1
Parameters of pedestrian flow for modeling purposes
V. V. Kholshevnikov1, D. A. Samoshin2
1
Professor, State Moscow University of Civil Engineering, Moscow, 127337,
Yaroslavskoe Highway, Russia, reglament2004@mail.ru
2
Ph.D, Lecturer of Academy of State Fire Service of Russia, 129366,
B.Galushkin, 4, info@FireEvacuation.ru
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 Milinskii’s 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 nonhomogeneity 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
2
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:
D
Nf
lb
where
N
=
number of people,
l
=
length of the pathway (m),
3
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:
qi,jbi
qi1,j 
bi1
(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:
qb

q
i
1
,j 
i,j i
b
i
1
(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
P
capacity of the adjacent sector as Qi+1,j= qmax,jbi+1 then, if Q
i
1,j 
i,j the flow is
P
unimpeded. Alternatively, if Q
i
1,j 
i,j at the interface with the adjacent sector
4
1
1
t
N

)

i(
i+1, movement delay develops with the duration 
Q
P. The
i

1
,j

i
,j
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:
q1 q2
V
1
D
1 D
2
(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
5
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.
Predtechenskii V.M., Milinskii A.I. Evakuace osobz budov. - Ceskoslovensky Svaz
pozarni ochrany. Praha, 1972.
Predtechenskii V.M., Milinskii A.I. Planning for foot traffic flow in buildings.
Revised and updated edition. Stoiizdat, Moscow, 1979.
The State Council of Ministers of USSR Act. 14th of January 1971.
[20]
[21]
[22]
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
6
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 body’s 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.:
D
if Di>Do,j
(1)
VDE, j  V0E, j (1  a j  ln i )
D0
V V
E
D
where, a j ln
Di
D0
E
0, j
if Di  Do,j
(2)
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
7
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
length of the route (l): b=4 m, if N<100 and l  6m , and b =6m in all the rest cases22.
Movement through door aperture
This type of movement is the most crucial during the evacuation movement,
because their insufficient traffic capacity is often the reason for fatalities. In general,
travel speed is somewhat higher, because pedestrians try to overcome potentially
dangerous door aperture quicker. In the study11 the adjustment coefficient, applying if
8
density of flow is higher 0.5 m2/ m2, considering phenomenon called “false aperture”
was established:
m=1.25-0.5D
(3)
The “false aperture” phenomenon is that if density of flow is higher 0.5 m2/ m2,
than the people passing an aperture on the edge of flow are driven against the door
surrounds by the dense flow. So, they try to push themselves away from the exit
surrounds to the centre of the aperture, decreasing its width.
At the maximum density 0.9 m2/ m2 the intensity of flow movement (q) through
door of different width is taken by the formula, based on minimum values of q:
q=2.5+3.75b m2/ m min
(4)
MODELLING OF PEDESTRIANS MOVEMENT IN A FLOW
For realisation of theoretical and practical research the stochastic models were
developed14, 24: ADLPV (analysis of foot traffic flows, probability) and SDLP (free
foot traffic flows). The models for complicated cases of movement were also
developed: contrary and crossing flows, movement on unlimited width routes25-28. The
results of different situations modelling show the high models’ reliability (Fig. 3).
Nowadays, capability of IBM allows modelling each pedestrian in a flow. To
do it, we need:
1. The law of flow density influence to pedestrians’ travel speed.
2. Travel speed values for people with different emotional state, for people with
different age and gender.
1. As it has been shown above, the density of flow affects by limiting the space
for movement. The most simple and quite reliable criteria for modelling is inter-person
distance. That is why this approach is widely spread today, for example29. The most
important issue here is a choice of correct relations.
Taking the formulae, connecting the density of flow in person/m2 with linear
density in m/person11, 30, the formula for inter-person distance and density of flow
might be derived. In their turn, formula for inter-person distance and travel speed
might be obtained:
VDE, j  V0E, j (1  a j  ln
l0
)
lD
(5)
1
- inter-person distance at Di, m
c  Di
1
l0 
- inter-person distance at D0, m
c  Do
lD 
с – average body width (taken 0,5 m).
Graphical relation between travel speed and inter-person distance, and interperson distance and density of flow is given on Fig. 4, 5.
9
At that it should be realized, that the l is a distance between geometrical body
centres. That is why, at high density of flow, where the physical compression takes
place11, the distance is 20 cm only.
Moreover, relatively high values of distance l0 is because it is the distance for
ahead ahead person, because just ahead person is not an obstruction, so as he might be
overtaken easily. The overtake possibility is restricted by a density of flow equal 0.15 0.20 m2/ m2. If overtake is impossible, l should be considered as a distance to the
closest person ahead (Fig. 6).
2. A pedestrians in a flow, does not go as a machine with a constant travel
speed (at all other condition being equal) they sometimes either decelerate speed to
avoid collisions or accelerate for overtaking. That is why assigning the certain labels
for people of different age or gender is very provisional. But computer modelling,
require exactly the labels, so we have to make a step aside from the real process.
Analysis of field observation data allows to conclude, that for evacuation
computations, the category “of increased activity” should be used. The free travel
speed range for the interval is from 1.5 m/s to 2.0 m/s. The values 1.66m/s (100
m/min) is accepted as an average value for evacuation computation in Russian
Buildings Codes. If we turn to Table 4, which is used in for forensic road accidents
analysis, we can see, that average travel speed of almost all people from the category
“walk with hurried steps” fit the range “of increased activity” providing required
integration for gender and age. For people who walk with hurried steps with a speed
lower than 1.5 m/s, their travel speed should be taken 1.5 m/s anyway, because they
would apply more efforts (run) to keep themselves in a flow. Hence, for individual
pedestrian modelling in a flow, the value Vo,jE for formulas (1) and (5) could be taken
from table 4. But evacuation is a casual process, so all computations (modelling)
should be done many times to collect all require statistic for egress time and other
parameters. In that case, individual travel speed might be taken randomly from a
provided range (Table 4).
For foot traffic modelling in other emotional states, the reducing coefficient
should be use, equal ratio of average travel speed of considered emotional state to
average travel speed “of increased activity” category (105 m/min).
CONCLUSION
Intense foot traffic flow research facilitated to gathering of valuable empirical
data, to find general laws, to work out and validate the theory, that has been use in fire
prevention buildings codes for 20 years32, 33. On the base of studies conducted,
algorithms, each pedestrian in a flow base on age, gender, emotional state, type of
egress route and density of flow (expressed as inter-person distance) have been
developed. For more precise modelling, the cases that have special characteristics are
considered in more detail. The material presented in the paper provides reliable data
for pedestrian flow modelling.
REFERENCES
10
1. A.I. Milinskii. “The study of egress processes from public buildings of mass
use” (In Russian). Ph. D. Thesis, Moscow Civil Engineering Institute, 1951.
2. Kalincev V.A. “Planning for the foot traffic flow in cinemas” (In Russian).
Ph.D. Thesis, Moscow Civil Engineering Institute, 1966.
3. Kholshevnikiv V.V. “Dmitriev A.S. Study of human flows regularity on
footways in transport traffic centres” (In Russian). Deposited in CNIIS №988,
Moscow, 1978.
4. Duvidzon R.M. “Planning for the foot traffic flow in sport building” (In
Russian). Ph. D. Thesis, Moscow Civil Engineering Institute, 1974.
5. Grigorjanc R. G. “The study of permanent human flows” (In Russian). Ph. D.
Thesis, Moscow Civil Engineering Institute, 1971.
6. Eremchenko, M.A. Predtechensky, V.M. Kholschevnikov V.V.
“Standartization of communicating routes in schools” (In Russian). Residentional
construction, №10, 1977.
7. Sapelovskay, A.A. “Pedestrian and transport flows formation in urban
changing railway station for suburban connection” (In Russian). Ph. D. Thesis,
Moscow Civil Engineering Institute, 1980.
8. Buga P.G. “Study of foot traffic flows in city traffic units” (In Russian). Ph.
D. Thesis, Moscow Civil Engineering Institute, 1974
9. Gvozdaykov V. S. “Regularity of human flow movement in traffic
structures” (In Russian). Ph. D. Thesis, Moscow Civil Engineering Institute, 1977.
10. Predtechenskii V. M., Tarasova G.A. and other. “The study of people
movement in the conditions close to emergency” (In Russian). The report /Higher
School MOOP RSFSR., Moscow 1964.
11. V.A. Kopylov “The study of people’ motion parameters under forced egress
situations” (In Russian). Ph. D. Thesis, Moscow Civil Engineering Institute, 1974.
12. Predtechenskii V.M., Milinskii A.I. “Planning for the foot traffic flow in
buildings” (In Russian). New Delhi, 1978.
13. Piir R. L. “Pedestrian traffic flow study on city’s main streets” (In Russian).
PhD thesis, Leningrad, – 1971.
14. Kholshevnikov V.V. “Human flows in buildings, structures and on
adjoining territories” (In Russian). Doctor of Science Thesis. –MISI, Moscow, 1983.
15. Kholshevnikov V.V. “Foot traffic flow study and methodology for people’s
evacuation standardization” (In Russian). MIPB, Moscow, 1999.
16. 5. M.A. Eremchenko, V.M. Predtechensky, V.V. Kholschevnikov
“Standartization of communicating routes in schools” (In Russian). – Residentional
construction, №10, 1977.
17. Zabrodin J. M., Lebedev A. T. “Psychology and psychophysics” (In
Russian). Moscow, 1977.
18. Volkov P.P., Oksen V.H. “Informational modelling of emotional states” (In
Russian). Moscow, 1978.
19. G u m b e l E . I . “Statistical Theory of Extreme Values and Some Practical
Applications”. Washington, 1954.
32. Volgin A. N. “The principles of coordinated optimum” (In Russian).
Moscow, 1977.
11
21. Isaevich I.I. “Working out the basics of multi-variation analysis of planning
design solution of subway stations and transfer knots on modelling relationships of
people’ foot traffic flow’ basic” (In Russian). Ph. D. Thesis, (Supervisor V.V.
Kholshevnikov). MISI, Moscow,1990.
22. Ovsyannikov A. N. “The regularity of communication routes design in
covered stadiums” (In Russian). Ph. D. Thesis, (Supervisor V.V. Kholshevnikov).
MISI, Moscow,1981.
23. Kholshevnikov, V. V., Kopylov, V. A. “Foot traffic flow through door
aperture” (In Russian)//Firemanship, 1982. № 3.
24. Kholshevnikov, V. V. “Foot traffic flow modelling.” In: Fire and explosions
modelling” (In Russian) (Eds: Brushlinskii, N. N., Korolchenko, A. Y.) Moscow,
Pozshnauka, 2000.
25. Kholshevnikov, V. V. Isaevitch, I. I. “Modelling of contrary flows” (In
Russian). Deposited in VNIINTPI Gosstroi USSR, №9428, Moscow, 1988.
26. Kholshevnikov, V. V. Isaevitch, I. I. “Modelling of crossing flows” (In
Russian). Deposited in VNIINTPI Gosstroi USSR, №9429, Moscow, 1988.
27. Kholshevnikov, V. V. Isaevitch, I. I. “Modelling of pedestrians flows on
platforms of underground stations” (In Russian). Deposited in VNIINTPI Gosstroi
USSR, №9430, Moscow, 1988.
28. Kholshevnikov, V. V. Isaevitch, I. I. “Pedestrian flow modelling on unlimited
routs width” (In Russian). Deposited in VNIINTPI Gosstroi USSR, №9427, Moscow,
1988.
29. Thompson, P. A. Simulex: “Development New Computer Modeling
techniques for evacuation”. Proceedings of the Fourth International Symposium on
Fire Safety Science, 1994, pp. 613-624.
30. Belyaev S. V. “Public building evacuation” (In Russian), All-Russian
Academy of the Architectures Publisher. Moscow. 1938.
31. Bekasov, V .A., Bograd, G. Y., Zotov, B. L., Indichenko, G. G.
“Autotechnical expertise” (In Russian). Moscow, Yuridicheskay Literatura, 1967.
32. Building regulations. SNiP II-2-80. “Fire regulations for buildings’ and
structures’ design” (In Russian). Moscow, Stroiizdat, 1981.
33. State standard. GOST 12.1.004-91. “Fire safety. General requirement” (In
Russian). Moscow, Stoiizdat, 1992.
Table 1. Categories of foot traffic flows
Flow density,
D, m2/m2
0 – 0.05
0.05 – 1.15
0.15-0.40
Category
FREE (UNIMPEDED)
STREAMLINED UNIMPEDED
Without contact
interferences
CONSTRAINED
12
0.40 – 0.75
0.75 – 0.92
0.92 – 1.0
1.0 – 0.15
With contact interferences
Conjoint
With shape changing
With compressing
CONSTRAINED, WITH
FORCE IMPACT
Table 2. Values of aj and Do,j for each route type
Route type
Horizontal outdoors
Horizontal indoors
Door aperture
Stair downwards
Stair upwards
aj
0,407
0,295
0,295
0,400
0,305
Do,
person/m2
0,69
0,51
0,65
0,89
0,67
Table 3. Categories of movement, emotional state and free travel speed.
Free travel speed
m/min (m/s)
Categories of
movement
Comfortable
Quiet
Active
Of increased
activity
Emotional state
level
0,00
0,45
0,68
Horizontal way, door
aperture, stairs
downward:
49,0 (0,82)
66,0 (1,10)
90,0 (1,50)
27,0 (0,45)
38,0 (0,63)
55,0 (0,92)
0,70
120,0 (2,00)
75,0 (1,25)
Stairs
upward:
13
Table 4. Pedestrians’ travel speed depend on pace.
Age group, years
G
e
n
d
e
r
M
F
M
8-10
F
M
10-12
F
M
12 -15
F
M
15 - 20
F
M
20 - 30
F
M
30 - 40
F
M
40 – 50
F
M
50 - 60
F
M
60 - 70
F
M
Over 70
F
Amputees
М
Drank
М
Child led by adult F
by hand
Adult carrying a M
child
F
With large
M
package
F
With baby
F
carriage
Walking hand in hand
7-8
Nu
mb
er
of
co
unt
s
23
29
56
54
43
48
76
78
38
20
57
72
51
53
55
74
46
50
33
42
19
71
10
19
28
Walk with
hurried
steps, m/s
Aver Nu
age mbe
speed r of
, m/s cou
nts
Calm
running,
m/s
Average
speed,
m/s
1,50 – 1,81
1,39 – 1,72
1,56 – 1,86
1,44 – 1,78
1,58 – 1,92
1,50 – 1,83
1,64 – 1,97
1,56 – 1,89
1,67 – 2,17
1,58 – 1,92
1,75 – 2,17
1,67 – 2,06
1,75 – 2,17
1,64 – 2,00
1,67 – 2,00
1,53 – 2,00
1,50 – 1,89
1,44 – 1,81
1,25 – 1,67
1,25 – 1,56
1,00 – 1,39
1,00 – 1,33
1,11 - 1,47
1,39 – 1,78
1,31 – 1,53
1,63
1,47
1,67
1,53
1,72
1,61
1,81
1,69
1,89
1,75
1,92
1,83
1,89
1,81
1,86
1,69
1,67
1,56
1,42
1,36
1,17
1,14
1,25
1,5
1,44
28
31
62
53
46
48
118
75
12
11
25
47
29
45
25
41
15
24
8
17
20
26
4
22
16
2,00 – 2,89
1,94 – 2,78
2,06 – 2,97
2,00 – 2,86
2,11 – 3,08
2,06 – 2,97
2,17 – 3,25
2,14 – 3,11
2,99 – 3,61
2,25 – 3,50
2,44 – 3,61
2,36 – 3,56
2,28 – 3,33
2,25 – 3,22
2,11 – 3,08
2,11 – 2,94
1,94 – 2,78
1,92 – 2,50
1,72 – 2,11
1,72 – 2,08
1,42 – 1,81
1,36 – 1,72
1,53 – 1,86
1,94 – 2,39
1,61 – 2,31
2,36
2,22
2,47
2,33
2,58
2,47
2,78
2,64
2,86
2,78
3,06
2,94
2,94
2,72
2,67
2,47
2,39
2,19
1,94
1,89
1,56
1,53
1,67
2,28
1,92
6
18
9
4
5
1,39 – 1,53
1,33 – 1,56
1,5 – 1,75
1,47 – 1,67
1,31 – 1,58
1,47
1,42
1,61
1,53
1,44
2
3
8
2
1,72 – 2,00
2,36- 2,78
1,92 – 2,61
1,83 – 2,00
1,86
2,50
2,31
1,92
22
1,53 – 1,86
1,67
9
2,08 – 3,14
2,5
14
V
m/min
D, person/m2
Figure 1. Empirical relations between travel speed and density of pedestrian flow.
Horizontal ways (№ of the series; reference [ ] ):
Buildings: theatres, cinemas 1- [1], 5- [2]; universities 2- [1]; industrial 3- [1];
transport structures 4- [1], 13, 14 - [3]; sports 6- [4]; other 7- [1]; trade 8- [5];
schools: senior group 9 - [6], middle 10 - [6], young 11- [6];
Streets: shopping centre 12- [5]; transport junction 15 - [3], 16 - [7], 18- [8],
Industrial unit: 19- [8];
Underground stations: 20 - [9], 21- [10];
Experiment: 22, 23 - [11].
Figure 2. Pedestrians’ trajectory in a flow.
15
P, person/min
100
80
а)
60
40
20
0
0
2
4
6
8
10 12 14 16 18 20 22
t, min
N, people
300
250
b)
200
150
100
50
0
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
t, min
Figure 3. The comparison of field observation (
) and modelling (-----):
а) model SDLP – plant territory;
b) model АDLPV – communication route of Moscow’s underground system;
V, m/min
100
80
60
Horizontal
Door appert.
40
Stairs dow n
Stairs up
20
0
l,m
0
0.5
1
1.5
2
2.5
3
3.5
4
Figure 4. Graph of travel speed (at mean value of unimpeded
pedestrians’ speed (V0) at high active emotional state equal V0=60 m/min
for stairs up and V0=100 m/min for the rest types of routes) against
distance between geometrical centers of person l.
16
l,m
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
D, per/m2
Figure 5. Graph of inter-person distance and flow density
D< 0.15 – 0.20 m2/ m2
D  0.15 – 0.20 m2/ m2
l, m
l
,
а)
m
b)
l, m
Figure 6. Inter-person distance and density of a flow.
а) overtake is possible; b) overtake is impossible;