Foot traffic flows: background for modelling
PAGE
12
Parameters of pedestrian flow for modeling purposes
V. V. Kholshevnikov1, D. A. Samoshin2
1Professor, State Moscow University of Civil Engineering,
Moscow, 127337, Yaroslavskoe Highway, Russia,
[email protected]
2Ph.D, Lecturer of Academy of State Fire Service of Russia,
129366, B.Galushkin, 4, [email protected]
ABSTRACT
Seventy years of foot traffic flow research in Russia provided
unique empirical data base of travel speed values at different flow
density, ranging from 0 up to 13-14 persons/m2 obtained in
approximately 35.000 counts in 100 series of observations and
experiments in the different buildings, city territories, route
types and experimental settings.
The laws for crossing of boundaries of adjacent sectors of
paths, crowding of people, merging, reforming and diffusion of
flows were developed. The flow traffic through door openings, cross
and contra-flows, movement on a router with "unlimited" width and
other special cases were also investigated.
Accumulated empirical database was used to establish valid
psychophysiological law describes relation between flow travel
speed and flow density considering emotional state of people. This
law was expressed as random function.
Established relations were validated against actual
observations, experiments and unannounced evacuations which
involved able-body and disabled people. Due to high reliability of
established laws they were used in all related Russian building
codes and also used for flow/evacuation modelling aimed to provide
safety of building occupants. Obtained results are presented in the
given paper.
INTRODUCTION
Predtechenskii and Milinskiis seminal work [1] in relation to
pedestrian flows is well known. However, analysis of the
experimental results and observations obtained from this series of
experimental studies revealed the inherent statistical
non-homogeneity of pedestrian flow speeds [2]. As such, the results
of these individual experiments cannot be integrated to produce a
valid general expression V=f(D) for each type of pedestrian flow
path where V is the flow velocity and D is the flow density. In
this paper pedestrian flow is treated as a stochastic process, ie,
that which might be observed in a series of experiments as a
manifestation of the random function V=f(D). A fundamentally new
random methodology to mathematically describe this function is
presented. The high degree of correspondence between observed
pedestrian flows and the output from these models has been
sufficient for the models to be accepted by statutory authorities
and used in building design and regulation in Russia [12-14] for
many years.
A shift to performance based design revealed a need for new
advanced algorithm, describing movement of each pedestrian in a
flow. Together with wide range of analysed special cases of
pedestrian flow (e.g. movement at high density conditions, crossing
flows and contra flows etc) it makes possible to describe with high
preciseness movement of people within a flow.
FUNDAMENTAL LAWS OF PEDESTRIAN FLOW
In 1951 Milinskii established a statistical data base of human
flow parameters, comprising field observations of some 3585 counts
of travel speed against density of flow, together with 2303 counts
of door traffic capacity for doors which ranged from 0.5m to 2.4m
wide at densities of 1-9 persons/m2 [21]. The visual method of
observations which was used required the participation of 160
observers. 148 counts of body dimensions were also recorded and
presented as f, the horizontal projected area, m2, in order to
express density of flow (D) in m2/m2 as:
0
50
100
150
200
250
300
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
N, people
t, min
where N =number of people,
l=length of the pathway (m),
b =width of pathway (m).
For the first time, in cooperation with Prof Predtechenskii
fundamental laws of pedestrian flow relating to:
changes of flow characteristics at the interface of route
sectors with different widths or route types (j);
merging and branching of flows;
dynamics of crowding and bottlenecking at the interface of a
sector with insufficient traffic capacity, and
convergence and divergence of a flow
were determined.
The results of this work have been presented in [1, 17-20], and
the most important outcomes of this work are briefly summarized
below.
Changes of flow characteristics (V and D) at the interface of a
sector of width bi to a sector with width bi+1 is determined by
changes of intensity of flow from qi to qi+1:
1
,
,
1
+
+
=
i
i
j
i
j
i
b
b
q
q
(1)
The intensity of flow q=VD person/(m/min) or m2/(m/min) is the
product of flow velocity and density of flow.
In the case of the merging of several flows, the intensity of
flow can be described as:
1
,
,
1
+
+
=
i
i
j
i
j
i
b
b
q
q
(2)
Delay of a flow at the interface of the next sector occurs
because of its inherent traffic capacity, i.e. if the sector cannot
accommodate all the people approaching it. Denoting the number of
people coming from the previous sector as Pi,j= qi,jbi, and the
traffic capacity of the adjacent sector as Qi+1,j= qmax,jbi+1 then,
if
+
j
i
j
i
P
Q
,
,
1
the flow is unimpeded. Alternatively, if
p+/p
pj/p
pi/p
pj/p
pi/p
pP/p
pQ/p
p,/p
p,/p
p1/p
at the interface with the adjacent sector i+1, movement delay
develops with the duration div class="embedded"
id="_105908180"/p)/p
p1/p
p1/p
p(/p
p,/p
p,/p
p1/p
p/p
p/p
p-/p
p=/p
pD/p
p+/p
pj/p
pi/p
pj/p
pi/p
pi/p
pP/p
pQ/p
pN/p
pt/p
. The condition qi+1,j>qmax,j used in the calculations is
indicative of imminent movement delay.
The speed (V1) of movement at the interface between two parts of
a flow of different densities, so called reforming or converging,
is given by:
2
1
2
1
1
D
D
q
q
V
-
-
=
(3)
where:
D1 and q1 are the density of the first part of the flow and
intensity of its movement, and
D2 and q2 are the density of the second part of the flow and
intensity of its movement,
The graphical method used in the analysis, which clearly
illustrates flow movement, was developed in the fifties based on
the above expressions and the linear relation l=Vt. [1,21] Given
the lack of available computing power at the time, this was the
method of calculation developed to describe human flow movement
along egress routes, and flow formations towards building
exits.
It is clear that, for such calculations, a mathematical
relationship between V and D was required [22].
The results of 69 experiments and observations, conducted in
Russia, which generated 24000 values of travel speed with
associated densities are presented in Figs 1-4. However,
examination of the data sets from which Figs. 1-4 are derived
indicated their non-homogeneity [3]. This can also be said for the
datasets describing horizontal pedestrian flows [1]. Whilst a
relationship between pedestrian flow, speed and density existed,
the fundamentals underpinning this relationship V=f(D) had not yet
been addressed
The widespread use and acceptance of empiricism and mechanistic
approximations re travel speed and flow density continues. However,
the fundamental theory is lacking. Building design decisions,
whether forced by compliance with prescriptive codes or as a part
of performance based design, should be based on fundamentals, not
mechanistic approximations derived from one off, seldom if ever to
be repeated, experiments. This paper focuses on the research
conducted in Russia to develop and validate fundamental theories in
this respect. In the following paragraphs the potential impact of
emotional state on travel speed is introduced and a theory of
pedestrian movement which relates speed of movement to flow
density, nature of pathway traversed and emotional state is
developed.
[1]Predtechenskii V.M., Milinskii A.I. Planning for foot traffic
flow in buildings. Revised and updated edition. Stoiizdat, Moscow,
1969.
[2]Kholshevnikov V.V. The study of human flows and methodology
of evacuation standardisation. Moscow, MIFS, 1999.
[3] Kholshevnikov V.V. Human flows in buildings, structures and
on their adjoining territories. Doctor of Science Thesis. MISI,
Moscow, 1983.
.[12]Building regulations. Fire safety of buildings and
structures. SNiP II-2-80. Moscow, Stroizdat, 1981.
[13] State Standard 12.1.0004 91 (GOST) Fire Safety. General
requirements. Moscow, 1992.
[14] Building regulations. Building accessibility for disabled
people. SNiP 35-01-2000. Moscow, Stroizdat, 2000.
[17] A.I. Milinskii. The study of egress processes from public
buildings of mass use. Ph. D. Thesis, Moscow Civil Engineering
Institute, 1951.
[18]Predtechenskii V.M., Milinskii A.I. Planning for foot
traffic flow in buildings. Amerind Publisher, New Delhi, 1978.
[19]Predtechenskii V.M., Milinskii A.I. Personenstrome in
Gebauden.-
Berechnungsmehoden fur die Projektierung. Koln Braunsfeld,
1971.
[20]Predtechenskii V.M., Milinskii A.I. Evakuace osobz budov. -
Ceskoslovensky Svaz pozarni ochrany. Praha, 1972.
[21]Predtechenskii V.M., Milinskii A.I. Planning for foot
traffic flow in buildings. Revised and updated edition. Stoiizdat,
Moscow, 1979.
[22] The State Council of Ministers of USSR Act. 14th of January
1971.
THE THEORY FOR EMOTIONAL STATE, DENSITY OF FLOW AND TRAVEL SPEED
LAW
Two concepts determinate the new methodology development for
emotional state, density of flow and travel speed relation 14, 15.
The first is the foot traffic flow is a random process and that
travel speed fluctuation is consequence of that random function.
The second is that travel speed is a behavioural indicator, i.e. an
indicator of motional activity, that is the result of human bodys
system intercooperation16. The general law described by a random
function, was base on 24 thousand measures obtained from a series
of 69 field observations and experiments (the series for horizontal
paths are given on a Fig. 1), i.e.:
)
ln
1
(
0
,
0
,
D
D
a
V
V
i
j
E
j
E
j
D
-
=
if Di>Do,j
(1)
E
j
E
D
V
V
,
0
=
if Di
Do,j
(2)
where,
0
ln
D
D
a
i
j
is general psychophysiological law17 in its particular case
Weber-Fekhner law. VED,j random magnitude of pedestrian flow speed,
at the density Di at the movement on route type j at emotional
state E, m/min; Do,j- is a threshold value of flow density on the j
route type. As soon as the threshold density is exceeded it
influences flow speed. VEo,j - random magnitude pedestrians travel
speed on a route j without the influence of density. Di is the
current density of the flow; aj -is an empirical dimensionless
coefficient, depends on route type;
The conception of motion activity indicators and emotional state
levels might be obtained from the data18 used in emotional states
modelling. The sample extremities law19 and double mean exceeding
law20 were used. The law was validated by actual observations, i.e.
35 thousand of observations. The values of aj and Do,j are given in
a table 2. The values of travels speed ranges dependent on the
emotional states of people are given in table 3.
The developed type of law describes the relation between
parameters with high degrees of correlation (for all types of path
they exceed 0.98).
SPECIAL CASES OF FOOT TRAFFIC FLOWS
In general, its travel speed of people in a flow depends on
their physical abilities and its density of crowd. In the main part
of a flow, displacement of people is always nonuniform and often
random. The distance between moving people constantly changes, with
local increases in densities which are resolve only to reoccur 12
[pp. 24-25]. The trajectory of person movement in a flow is given
on Fig. 2.
The maximum observed density is often 9 person/m2 1. The density
13-14 person/m2 was obtained during the special experiment 11.
Maximum density taken for evacuation computation in Russian
building codes is 9 m2/m2 (i.e. 9 person with the square of
horizontal projection equal 0.1 m2). Predtechenskii and Milinskii
distinguish foot traffic flows as shown in table 1.
At the low density (up to 1-1.5 person/m2) pedestrians dynamic
size might be observed. This is the area (considered as a
rectangle), which pedestrians try to keep clear for manoeuvring.
Average size is 0.8 x 2.0 m13.
It is of interest to note, how precisely density affects travel
speed. Travel speed depends on two factors: length of the step and
a frequency of steps. Density of flow, from this point of view,
limits the length of a step. But if we analyse the inter-person
distance, it might be seen, that at a density of 2-2.5 person/m2
the area for full-step movement (average step is equal 0.7m) is
available, but travel speed is less than free speed (i.e at the
range where density does not affect travel speed, approximately up
to 0.6 person/m2). It means, that the density of flow affect also
influenced by limiting the space for manoeuvring, which also cause
the flow speed to decrease. But if overtaking is possible, the
person estimates distance up to a person or several person ahead
(not just next person) and travel speed might not be reduced.
Cross flows
Cross flows create if inflows and outflows (flow gravity points)
are in the same location9, 21. The maximum density is in areas,
called conflict points. The maximum density at which flows can
cross is 0.4 m2/m2. At flow densities approaching 0.4 m2/m2, the
flow expands, because people deviate from the shortest route
between inflow and outflow. People take a bigger trajectory around
its conflict point. The flow density value, that pedestrians
tolerate around themselves is around 0.2 m2/m2 21 or at average
square of horizontal projection equal 0.15 m2 in underground
stations 1.5 persons/m2. In general, travel speed is much higher at
the cross point because people try to overcome the uncomfortable
zone quicker.
Contra flows
The studies5, 21 showed, that in case of contrary flows the
intensity (and consequently travel speed) of people in a boundary
area between flows is lower, that at same condition for one-way
flow. Pedestrians moving along the boundary of flows are afraid of
collisions, and they keep their speed lower. Field observations5
establish of the speed-reducing coefficient for entire flow - 0.85.
Possibly, in case of wide communications routes, the travel speed
deceleration spreads only for pedestrians of boundary layer of both
contraries flows. So, the travel speed reduction might be accepted
for outer lane pedestrians only. The studies5,9,21 showed the cross
and contrary flows should be strictly avoided during
evacuation.
Movement on routs with unlimited width
If a flow exits on a route with unlimited width (e.g. foyer of
vestibule), it does not spread themselves in width infinitely and
its density is stills higher then at Do,j. Apparently, density of
the flow is a kind of compromise between high travel speed and
traffic along the remote route, and low travel speed and traffic
along the direct route. The flow is a cigar-shape: at the entering
the sector, it spreads at 300 angle, and at exiting the sector, it
converges at 450 angle. The average flow density is 1.5 persons/m2
22 The width of a flow (b) depends on a number of people within and
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