journal of

Transport and Land Use, 1, 2, 89-119.

Talen, E. & Anselin, L. (1998) Assessing spatial equity: an evaluation of measures of accessibility to

public playgrounds. Environment and Planning A, 30, 4, 595-613.

Theil, H. (1967) Economics and Information Theory. Chicago, IL: Rand McNally and Company.

Tindemans, H., Van Hofstraeten, D., Verhetsel, A. & Witlox, F. (2005) Spatial analysis and modeling

based on activities. A pilot study for Antwerp and Ghent, Belgium. In Spatial Planning, Urban

Form and Sustainable Transport, ed. K. Williams, Aldershot: Ashgate Publishers, 61-82.

Tsou, K. W., Hung, Y. T. & Chang, Y. L. (2005) An accessibility-based integrated measure of relative

spatial equity in urban public facilities. Cities, 22, 6, 424-435.

Weber, J. & Kwan, M. P. (2002) Bringing time back in: A study on the influence of travel time

variations and facility opening hours on individual accessibility. Professional Geographer, 54,

2, 226-240.

Discussion and conclusions 253

12 Discussion and conclusions

This concluding chapter discusses the main contributions, results, and findings of this

dissertation, as well as the limitations of these achievements and opportunities for further

research. Given that specific contributions and conclusions have already been stated within

each chapter, this section in addition intends to disclose the links that interconnect these

chapters as well as their situation within the broader literature. In support of the discussion

and to offer feedback on the earlier stated objectives and research questions (section 1.2),

an overview table of main and application-oriented contributions is presented in Table 12.1.

Part I – Moving objects

To begin with, a number of important contributions are made to the Qualitative Trajectory

Calculus (QTC). Given that QTC is unique in being a qualitative spatiotemporal calculus

dedicated to handling interactions among moving objects, these contributions add to a

notably exclusive framework in the research field of moving objects. The theoretical

overview presented in Chapter 2 may in the first place be contemplated an umbrella

contribution vis-à-vis QTC in general, and the related chapters of this work in particular

(Chapters 3-5). However, the chapter also makes some prominent theoretical contributions,

including the introduction of a conceptual neighbourhood diagram (CND) and composition-

rule tables (CRTs) for QTCC. These additions supply to the missing links in earlier works and

augment the reasoning power of QTCC significantly. Furthermore, Chapter 2 discusses some

vital issues regarding QTC-based information systems, such as potential extensions of QTC

and how the calculus can deal with incomplete information (e.g. tracking data).

Chapter 3 contributes to the formal definition of QTCN and explores its reasoning power

through elaborating the composition of QTCN relations and examining the ability to use QTCN

for answering qualitative questions. QTCN is a key type of QTC due to its consideration of

network-constrained movement, since networks are by far the most commonly modelled

and studied travel environment for conducting mobile objects in geographical space. Its

application field therefore primarily lies in transportation, and particularly in geographical

information systems for transportation (GIS-T) (Shaw 2010). The restriction of QTCN to static

networks may however be regarded as a harmful limitation, given that in many cases

transportation networks can be more realistically modelled as dynamic environments with

time-varying properties. Chapter 4 tackles this issue through investigating how dynamic

networks would affect QTCN relations as well as their transitions, conceptual

neighbourhoods and compositions. These findings are embraced in the definition of a novel

calculus (QTCDN’) which differs from QTCN in its underpinning of dynamic networks able to

undergo topological changes. Although other types of changes may influence QTCN relations,

topological changes merit particular attention since they are the most fundamental changes

in a network, impinging on its structure of connected nodes and edges. It is worthwhile to

254 Chapter 12

Cap Main contributions

(objective 1)

Application-oriented contributions (objective 2)

Pa

rt

I

– M

ov

ing

ob

je

ct

s 2

Overview of QTC

CND and CRTs for QTCC

Extensions of QTC

Representing incomplete information

Traffic scene example

3

Formal definition of QTCN

Canonical cases for QTCN

Composition of QTCN relations

Transformation to RTCN relations

Police/gangster example

Collision avoidance applications

4 Definition of QTCDN’

CND for QTCDN’ Extension of QTCN to dynamic

networks

5

Conceptual model for QTC-based information systems

Implementation methodology

Implementation prototype

QTC-based information system

Traffic scene case study

Squash rally case study

6 Extension of sketch map ontology

Typology of MPO trajectory representations in sketch maps

Theoretical support for sketch-based information systems

Pa

rt

II

–

Tr

av

ell

ing

su

bj

ec

ts

7 Application of sequence alignment

methods to analyse patterns in Bluetooth tracking data

Empirical case study on visitors at a trade fair

8 Incorporation of uncertainty in STPs

Formal definition of rough obstacle-constrained STPs

Implementation of rough obstacle-constrained STPs

Example case study

9

Formal definition of reverse STPs

Formal definition and implementation of place-based accessibility measures derived from reverse STPs

User-friendly designed end-user GIS toolkit for measuring and mapping accessibility

Example case study

10 Procedure for scheduling service

opening hours to optimise individual accessibility

Empirical case study on accessibility of government offices

11

Generalisation of scheduling procedure of Chapter 10

Utilitarian, egalitarian and distributive scheduling approaches

Empirical case study on accessibility of municipal libraries

Table 12.1 – Main and application-oriented contributions.

remark that the topological changes modelled in QTCDN’ may not only represent physical

topological changes, such as those controlled by switches in railway networks. They may also

model virtual changes such as temporary disconnections of roads at a red traffic light (Ding

& Güting 2004), or temporary connections among different transport modes in multi-modal

transportation networks (Lysgaard 1992). The definition of QTCDN’ is a major step forward in

view of potential network analysis applications for QTC, also because nowadays information

systems such as routing services and monitoring systems increasingly adopt dynamic

networks (Jahn et al. 2005, Zografos & Androutsopoulos 2008, Köhler, Möhring & Skutella


2009). Although discrete topological changes support the modelling of many different types

of changes in dynamic networks, they are inappropriate to represent changes that affect

travel costs continuously. The effect on travel time of a growing traffic jam in a road

network, for example, may be more adequately modelled as a continuous function rather

than a discontinuous shift. This particularly concerns to QTC because of its consideration of

continuous space and time. Although this issue has already been briefly studied in earlier

work (Delafontaine et al. 2006, Bogaert & Delafontaine 2006), a dedicated extension of QTCN

to formally incorporate continuous network changes would be a significant complementary

step.

Although Chapters 3 and 4 have not explicitly addressed the implementation of network-

based QTC calculi in information systems, they at least provide the necessary theoretical

basis to support such operationalizations. The issue of implementing QTC is thoroughly

addressed in Chapter 5, presenting a conceptual data model for QTC-based information

systems, an application prototype (QTCAnalyst), and two illustrative case studies. Although

QTCAnalyst is confined to the basic (QTCB) and double-cross (QTCC) calculi, the proposed

conceptual model is generic for QTC, thus including the network-based calculi. Therefore,

the contributions of Chapter 5 have taken QTC from a purely theoretical formalism to the

point where it can be picked up by computer scientists, software engineers and information

system developers.

The use of QTC in applications has been highlighted in several discussions and case studies

throughout Chapters 2-5. Especially applications related to traffic scene analysis and

monitoring have been put forward (e.g. sections 2.8, 3.7.2, and 5.4.1). Importantly, even

though most traffic scenes are embedded in networks, the traffic scene examples in

Chapters 2 and 5 have been elaborated using non-network-constrained calculi. This reveals

how the complementarities among different QTC types may support a certain scaling ability

in the analysis. For example, while road networks may be modelled at the overall spatial

level by the graph-based sets of interconnected linear features adopted in QTCN and QTCDN’,

a two-dimensional constrained open space will be more appropriate for an analysis of car

interactions and driving behaviour at the level of individual roads and lanes. The scaling

ability of QTC could be extended further by defining even more types of QTC, thereby

considering increasingly finer categorisations of the quantity spaces that underlie the

qualitative relations, ultimately arriving at quantitative information in case of an infinite

discretisation. This idea, however, conflicts with the basic tenet of qualitative information

which intends to distinguish categories that are relevant and essential to the behaviour

being modelled (Cohn 1996). In QTC, simple {-,0,+} quantity spaces are adopted, and

therefore, QTC relations involve a fair degree of abstraction. Whether or not, and to what

extent this level of abstraction restricts the applicability of the calculus remains a pertinent

question which has only been answered partly in this dissertation.

256 Chapter 12

When reconsidering the first and second research questions of section 1.2, it is noted that,

while the adequacy of QTC to represent and reason about moving objects in realistic

scenarios has been discussed and illustrated in several applications, a profound study of the

added value of the calculus versus other (prevailing) formalisms, e.g. alternative qualitative

approaches such as those of Dylla et al. (2007), Wolter et al. (2007), Hornsby & King (2008),

and Pommerening, Wölfl & Westphal (2009), has been lacking in each of these cases. Given

the yet mentioned abstraction of QTC relations, one of the calculus’ plus-points may be its

robustness to handle large sets of moving objects, e.g. moving objects databases (MODs)

(Güting & Schneider 2005, Wolfson & Mena 2005, Revesz 2010). Yet, since each of the

examples in Part I has involved but a limited number of objects, an empirical assessment of

this robustness is still to be done. Also, and despite this potential robustness, it is

questionable whether a calculus of binary relations is suitable for reasoning about multiple

objects. Although the matrix representation proposed in section 2.7.1 offers an elegant

solution, it bypasses the question of whether reasoning about more than two moving

objects also requires relations that associate more than two objects.

Against the above implied opportunities for further elaboration, it is observed that some

theoretical results of Part I warrant weaknesses of the QTC calculus that should not be

denied. Among these are the weak results obtained from the composition of QTCN1 relations

(section 3.5), and the granularity dependence of stable relations (section 5.5(e)). An

important lesson to be learned from these deficiencies is that implementations such as

QTCAnalyst should not be regarded as stand-alone solutions. Rather they require to be

embedded as assistant tools which confront and integrate QTC results with information

obtained from other sources or formalisms. In this respect, an important opportunity to

underpin the further development of QTCAnalyst to one or more genuine and application-

specific end-user information systems consists of equipping the prototype with quantitative

information and operations. Quantitative information and methods are known to

complement their qualitative counterparts, and – given the limitations of QTCAnalyst listed

in section 5.5 – their integration may hence be inevitable in order to maximise the

application capabilities. For instance, when applying QTC for reasoning about large

databases of moving objects, such as cars in a city or visitors at a mass event, a function for a

priory selecting those objects that are possibly interacting with each other would be

recommended (cf. section 5.5(g)). Such a selection function cannot be obtained via QTC

alone. Instead, a quantitative distance measure could be introduced to implement such a

function. Quantitative methods would also be useful in support of more detailed posterior

analyses of relevant events, situations, or behaviours that have been a priory detected

through the analysis of QTC relations.

1 Even weaker composition results may be expected for QTCDN’ due to the relaxation of spatiotemporal

constraints in dynamic networks.


In addition and in contrast to the integration of quantitative methods, another worthwhile

opportunity to extent the QTCAnalyst prototype relates to the competence of qualitative

formalisms to handle incomplete or imperfect information (Kuipers 1994), in particular

information originating from human cognition or communication such as natural language

expressions and freehand drawings (Forbus 1997, Kuehne & Forbus 2002, Van de Weghe et

al. 2007). To this end, appropriate modalities to input and extract moving objects data

stemming from such sources are to be developed. In this respect, Chapter 6 contributes to

the support of sketch-based input, by extending the concept and ontology of freehand

sketch maps in order to represent moving point objects and their trajectories. A typology of

glyphs representing trajectories in sketch maps is introduced and some important links

between spatiotemporal characteristics of trajectories and such glyphs are revealed. These

are relevant in order to automate the interpretation of trajectories from sketches.

Information systems to reason about moving objects interpreted from sketch maps could be

useful to assist empirical evaluations of human sketching behaviour observed when

sketching about dynamic phenomena (cf. Blaser 2000), e.g. to substantiate an objective

categorisation of sketching behaviour, or to appraise human adequacy and skills in sketching

about moving objects and/or in understanding such sketches. Such systems are, among

others, relevant to the field of cognitive mapping and wayfinding (Golledge 1999), which

often relies on sketch maps in empirical studies, in order to enhance the interpretation of

human travelling behaviour (cf. Part II). However, the typology presented in Chapter 6 also

heralds some pitfalls which hamper a straightforward operationalization of information

systems involving sketch-based moving objects. Perhaps the most stringent of these is the

difficulty to represent objects that evolve continuously and simultaneously in time through

conventional freehand sketching. This shortcoming is also relevant in view of the possible

development of sketch-based input modalities for QTCAnalyst given the continuous

interactions which underlie QTC relations. One solution to this problem, left for future

research, may be the consideration of additional sketch content obtained from other

communication means apart from sketching s.s., such as speech and annotations.

Yet another avenue for further development lies in the extraction of information through

the analysis of conceptual animations or patterns of QTC relations, such as the overtake

events or squash rally patterns extracted in section 5.4. Conceptual animations may offer

insights into movement behaviour over a longer time window. For instance, drawing on the

cognitive aspects of the QTCC reference frame, which is based on Freksa’s (1992) double

cross, the observed relation patterns in the squash rally example (section 5.4.2) may actually

capture essential distinctions about the movement interaction perceived by both players

and by consequence reflect their perception and cognition during the course of the rally. If

the existence of such correlations can be empirically assessed, this would allow comparative

analyses of QTC animations across both games and players to be linked to the results of the

games and to the performance of the players, and in this respect for instance assist

258 Chapter 12

applications in sports performance analysis and management (Gratton & Jones 2009,

O’Donoghue 2009, Horne et al. 2011, Skinner & Edwards 2011). One notable technique to

consider in order to further elaborate the analysis of QTC animations is sequence alignment

(Morrison 2010). Alike qualitative calculi, sequence alignment methods (SAM) rely on a

discrete categorisation of quantitative information and they employ an explicit capability to

handle incomplete knowledge. Moreover, SAM may offer an interesting opportunity to

extract information across multiple objects in order to make inferences about individual QTC

animations.

Part II – Travelling subjects

The issue of SAM leads to the second part of this dissertation. In Chapter 7, SAM have been

applied as a data mining technique to detect behavioural patterns from Bluetooth tracking

data of visitors at a big indoor trade fair. The empirical results suggest that the approach is

suitable to discover knowledge about revealed space-time behaviour, for instance, to

underpin a typology of behavioural patterns. Furthermore, the case study demonstrates that

Bluetooth tracking is a powerful data acquisition method in this context which allows for the

anonymous and unannounced tracking of a mass of individuals. Although the positional and

temporal accuracy of Bluetooth sensing is limited, it is to some degree controllable and

perhaps preferable to other techniques, thereby considering that GPS signals are usually

obstructed in indoor environments. Chapter 7 shows that the limitations of Bluetooth

tracking data are partially offset by the theoretical ingenuity of SAM, which underlines the

usefulness of the approach. For example, to fill the gaps in the observation sequences of one

individual, SAM exploit the entire dataset of Bluetooth observations. A further validation of

the empirical results would however benefit from ongoing research regarding the

calibration, reliability, and scalability of SAM when applied to tracking data (Wilson 2006,

Shoval & Isaacson 2007).

Apart from its yet described strengths, some significant weaknesses of Bluetooth tracking

techniques are worthwhile discussing in the light of the third research question (section 1.2).

To begin with, apart from increasing the data acquisition accuracy and reducing data noise,

an important sampling problem has to be tackled. The uncertainty about the ratio of tracked

individuals to the total population considerably limits the interpretation and extrapolation of

results of analyses of Bluetooth observations. Given that the actual ratio of tracked devices

may well fluctuate in space and time as well as across different socio-economic groups of

individuals, the applicability of Bluetooth tracking experiments that do not include an

alternative reference data collection method is questionable. According to Girardin et al.

(2008), Bluetooth tracking experiments also suffer from a low scalability in terms of the

ability to deploy these across different spatial contexts. Another of their concerns relates to

the privacy and ethical issues of Bluetooth tracking experiments without individual’s consent

(see also Wong & Stajano 2005, Gutman & Stern 2007, Hay & Harle 2009). The risk of


identifying individuals or organisations is especially pertinent in view of the improvement of

the sensing accuracy. Furthermore, unannounced tracking experiments generally go hand in

hand with a lack of additional attributes such as socio-economical variables, which severely

reduces the potential for conducting empirical studies beyond investigations of strictly

spatiotemporal behaviour. Therefore, important research challenges lie ahead with respect

to combining and enriching Bluetooth tracking with other data collection techniques.

Bluetooth tracking data usually consists of discrete time-stamped observations of individuals

– or rather their devices – in the neighbourhood of Bluetooth sensors. In many cases, the

chronological path of Bluetooth observations sampled from one individual cannot be

interpolated to a representative continuous trajectory, which precludes the derivation of

higher motion attributes such as motion azimuth and velocity, and by consequence

conducting analyses building on these attributes, such as reasoning with QTC. One way to

cope with this shortcoming is to consider potential paths. In other words, while failing to

delineate an individual’s precise trajectory (i.e. revealed behaviour), we may focus on where

(s)he could (not) have been given the information at hand (i.e. potential behaviour).

Chapter 8 offers an original approach to enable the analysis of potential behaviour starting

from raw tracking data. To this end, the classical time geographical concept of a space-time

prism (STP) is enriched in two ways. First, since each data acquisition method involves a

certain amount of uncertainty stemming from spatial and temporal inaccuracies, errors and

failures, noise, etc., the traditional STP is extended to account for the uncertainty of sampled

anchor points. Drawing on the principles of rough set theory, this uncertainty is accounted

for through the definition of rough STPs. Second, to overcome the restriction of

conventional STPs to model travel in isotropic unconstrained spaces, these are embedded in

a travel environment constrained by discrete impassable obstacles.

The consideration of obstacle-constrained environments goes against the tendency to model

STPs in network-constrained environments (e.g. Neutens et al. 2008b, Miller & Bridwell

2009, Kuijpers & Othman 2009, Kuijpers et al. 2010). Actually, it complements this tendency

because network-based models are inappropriate to handle constrained open spaces such as

public parks and gardens, golf courses, or beaches. Also, more than network-based

frameworks, the obstacle-constrained worldview supports analyses at a micro level spatial

scale. Especially when zooming in on dense urban and built areas, many environments,

including indoor locations (e.g. the trade fair in Chapter 7), may be perceived as accessible

spaces populated with inaccessible obstacles. The combination of both rough and obstacle-

constrained STPs affords analysts the valuable potential to study potential behaviour starting

from tracking data collected within obstacle-constrained environments. Not only does

Chapter 8 provide a formal definition for rough obstacle-constrained STPs, an algorithm to

automatically generate these prisms given a set of individual sample points, uncertainty

parameters, and obstacles is developed and illustrated as well. Hence, beyond theoretically

260 Chapter 12

contributing to time geography, the chapter offers a ready-made procedure which opens the

door for empirical investigations of potential behaviour.

One theme of empirical studies where the analysis of potential behaviour by definition plays

a key role is accessibility. Accessibility relates to the ease with which people can conduct

activities in time and across space. Notwithstanding the central role of persons, accessibility

is usually measured as an attribute of locations (place-based perspective) in lieu of

individuals (person-based perspective) (Neutens et al. 2010). Chapter 9 adds to the

incorporation of potential behaviour in place-based assessments of accessibility to services.

Through the introduction of location-centred STPs – in lieu of conventional STPs which join

individual anchor points – a theoretical basis is formed for measuring and mapping place-

based accessibility while reckoning with person-based constraints, albeit universally

postulated constraints rather than genuine individualised constraints. More than that,

founded on this framework, a toolkit PrismMapper, which implements some complementary

network-based accessibility measures in a GIS, is developed and released in order to offer

scientists, planners and decision makers the ability to employ these novel place-based

measures for a GIS-based evaluation of accessibility.

Given that, on the one hand, place-based approaches have hitherto been by far the most

frequently applied in accessibility evaluations, and that, on the other hand, this trend is

being heavily criticised in scientific literature from a person-based perspective (Miller 2007,

Kwan 2009), the contributions of Chapter 9 – the toolkit in particular – are unique in bridging

both perspectives. Also, PrismMapper has been designed with specific attention to

transparency, user-friendliness, employability, and comprehensibility with respect to non-

technically oriented end-users who may not be acquainted with the theoretical background

of accessibility research. The toolkit thereby copes with the disadvantages of related tools

which implement procedures that are often obscure to the user, and/or which settings and

results are too complex to handle by non-specialists, such as the benefit values produced by

the tools of Miller & Wu (2000) or Neutens, Versichele & Schwanen (2010).

Chapter 9 tackles another persistent shortcoming of place-based evaluations of accessibility:

the negligence of temporal constraints on the opportunities to be accessed. Services, for

example, are only delivered within a regime of well-chosen opening hours. This is illustrated

in a case study where it is shown how the possibilities to pay an evening library visit in Ghent

(Belgium) differ strongly between different days of the week. Chapter 10 enables a more

systematic investigation of the gravity of overlooking the effects of service opening hours on

accessibility. It is examined and demonstrated how the accessibility of services to individuals

largely depends on their opening hour schedules and how these timetables can be

manipulated in order to optimise the absolute level of accessibility. In an empirical case

study on the accessibility of government offices to citizens in Ghent, the approach is shown

to be successful in increasing the average level of individual accessibility drastically.


In Chapter 11, the optimisation procedure to distribute opening hours among service

facilities in function of individual accessibility has been generalised in support of any

function of accessibility, rather than solely the absolute level of accessibility cumulated

across the population. Thus, a generic approach is obtained for allocating opening hours in

function of other aspects related to individual accessibility. In the case of Chapter 11, the

aspect under scrutiny is the equity of accessibility across individuals, which is an important

issue within the evaluation of social exclusion (Cass, Shove & Urry 2005). Three different

scheduling approaches are put forward according to three different equity principles and

these are implemented in an empirical case study concerning the accessibility of public

libraries in Ghent. The results illustrate how the rescheduling of library opening hours can be

an instrument to effectively control the (un)equity of accessibility among individuals. These

outcomes may assist library policies that focus on attracting specific social groups or on

increasing the average number of book issues per capita. A striking outcome of the study is

that, through rescheduling, both the absolute level of individual accessibility as well as the

equity of its distribution across individuals can be increased considerably whilst preserving

or even reducing the total amount of allocated service opening hours. The accomplishment

of this threefold condition is in particular appealing to public authorities, planners and

decision makers who are expected to fulfil this triple aim, particularly in the context of

austerity measures including budget cuts and service declination (e.g. Muir & Douglas 2001).

Beyond the application potential of the procedures developed in Chapters 10 and 11, these

chapters pioneer an innovative research direction, considering that comparable detailed

investigations of the effects of opening hours on person-based accessibility are – to our

knowledge – non-existing. Obviously, this novel line of research may be deepened further in

many respects. To this end, in order to better attune the scheduling procedure and in line

with the generalisation made in Chapter 11, many opportunities consist of incorporating

other aspects that relate to accessibility on the one hand or by including additional effects of

changes in opening hours on the other hand. For instance, one could explore the

consequences of rescheduling on the uncoupling and temporal fragmentation of everyday

human activities (Schwanen, Dijst & Kwan 2008, Hubers, Schwanen & Dijst 2008), intra-

household relations (Schwanen, Ettema & Timmermans 2007, Schwanen, Kwan & Ren 2008,

Schwanen & de Jong 2008), joint accessibility (Neutens et al. 2008a), etc. To reinforce the

practicability of the scheduling procedures elaborated in Chapters 10 and 11, a pertinent

challenge lies in obtaining an objective estimation of the feasibility of modifications to

opening hour regimes from the viewpoint of service suppliers, as well as service users. From

the supply side, the scheduling algorithms should account for the costs and benefits related

to each specific candidate regime, including a trade-off with individual accessibility. From the

demand side, on the other hand, challenges lie in estimating a population’s adaptability to

opening hour modifications as well as in integrating individual desirability for certain

(combinations of) opening hours. The latter aspect would benefit from the consideration of

262 Chapter 12

probabilistic models of human behaviour such as random utility models (Manski 1977,

Cascetta 2009), Markov chains (Brémaud 1999), and stochastic frontiers (Kumbhakar & Knox

Lovell 2000).

In view of the common focus of Chapters 9-11, a more general discussion on accessibility

measures is apposite here. Although Chapter 9 seeks to combine the best of both place- and

person-based accessibility measures, sides have to be taken in the end, given the

fundamental discordance between both approaches. In this case, place-based measures

have been obtained. Yet, this outcome is not indiscriminate given PrismMapper’s target

audience of planners, decision makers and authorities, who employ practically exclusively

place-based approaches to date (e.g. see the indicators included in the Stadsmonitor 2008

report, available on the Flemish urban policy website http://www.thuisindestad.be). Yet, the

lack of person-based accessibility measures in applied science provokes thought, since these

are believed to complement place-based measures and to articulate personal and social

differences in accessibility much more nuanced (Kwan 1998, Neutens et al. 2010). However,

little discussion has addressed the reasons for this hiatus. As already argued in Chapter 9,

these may be found in two interrelated aspects: (i) the absence of appropriate data sources

or the difficulty to acquire these, and (ii) their reliability and representativeness. The

importance of the latter aspect may not be underestimated, in particular vis-à-vis decision

makers or authorities responsible for entire spatial districts and their inhabitants. While

Chapters 10 and 11 provide substantial insights on person-based accessibility, it remains

undetermined whether the behaviour extracted from the pooled activity-travel dairy

samples underlying their analyses are representative for the behaviour of Ghent’s citizens,

and by consequence which lessons the city council of Ghent should draw from such analyses.

A straightforward answer to the question of representativeness is hampered by the fact that

individual behaviour is highly complex and in many cases unpredictable, if not indeterminate

(Cziko 1989) on the one hand, and by its unstableness and changeability in time on the

other. This variability is inconvenient in empirical studies with eye on long-term planning and

policies, which explains their appeal for place-based approaches which outcomes can be

considered far less a product of time. From the viewpoint of the individual, this

inconvenience may however be to a certain extent unjust, in the sense that person-based

approaches call for a change of mentality towards a dynamic and individualized planning of

service delivery, rather than a static permanent operating regime at fixed locations and

regular times, as is and will be increasingly supported by location-aware technologies and

ICTs in nowadays and future information societies.

Conclusion

In conclusion, it is noticed that the modelling and analysis of moving objects and travelling

subjects has resulted in a broad and fairly diverse, yet fascinating assembly of original

contributions with respect to both theoretical and application-oriented research. The


contribution of this dissertation cuts across fundamental models as well as empirical

findings, including results ranging from theorem proofs and formal axiomatisations to clear-

cut end-user deliverables such as PrismMapper. Existing frameworks and common research

practices have been adapted or extended, novel methods have been proposed and

implemented, and these efforts have been illustrated in a wide variety of conceptual

examples and empirical case studies offering important insights and lessons to be learned.

The merit of this dissertation is therefore believed to be in its application-oriented

achievements which open up the further continuation and application of its outcomes.

A final remark concerns the observation that each of the research questions addressed in

this work has been answered only partially. In part, this is due to the fact that alternative

answers to these comprehensive questions already exist in science. In that sense, this

dissertation has contributed by closing some well-chosen gaps in GIScience and related

fields. On the other hand, numerous unresolved issues leave room for improvement and

open avenues for further investigation. Since much of the research on analysing moving

entities is driven by technological progress (e.g. positioning systems), new answers may be

searched for in that direction as well. One remarkable challenge in this respect – perhaps the

most exciting one – lies in a profound integration of information stemming from different

data collection technologies. In the context of travelling individuals such an integration may

encompass technologies such as, among others, satellite positioning systems (e.g. GPS),

wireless communication technologies (e.g. Wi-Fi, Bluetooth, IrDA, NFC, RFID, GPRS, UMTS),

nanotechnology, microchip implants, camera surveillance and monitoring systems, and

automated ticketing, counting, and money tracking systems (e.g. see Shlesinger 2006). Such

multi-technological approaches have the potential to revolutionize both the spatial and

temporal scalability of tracking experiments and consequently increase the abilities to

capture the longitudinal travelling behaviour of a large number of individuals across diverse

environments (e.g. indoor and outdoor) and geographical scales. On the other side of the

medal, a far-reaching integration and scalability of tracking data may come at the prize of

location privacy (Duckham 2009) and will therefore require sufficient legislative adaptations

as well. Yet, this evolution is already palpable through the recent trends of neogeography

(Turner 2006, Graham 2010) and volunteered geographic information (Goodchild 2007,

Goodchild 2010), and ambient intelligence (Weber, Rabaey & Aarts 2005, Mikulecký et al.

2009, Augusto et al. 2010).

References

Augusto, J. C., Corchado, J. M., Novais, P. & Analide, C. (2010) Ambient Intelligence and Future

Trends: International Symposium on Ambient Intelligence (ISAmI 2010), Springer, 220.

Blaser, A. D. (2000) A study of people's sketching habits in GIS. Spatial Cognition and Computation, 2,

4, 393-419.

Bogaert, P. & Delafontaine, M. (2006) QTCN in static and dynamic environments. In Spatial Cognition

Workshop on Talking About and Perceiving Moving Objects: Exploring the Bridge Between

264 Chapter 12

Natural Language, Perception and Formal Ontologies of Space, eds. N. Van de Weghe, P.

Bogaert & P. De Maeyer, Bremen, Germany, 13-17.

Brémaud, P. (1999) Markov chains: Gibbs fields, Monte Carlo simulation and queues. New York, NY,

USA: Springer, 444.

Cascetta, E. (2009) Random utility theory. In Transportation Systems Analysis: Optimization and Its

Applications, Springer US, 29, 89-167.

Cass, N., Shove, E. & Urry, J. (2005) Social exclusion, mobility and access. The Sociological Review, 53,

3, 539-555.

Cohn, A. (1996) Calculi for qualitative spatial reasoning. In Artificial Intelligence and Symbolic

Mathematical Computation, eds. J. Calmet, J. Campbell & J. Pfalzgraf, Springer Berlin /


Cziko, G. A. (1989) Unpredictability and indeterminism in human behavior: Arguments and

implications for educational research. Educational Researcher, 18, 3, 17-25.

Delafontaine, M., Van de Weghe, N., Bogaert, P. & De Maeyer, P. (2006) Een kwalitatieve calculus

van bewegende objecten in een dynamisch netwerk. In Studiedag Cartografie en GIS: Jonge

Onderzoekers aan het Woord over Geomatica, eds. P. De Maeyer, P. Bogaert & D. Godfroid,

Ghent, Belgium, 41-47.

Ding, Z. & Güting, R. H. (2004) Managing moving objects on dynamic transportation networks. In

Proceedings of the 16th International Conference on Scientific and Statistical Database

Management (SSDBM'04), 287-287.

Duckham, M. (2009) Location privacy. In Handbook of Research on Geoinformatics, ed. H. A. Karimi,

Hershey, PA: IGI Global, 254-259.

Dylla, F., Frommberger, L., Wallgrün, J. O., Wolter, D., Nebel, B. & Wölfl, S. (2007) SailAway:

Formalizing navigation rules. In Proceedings of the Artificial and Ambient Intelligence

Symposium on Spatial Reasoning and Communication (AISB'07), 470-474.

Forbus, K. D. (1997) Qualitative reasoning. In The Computer Science and Engineering Handbook, ed. J.

A. Tucker, CRC Press, 715-733.

Freksa, C. (1992) Using orientation information for qualitative spatial reasoning. In Theories and



Girardin, F., Fiore, F. D., Ratti, C. & Blat, J. (2008) Leveraging explicitly disclosed location information

to understand tourist dynamics: a case study. Journal of Location Based Services, 2, 1, 41-56.

Golledge, R. G. (1999) Wayfinding Behavior: Cognitive Mapping and Other Spatial Processes.

Baltimore, Maryland: Johns Hopkins University Press, 433.

Goodchild, M. (2007) Citizens as sensors: The world of volunteered geography. GeoJournal, 69, 4,

211-221.

Goodchild, M. F. (2010) Twenty years of progress: GIScience in 2010. Journal of Spatial Information

Science, 1, 3-20.

Graham, M. (2010) Neogeography and the palimpsest of place: Web 2.0 and the construction of a

virtual earth. Journal of Economic and Social Geography, 101, 4, 422-436.

Gratton, C. & Jones, I. (2009) Research Methods for Sports Studies. Routledge, 304.

Güting, R. H. & Schneider, M. (2005) Moving Objects Databases. San Fransisco, CA, USA: Morgan

Kaufmann, 389.


Gutman, M. & Stern, P. (2007) Putting People on the Map: Protecting Confidentiality with Linked

Social-Spatial Data. National Academies Press, 176.

Hay, S. & Harle, R. (2009) Bluetooth tracking without discoverability. In Proceedings of the 4th

International Workshop on Location- and Context-Awareness, eds. T. Choudhury, A. Quigley,

T. Strang & K. Suginuma, Tokyo, Japan, 120-137.

Horne, J., Tomlinson, A., Whannel, G. & Woodward, K. (2011) Understanding Sport: A Socio-Cultural

Analysis, Routledge, 264.

Hornsby, K. & King, K. (2008) Modeling motion relations for moving objects on road networks.


Hubers, C., Schwanen, T. & Dijst, M. (2008) ICT and temporal fragmentation of activities: an analytical

framework and initial empirical findings. Journal of Economic and Social Geography, 99, 5,

528-546.

Jahn, O., Mohring, R. H., Schulz, A. S. & Stier-Moses, N. E. (2005) System-optimal routing of traffic

flows with user constraints in networks with congestion. Operations Research, 53, 4, 600-

616.

Köhler, E., Möhring, R. & Skutella, M. (2009) Traffic networks and flows over time. In Algorithmics of

Large and Complex Networks, eds. J. Lerner, D. Wagner & K. Zweig, Springer Berlin /


Kuehne, S. E. & Forbus, K. D. (2002) Qualitative physics as a component in natural language

semantics: A progress report. In Proceedings of the 24th Annual Conference of the Cognitive

Science Society. George Mason University, Fairfax, VA, USA.

Kuipers, B. (1994) Qualitative reasoning: Modeling and simulation with incomplete knowledge.

Cambridge, MA, USA: MIT Press.



1248.


space–time prisms. International Journal of Geographical Information Science, 23, 9, 1095-

1117.

Kumbhakar, S. C. & Knox Lovell, C. A. (2000) Stochastic Frontier Analysis. Cambridge, United

Kingdom: Cambridge University Press, 344.



Kwan, M. P. (2009) From place-based to people-based exposure measures. Social Science &

Medicine, 69, 9, 1311-1313.

Lysgaard, J. (1992) Dynamic transportation networks in vehicle routing and scheduling. Interfaces, 22,

3, 45-55.

Manski, C. F. (1977) The structure of random utility models. Theory and Decision, Springer, 8, 3, 229-

254.


Compass, 1, 3, 503-535.



266 Chapter 12



Morrison, D. A. (2010) Sequence Alignment: Methods, Models, Concepts, and Strategies. Systematic

Biology, 59, 3, 363-365.

Muir, L. & Douglas, A. (2001) Where now for the UK public library service? Library Management, 22,

6-7, 266-271.

Mikulecký, P., Lišková, T., Čech, P. & Bureš, V. (2009) Ambient Intelligence and Smart Environments:

Ambient Intelligence Perspectives - Selected Papers from the First International Ambient

Intelligence Forum 2008, IOS Press.

Neutens, T., Schwanen, T., Witlox, F. & De Maeyer, P. (2008a) My space or your space? Towards a


Neutens, T., Schwanen, T., Witlox, F. & De Maeyer, P. (2010) Equity of urban service delivery: A


1635.

Neutens, T., Van de Weghe, N., Witlox, F. & De Maeyer, P. (2008b) A three-dimensional network-

based space-time prism. Journal of Geographical Systems, 10, 1, 89-107.

Neutens, T., Versichele, M. & Schwanen, T. (2010) Arranging place and time: A GIS toolkit to assess

person-based accessibility of urban opportunities. Applied Geography, 30, 4, 561-575.

O'Donoghue, P. (2009) Research Methods for Sports Performance Analysis. Routledge, 280.

Pommerening, F., Wölfl, S. & Westphal, M. (2009) Right-of-way rules as use case for integrating

GOLOG and qualitative reasoning. In Proceedings of KI 2009: Advances in Artificial

Intelligence, eds. B. Mertsching, M. Hund & Z. Aziz, Springer Berlin / Heidelberg, 468-475.

Revesz, P. (2010) Moving objects databases. In Introduction to Databases, Springer London, 111-135.



Schwanen, T., Dijst, M. & Kwan, M. P. (2008) ICTs and the decoupling of everyday activities, space

and time: introduction. Journal of Economic and Social Geography, 99, 5, 519-527.

Schwanen, T., Ettema, D. & Timmermans, H. (2007) If you pick up the children, I'll do the groceries:

spatial differences in between-partner interactions in out-of-home household activities.



constraints and geographies of everyday activities. Geoforum, 39, 6, 2109-2121.

Shaw, S.-L. (2010) Geographic information systems for transportation: from a static past to a dynamic

future. Annals of GIS, 16, 3, 129-140.

Shlesinger, M. F. (2006) Random walks: Follow the money. Nature Physics, 2, 2, 69-70.



Skinner, J. & Edwards, A. (2011) Research Methods for Sport Management. Routledge, 288.

Turner, A. (2006) Introduction to Neogeography. Sebastopol, CA: O'Reilly Media.

Van de Weghe, N., Bogaert, P., Cohn, A. G., Delafontaine, M., De Temmerman, L., Neutens, T., De

Maeyer, P. & Witlox, F. (2007) How to handle incomplete knowledge concerning moving

objects. In Workshop on Behaviour Monitoring and Interpretation (BMI'07), Osnabrück,

Germany, 91-101.


Weber, W., Rabaey, J. & Aarts, E. H. L. (2005) Ambient Intelligence, Springer, 374.

Wilson, C. (2006) Reliability of sequence-alignment analysis of social processes: Monte Carlo tests of

ClustalG software. Environment and Planning A, 38, 1, 187-204.

Wolfson, O. & Mena, E. (2005) Applications of moving objects databases. In Spatial Databases, eds. Y.

Manalopoulos, A. Papadopoulos & M. G. Vassilakopoulos, IGI Global, 186-203.

Wolter, D., Dylla, F., Frommberger, L. & Wallgrün, J. O. (2007) Qualitative spatial reasoning for rule

compliant agent navigation. In Proceedings of the 20th International Florida Artificial

Intelligence Research Society Conference, Key West, Florida, USA: AAAI Press.

Wong, F.-L. & Stajano, F. (2005) Location privacy in Bluetooth. In Security and Privacy in Ad-hoc and

Sensor Networks, 176-188.

Zografos, K. G. & Androutsopoulos, K. N. (2008) Algorithms for itinerary planning in multimodal

transportation networks. IEEE Transactions on Intelligent Transportation Systems, 9, 1, 175-

184.

268

Samenvatting (Dutch summary)

Bewegingen maken inherent deel uit van het gedrag van mensen, dieren, goederen en

gegevens. Bewegende entiteiten vormen daarom een fundamentele onderzoekseenheid in

heel wat wetenschappelijke disciplines, zoals artificiële intelligentie, gedragswetenschappen,

ethologie, geografische informatiewetenschap, robotica, sportwetenschappen en verkeer-

en vervoerslogistiek. De wetenschappelijke interesse in onderzoek over bewegende

objecten is de laatste decennia sterk aangezwengeld, voornamelijk omwille van

technologische vooruitgang. Enerzijds hebben steeds geavanceerdere transportmiddelen

ertoe geleid dat een groeiend volume aan entiteiten met toenemende snelheden over

grotere afstanden kan worden verplaatst. Anderzijds heeft de belangrijke progressie in de

ontwikkeling van positionering- en trackingsystemen zoals GPS de mogelijkheden tot het

verzamelen van gedetailleerde gegevens omtrent bewegende objecten in aanzienlijke mate

vergroot. Verder biedt de evolutie in informatie- en communicatietechnologie (ICT)

onderzoekers in ijl tempo de nodige ondersteuning aangaande het opslaan, beheren,

bevragen, verwerken en communiceren van alsmaar grotere datavolumes.

Dit proefschrift tracht een bijdrage te leveren aan het wetenschappelijk onderzoek dat

verband houdt met het modelleren en analyseren van bewegende objecten in het algemeen

en specifiek binnen het kader van de geografische informatiewetenschap. Geografische

informatiewetenschap (GIW) vormt de wetenschappelijke ruggengraat van geografische

informatiesystemen (GIS) en richt zich op het ontwikkelen en toepassen van theorieën,

methodes, technologieën en gegevens om geografische processen, relaties en patronen te

begrijpen (Mark 2003). Aan het onderzoek in GIW met betrekking tot bewegende objecten

zijn twee algemenere onderzoekstendensen voorafgegaan. Aangezien deze tendensen voor

een stuk tot op heden doorlopen, doorspekken zij in verschillende opzichten de inhoud van

dit werk. Een eerste trend houdt verband met het tijdruimtelijke fenomeen dat beweging is.

Het modelleren en analyseren van bewegende objecten omvat namelijk naast ruimtelijke

ook belangrijke temporele aspecten. Daarom volgt zij de strekking binnen GIW die zich heeft

gericht op de theoretische omkadering van de temporele component in geografische

informatie en de bijhorende ondersteuning van tijdruimtelijk GIS. De tweede

vermeldenswaardige verschuiving is ontsproten aan de vaststelling dat modellen, methodes

en technieken voor het bestuderen van individuen en hun gedrag binnen GIW doorgaans

een plaatsgebaseerde aanpak hanteren en zo voorbijgaan aan essentiële kenmerken van

personen (Miller 2007). Men gaat bijvoorbeeld onrechtstreeks het individu herleiden tot een

bepaalde – zogenaamd representatieve – locatie zoals zijn/haar woonplaats en maakt op die

manier een voor vele toepassingen onaanvaardbare abstractie van zijn/haar tijdruimtelijk

gedrag. Deze gedachte heeft in GIW een mentaliteitswijziging teweeggebracht van

plaatsgebaseerde naar persoonsgebaseerde benaderingen waarin individuen centraal staan.

Diezelfde gedachtegang is onder andere weerspiegeld in de onderverdeling van dit werk.

Samenvatting (Dutch Summary) 269

Deze doctoraatsverhandeling bestaat uit een compilatie van tien manuscripten

(Hoofdstukken 2-11) voorafgegaan door een algemene inleiding (Hoofdstuk 1) en afgesloten

met een concluderende discussie (Hoofdstuk 12). Elk manuscript is aan een internationaal

peer review proces onderworpen en in een internationaal wetenschappelijk tijdschrift of

boek verschenen, of ter publicatie voorgelegd. De manuscripten zijn ontwikkeld met het oog

op twee algemene objectieven:

Objectief 1 Een originele wetenschappelijke bijdrage leveren en in het bijzonder een

bijdrage tot de mogelijkheden die GIW biedt tot het modelleren en

analyseren van bewegende objecten en personen die zich verplaatsen.

Objectief 2 Bijdragen tot of verbetering brengen in het in praktijk brengen of inzetbaar

maken van bestaand theoretisch werk zodoende de kloof tussen wetenschap

en technologie en tussen theorie en praktijk te helpen dichten.

Het eerste objectief omschrijft de focus van dit werk en impliceert tevens de vereisten die de

redacteurs en uitgevers van de opgenomen manuscripten vooropstellen met betrekking tot

de originaliteit en toegevoegde waarde daarvan. Het tweede objectief vloeit voort uit het

gevaar dat elke wetenschap loopt om losgekoppeld te raken van de toepassingen en

technologieën die ze hoort te ondersteunen en zich te verliezen in een louter theoretisch

bestaan. Deze verhandeling poogt de kloof die aldus kan ontstaan, in dit geval specifiek die

tussen GIW en GIS, te overbruggen en schenkt daarom bijzondere aandacht aan het

implementeren en ontwikkelen van applicaties.

Een onderscheid werd gemaakt tussen de hoofdstukken die handelen over bewegende

objecten in het algemeen (Deel I, Hoofdstukken 2-6) en de hoofdstukken die betrekking

hebben op personen die zich verplaatsen (Deel II, Hoofdstukken, 7-11). Deel I beschouwt

bewegende objecten in hun meest elementaire vorm: entiteiten waarvan de positie en/of

geometrische kenmerken doorheen de tijd veranderen. In dit opzicht worden zij in Deel I,

zoals gebruikelijk in GIW, gemodelleerd als bewegende puntenobjecten. Deze kernachtige

conceptualisatie laat toe om abstractie te maken van complexere geometrieën die in

analyses vaak irrelevant zijn en bovendien vanuit algoritmisch oogpunt aanzienlijk minder

performant.

Het eerste deel richt zich tot het kwalitatief voorstellen van en redeneren over bewegende

objecten. Kwalitatief redeneren is een traditioneel onderzoeksdomein in artificiële

intelligentie dat later in GIW zijn intrede heeft gemaakt en zich richt op het ontwikkelen van

informatiesystemen die in staat zijn te redeneren over fysieke systemen zonder daarbij op

precieze kwantitatieve informatie te berusten (Weld & de Kleer 1989). Een van de

technieken die daartoe kan leiden is het opstellen van een kwalitatieve calculus, hetgeen

omschreven kan worden als een verzameling van paarsgewijs verschillende en onderling

exclusieve relaties en een verzameling bewerkingen om over deze relaties te redeneren

270

(Ligozat & Renz 2004). Hoofdstukken 2 tot 5 zijn toegewijd aan een specifieke kwalitatieve

calculus, namelijk de Qualitative Trajectory Calculus (QTC) (Van de Weghe 2004) die relaties

tussen twee bewegende puntobjecten definieert. Hoofdstuk 2 (Delafontaine et al. 2011b)

biedt een theoretisch overzicht van alle fundamentele types van QTC en bespreekt hoe de

calculus kan worden uitgebreid en hoe ze kan omgaan met onvolledige informatie en met

ruwe trajectgegevens. Hoofdstukken 3 en 4 werken een bepaald type van QTC, namelijk de

Qualitative Trajectory Calculus on Networks (QTCN) verder uit. QTCN beschouwt relaties

tussen objecten die bewegen in netwerken, zoals auto’s in wegennetwerken. In Hoofdstuk 3

(Delafontaine et al. 2011a) wordt QTCN formeel gedefinieerd en wordt nagegaan in welke

mate de calculus in staat is kwalitatieve vragen te beantwoorden. Hoofdstuk 4 (Delafontaine

et al. 2008) breidt QTCN uit naar dynamische netwerken, meer bepaald naar netwerken die

topologische veranderingen kunnen ondergaan. Deze uitbreiding is zinvol om het maken of

verbreken van fysieke en/of virtuele connecties te modelleren, zoals het tijdelijk blokkeren

van een weg aan een slagboom. Hoofdstuk 5 behandelt de implementatie van QTC in een

informatiesysteem. Daarbij wordt QTCAnalyst, een prototype van een op QTC gebaseerd

informatiesysteem, ontwikkeld en geïllustreerd aan de hand van twee gevalstudies.

Hoofdstuk 6 gaat dieper in op één van mogelijkheden om QTCAnalyst verder uit te breiden.

Aangezien het algemeen aanvaard is dat kwalitatieve meer dan kwantitatieve methodieken

overeenstemmen met de manier waarop mensen redeneren en communiceren, loont het de

moeite QTCAnalyst uit te breiden naar gegevens die direct uit menselijke communicatie

voortkomen en/of de menselijke perceptie weerspiegelen. Het ondersteunen van manueel

geschetste trajecten is één van die mogelijkheden. In Hoofdstuk 6 (Delafontaine & Van de

Weghe 2009) wordt onderzocht hoe bewegende objecten op basis van ingeschetste

trajecten in informatiesystemen kunnen worden gemodelleerd.

In het tweede deel wordt dieper ingegaan op het verplaatsingsgedrag van individuen.

Daarbij worden twee perspectieven gehanteerd. Enerzijds wordt het geobserveerd gedrag

van personen geanalyseerd. Daartoe worden in Hoofdstuk 7 twee onderzoekslijnen met

succes gecombineerd: op tracking gegevens verzameld door middel van Bluetooth sensoren

wordt sequence alignment – een techniek overgenomen uit de bio-informatica (Morrison

2010) – toegepast, zodoende gedragspatronen in kaart te brengen. Een van de nadelen van

Bluetooth gegevens is echter dat zij in de meeste gevallen niet toelaten een nauwkeurig

continu tijdruimtelijk traject van een individu af te leiden. Mogelijke individuele trajecten

kunnen daarentegen wel worden geëxtraheerd. Daarom is verder aandacht besteed aan het

modelleren en analyseren van potentieel gedrag. In Hoofdstuk 8 wordt het klassieke concept

van een tijd-ruimte prisma uit de tijdgeografie (Hägerstrand 1970) uitgebreid, zodoende een

analytisch kader te creëren dat toelaat op basis van discrete observaties het potentieel

verplaatsingsgedrag van individuen binnen open, door obstakels begrensde ruimtes te

analyseren. Deze uitbreiding is complementair ten opzichte van eerdere implementaties van

tijd-ruimte prisma’s die voornamelijk op netwerk omgevingen waren geënt. Ook Hoofdstuk 9

Samenvatting (Dutch Summary) 271

gaat dieper in op potentieel gedrag, namelijk op het aspect bereikbaarheid dat daarmee

verband houdt, maar dat desalniettemin het vaakst op een plaatsgebaseerde manier wordt

gemeten (bv. hoeveel winkels liggen er in een straal van 1 km van plaats x?). Tegenover

persoonsgebaseerde bereikbaarheidsindicatoren hebben plaatsgebaseerde indicatoren wel

het belangrijke voordeel dat ze in een gebiedsdekkende kaart kunnen worden voorgesteld.

Daarom wordt in Hoofdstuk 9 getracht, op basis van alweer een aangepast tijd-ruimte

prisma, plaatsgebaseerde indicatoren te verrijken met essentiële persoonsgebaseerde

kenmerken. Deze innovatieve bereikbaarheidsindicatoren worden dan geïmplementeerd in

een GIS-applicatie PrismMapper zodoende hun berekening en kartering te automatiseren,

hetgeen vervolgens in een gevalsstudie wordt geïllustreerd. PrismMapper is in de eerste

plaats bedoeld voor eindgebruikers zoals planologen, beleidsmakers, enz. en is daartoe heel

bewust op een gebruiksvriendelijke en bevattelijke manier ontworpen. Een andere

meerwaarde tegenover gerelateerde plaatsgebaseerde applicaties is dat PrismMapper in het

evalueren van de bereikbaarheid van voorzieningen rekening houdt met hun openingsuren.

Hoofdstukken 10 en 11 werken dit vernieuwende aspect verder uit in een systematische

studie over de effecten van verschillende openingsuren op individuele bereikbaarheid. In

Hoofdstuk 10 wordt een algoritme opgesteld dat toelaat een bepaalde hoeveelheid

openingsuren te verdelen over een gegeven aantal voorzieningen om zo hun bereikbaarheid

ten aanzien van een gegeven populatie te maximaliseren. De procedure wordt daarna

toegepast in een uitgebreide gevalsstudie betreffende de bereikbaarheid van

gemeentekantoren in Gent (België). In Hoofdstuk 11 ten slotte, wordt die procedure

gegeneraliseerd naar de maximalisatie van eender welke functie van individuele

bereikbaarheid en aansluitend toegepast op drie functies die overeenstemmen met

verschillende gelijkheidsprincipes ten aanzien van de verdeling van individuele

bereikbaarheid binnen de populatie. Deze drie benaderingen worden achtereenvolgens

geïllustreerd in een empirische studie over de bereikbaarheid van bibliotheken in Gent.

References

Delafontaine, M., Bogaert, P., Cohn, A. G., Witlox, F., De Maeyer, P. & Van de Weghe, N. (2011a)

Inferring additional knowledge from QTCN relations. Information Sciences, 181, 9, 1573-1590.

Delafontaine, M., Chavoshi, S. H., Cohn, A. G. & Van de Weghe, N. (2011b) A Qualitative Trajectory



USA: IGI Global.

Delafontaine, M. & Van de Weghe, N. (2009) Modelling moving objects in geospatial sketch maps. In

Proceedings of the AGILE Workshop on Adaptation in Spatial Communication, eds. M. Tomko

& K.-F. Richter, Hannover, Germany, 7-17.



Sciences, 178, 8, 1997-2006.

272


21.

Ligozat, G. & Renz, J. (2004) What is a qualitative calculus? A general framework. In Proceedings of

the 8th Pacific Rim International Conference on Artificial Intelligence (PRICAI04), Auckland,

New Zealand, 53-64.

Mark, D. M. (2003) Geographic information science: Defining the field. In Foundations of Geographic

Information Science, eds. M. Duckham, M. F. Goodchild & M. F. Worboys, New York: Taylor

and Francis, 1-18.


Compass, 1, 3, 503-535.

Morrison, D. A. (2010) Sequence alignment: Methods, models, concepts, and strategies. Systematic

Biology, 59, 3, 363-365.


Approach, Doctoral DissertationGhent: Ghent University, 268.



Biographical sketch 273

Biographical sketch

Matthias Delafontaine was born on April 20, 1984 in Bruges

(Belgium). After graduating from high school at Sint-Jozefsinstituut-

College in Torhout (Belgium) in 2002, he started his academic

education in geography and geomatics at Ghent University where

he obtained his Master’s degree magna cum laude in 2006. In the

same year he joined the Department of Geography (Ghent

University) and started working on various scientific projects in GIS,

cartography, and spatial planning. In 2007, he received a doctoral

grant of the Research Foundation – Flanders and became a PhD

student. As an assistant teacher, he was involved in the courses of

geographical information science, GIS programming, spatial

analysis, map algebra and geostatistics. In 2011, he obtained a

postgraduate degree from the Doctoral School of Natural Sciences

(Ghent University). Matthias has participated in many major

international conferences and symposia and he is the author of

several publications in leading international journals in geography,

geographical information science and GIS.

Documents

Modelling and Analysing Moving Objects and Travelling Subjects