2 2 EIGSI EIGSI ( Engineering School( Engineering School )) , La Rochelle - France , La Rochelle - France

1 1 Laboratory L3I - University La Rochelle - France Laboratory L3I - University La Rochelle - France

Jean-MarieBoussier 1,2

MichelAugeraud 1

PascalEstraillier 1

DavidSarramia 1

Laboratoire Informatique-Image-Interaction

Choice of one transport meansChoice of one transport means

of traffic network usersof traffic network users

Design approach of behavioural modelsDesign approach of behavioural models

Framework: 3D urban traffic simulatorFramework: 3D urban traffic simulator

activity-based model and multi agent technology

Signals ComposingGeneralStructure

Buildings

Ground

Requirements Modelling SimulationMAS Architecture

( UTS )

Properties

Logs

and

Properties

2D/3Danimation

Stateproperties

Adequacy

Model checking

UnderrunVerifications

UML models(patterns)

Finite StateSystems

semiautomaticgeneration

Interactionsmodelling

Servicesinformation

systems

UTS informationsystems

Observation/management

Urban Transport System

Behaviouralmodels

for pedestrians

for vehicles

for activity locationbuilding, park, car park …

Map of the studied city

2D Map of the virtual citywith square blocks 2D car park

3D ground model

Making of a virtual city : our ground modelMaking of a virtual city : our ground model

an assembling of 4 square blocks

a pattern of a square block

Each block contains predefined: areas, graphs, signals, parking places

Blocks can be reused, modified, specialized

Areas used by agents - Areas only for displaying scenery

Making of a virtual city : our 3D graphical toolMaking of a virtual city : our 3D graphical tool

3D representation

a made square blocka basic square block

EDITING

Assembling of square blocks

a BLOCK

EDITING

a SYSTEM

graphical editor produces 3D graphical representation from templates

set up a system of procedural construction of buildings in order to adapt their forms and their functions to available space

MODELLING ofRESPONSE

Design OfExperiments

Vigier’s Model

Selection of the Array and its Linear Graph

Identification of Factors and Response

Evaluation of Travel

Design of the Model with Analysis Of Variance

Design approach of behavioural modelsDesign approach of behavioural models

“average” behaviour for socio-demographic categories

MODELLING ofRESPONSE

Coupling of 4 concepts:

Design OfExperiments

Vigier’s Model

Selection of the Array and its Linear Graph

Identification of Factors and Responses

Evaluation of Travel

Design of Models with Analysis Of Variance

Fusion of Answer Data

Design approach of behavioural modelsDesign approach of behavioural models

“average” behaviour for socio-demographic categories

Dempster-Shafer’s Theory

RobustnessIndicator

CLASSIFICATION of RESPONSES

Choice of the most“robust” Response

* In our case and here, the responses are the transport means* In our case and here, the responses are the transport means

Example: choice of one transport means (on foot, car, bus, bicycle)

Design Of Experiments: making of a questionnaireDesign Of Experiments: making of a questionnaire

favourable

low

short

with parcel

to be in hurry

not favourable

high

long

without parcel

not to be in hurry

Level 1 Level 2

Weather

Risk of incidents

Distance

Travel conditions

Timing

(input) Factors

5 factors, each one has 2 levels5 factors, each one has 2 levels

2 = 32 combinations2 = 32 combinations

4 transport means: 4 x 32 = 128 questions4 transport means: 4 x 32 = 128 questions

55

there are too many questionsthere are too many questions

List of possible answers:

Linguistic evaluation

Crisp value

very rarely

sometimes

frequently

very frequently

1

2

3

4

. . . . .

. . . . .

. . . . .

. .

For each question, asked people choose one evaluation For each question, asked people choose one evaluation (see the list of…)(see the list of…)

Design Of Experiments: making of a questionnaireDesign Of Experiments: making of a questionnaire

List of possible answers:

Linguistic evaluation

Crisp value

very rarely

sometimes

frequently

very frequently

1

2

3

4

. . . . .

. . . . .

. . . . .

. .

favourable

low

short

with parcel

to be in hurry

not favourable

high

long

without parcel

not to be in hurry

Level 1 Level 2

Weather

Risk of incidents

Distance

Travel conditions

Timing

(input) Factors

5 factors, each one has 2 levels = 5 factors, each one has 2 levels = 32 combinaisons32 combinaisons

4 transport means: 4 x 32 = 4 transport means: 4 x 32 = 128 questions128 questions

there are too many questionsthere are too many questions

with Taguchi’s array, we can decrease the question with Taguchi’s array, we can decrease the question numbernumber

L8(2)7

Now, the questionnaire is made up of 32 specific Now, the questionnaire is made up of 32 specific questions.questions.

8 runs instead of 32 combinations8 runs instead of 32 combinations

Example: choice of one transport means (on foot, car, bus, bicycle)

32 = 4 trnsp means x 8 runs

Taguchi’s orthogonal array: L8(2)7

A

B D

EC

F

G

Run A

Factors (and interactions)

111

1

22

22

B112

2

11

22

C112

2

22

11

D121

2

12

12

E121

2

21

21

F122

1

12

21

G122

1

21

12

123

4

56

78

interactions

Design Of Experiments: making of a questionnaireDesign Of Experiments: making of a questionnaire

Linear graph:

List of possible answers:

Linguistic evaluation

Crisp value

very rarely

sometimes

frequently

very frequently

1

2

3

4

. . . . .

. . . . .

. . . . .

. .

favourable

low

short

with parcel

to be in hurry

not favourable

high

long

without parcel

not to be in hurry

Level 1 Level 2

Weather

Risk of incidents

Distance

Travel conditions

Timing

(input) FactorsColumn

A

B

C

D

G

Example: choice of one transport means (on foot, car, bus, bicycle)

Modelling of a response: answers are the average of crisp evaluations

Two Uses of the questionnaireTwo Uses of the questionnaire

Choice of one transport means: answers obtained by the information fusion

Weather(A)

Risk ofincidents (B)

Distance (C)

Travelconditions(D)

Timing (G)

1

6 not favourable

: . . . .

Answers of an asked person

Bicycle Car

low long withoutparcel

:

. . . . . . . . . . . . . . . . . . . .

to be in hurry

favourable

. . . .low short with

parcel. . . . . . . . . . . . . . . .

to be in hurry

very rarely frequently

sometimes sometimes

. . . .

(=V) (=C)

. . . .

. . . .

Factors

Question N°:Weather

(A)Risk of

incidents (B)Distance

(C)Travel

conditions(D)Timing

(G)

1

6 not favourable

: . . . .

Answers of an asked person

Bicycle

low long withoutparcel

:

. . . . . . . . . . . . . . . . . . . .

to be in hurry

favourable

. . . .low short with

parcel. . . . . . . . . . . . . . . .

to be in hurry

1

2

. . . .

(=V)(Run)

Question N°:

(Run)

Factors

, n being the response number with the same evaluation

Fusion of Information : our frameworkFusion of Information : our framework

Use of Dempster-Shafer’s theory

Frame of discernmentSet power

Mass assignement

Θ = Bicycle, Car, Bus, on FootV C B F

2 = Φ , Bicycle, …, Bicycle Car, …, ΘΘ

m : 2 → [ 0, 1 ]Θ

Θm (A) = 1 Σ

AΘΘ

m (Φ) = 0 ;Θ

Example: each asked person is one source of information

for the scenario y

Bicycle Car Bus On footsometimes frequentely very frequentelyvery rarely

0.2 , 0.3 , 0.1 , 0.4

for an asked person giving the same answer for several transport means

a normalization and a redistribution of masses are done

a discounting operation is done

where N being the number of responses

n - 1N

α = 1 -

m (A) = α m(A) , for any AΘ ; m (Θ) = (1 - α) + α m(Θ)α α

Here, response number = number of transport means

Fusion of Information : Calculation of MassesFusion of Information : Calculation of Masses

Orthogonal Sum

m = m . . . m S1

Θ= m m m . . . m

S1

Θ

S2

Θ

S3

Θ

SM

ΘΘ

SM mSM

Θ

S1 mS1

Θ

S2 mS2

Θ

S12 mS12

Θ

S3 mS3

Θ mΘ

Fusion of 2 sources:

m = m m S1 S2

m(A) = m (B) . m (C) Σ S1 S2

B∩C=A

a source

For a conflict: m(A) =1 -

m (B) . m (C) Σ S1 S2

B∩C=A

m (B) . m (C) Σ S1 S2

B∩C=Ø= 0 if no conflict

SM

Θ

Fusion of Information : Pignistic probabilitiesFusion of Information : Pignistic probabilities

Use of the Transferable Belief Model ( T B M )

the number of transport means might change

for example , buses are not available at night

Initial survey results:

New pignistic transform:

28.0 29.6 4.4 33.8 0.0 0.0 4.2

46.3 47.9 5.8 - - - -

on Foot Bicycle Car F V F C V C F V C

F: on Foot - V: Bicycle - B: Bus - C: Car

By using the pignistic probabilities ,masses are redistributed on singleton hypothesises .

Hi Θ , P (Hi ) = m (A) ΣHiA

Θ1

|A| ΘA2Θ

cardinality of A

F V B C

17 11.1 12.4 3.9

3.9

FV

14.8

FB

7.5

FC

0

VB

14.8

VC

0

BC

0

FVB

14.8

FVC

0

FBC

0

VBC

0

FVBC

3.7

33 28.434.3

sub-set coupling hypothesis ignorance

singleton hypothesis

F: on Foot - V: Bicycle - B: Bus - C: Car

survey results:Pignistic transform:

mean effect of a factor:

mean effect of an interaction:

Example of a behavioural model: bicycle – students - age 22.3 -

with

after ANOVA, only A (weather), C (distance), D (travel conditions) after ANOVA, only A (weather), C (distance), D (travel conditions)

For each category of agents, the model can be different

is an arbitrary constant

Vigier’s modelVigier’s modelfor each scenario j and each transport means k, a score is defined

Possibility to reduce the number of information for an agent

are significant as factors for the category of are significant as factors for the category of “student” “student” agentsagents

ai = Smean (Ai ) - Smean

1,472 answers

S = 2.3 + (0.081 -0.081)A + (0.022 -0.022)B + (0.345 -0.345)Cbicycle

+ (0.085 -0.085)D + (0.059 -0.059)G + AD + BD-0.02 0.02 0.04 -0.04

0.02 -0.02 -0.04 0.04

ai bj = Smean (Ai , Bj ) - Smean - ai - bj

S = Smean + (a1 a2)A + (b1 b2)B + . . . + AB + . . . + εa1b1 a1b2

a2b1 a2b2

S = λ . PΘ (Hk )j

j

k

IT IS A SYMBOLIC WRITING

Input variablesAccessibility

(H)

Scenario 4

2.8 2.1 2.2 1.9

: …. …. …. …. ….

…. ….…. ….

L8(2)7

Ext

erna

lcon

dit

ion

s

L4(2)3

Score 321

good

good

bad

bad

…. ….…. ….1.6 1.4 1.2 1.3

in hurrywith parcelshortlowfavourable1

in hurrywithout parcelgreatlownot favourable6: …. …. …. …. ….

Weather(A)

Risk ofincidents (B)

Distance(C)

Conditionsto travel (D)

Timing(G)

Road safety(I) go

od

bad

good

bad

Information(J) ye

s

no no yes

Input variablesAccessibility

(H)

Scenario 4

2.8 2.1 2.2 1.9

: …. …. …. …. ….

…. ….…. ….

L8(2)7

Ext

erna

lcon

dit

ion

s

L4(2)3

Score 321

good

good

bad

bad

…. ….…. ….1.6 1.4 1.2 1.3

in hurrywith parcelshortlowfavourable1

in hurrywithout parcelgreatlownot favourable6: …. …. …. …. ….

Weather(A)

Risk ofincidents (B)

Distance(C)

Conditionsto travel (D)

Timing(G)

Road safety(I) go

od

bad

good

bad

Information(J) ye

s

no no yes

for the next travel (same scenario), the agent "individual" will select another

example: bicycle, student

Concept of robustnessConcept of robustness (1)(1)

Feedback: used for the memory effect

transport means if the score of the bicycle is lower than those of others

if no information is given during the travel and the road safetyis bad, the score of the next travel (same scenario) will be: S = 2.1

the first score used by an agent is in the first column wherein are the best external conditions (e.g. score of scenario 1: S = 2.8 )

TravelConditions (D)

Control Factors

Noise Factors

(Run n°)

Scenario

( signal-to-noise ratios)

becausebecause

Concept of robustnessConcept of robustness

Selection of the “most” robust transport means

the choice of one transport means is not the choice of one transport means is not affectedaffected by external conditionsby external conditions

Given a scenario,Given a scenario, the scores of two transport means are nearly the scores of two transport means are nearly equalequal

The agent "individual" selects the transport means whenThe agent "individual" selects the transport means when

S

Nis maximalis maximal

S

σ

k

j

= 20 logmean j

k

j

k

S

N

(2)(2)

Design of models describing “average” behaviours of individual agents

Possibility to upgrade models (Dempster-Schafer’s theory)- new sources of information (people answers) can enhance the database- the number of transport means can be changed

Determination of the “sufficient” number of information used by an

Feedback for the memory effect (robustness indicator)

Selection of the most “robust” transport means (robustness indicator)

Use of Dezert-Smarandache’s theory for the fusion of information

Taking answers of asked people into account as fuzzy values

ConclusionsConclusions

PerspectivesPerspectives

classified in various socio-demographic categories (Vigier’s model)

agent “individual” (thanks to ANOVA, the initial number can be reduced)

- conflicts between people answers are taken into account

( Better taking conflicts between people answers into account )

Design approach of behavioural modelsDesign approach of behavioural models

Thank you for your attention

2 2 EIGSI EIGSI ( Engineering School( Engineering School )) , La Rochelle - France , La Rochelle - France

1 1 Laboratory L3I - University La Rochelle - France Laboratory L3I - University La Rochelle - France

Jean-Marie Boussier 1,2

Michel Augeraud 1

Pascal Estraillier 1

David Sarramia 1

Laboratoire Informatique-Image-Interaction

Choice of one transport meansChoice of one transport means

of traffic network usersof traffic network users

Design Of Experiments (D.O.E.)Design Of Experiments (D.O.E.)

Approach of Taguchi: optimization of industrial process

About 7 days before my paper proposaI, I discoveried one paper of Louviere

Field of J. Louviere: Marketing research

Warren F. Kuhfeld ; January 1, 2005 - Marketing Research Methods in SAS

“ Some STATISTICIANS hate Taguchi’s approach ”

back

Stated Preference Methods

RatingRanking Stated Choice

ReferendumContingent Valuation

Other ChoiceMethodsAttribute Based

Stated Choice

This declaration was on a slide of a conference in USA

Other methods and approaches …

Design Of Experiments (D.O.E.)Design Of Experiments (D.O.E.)

Taguchi’s method

About 7 days before I sent the paper, I discoveried one paper of LouviereIn this last one, About fractional factorial designs (arrays orthogonal )

Research field of Louviere

In some countries (e.g. USA), some people won’t hear of Taguchi

Marketing Research Methods in SAS

Warren F. Kuhfeld January 1, 2005SAS 9.1 Edition

Some STATISTICIANS hate Taguchi’s approach

Fractional factorial designs