RETROSPECTIVE REVIEW OF RESEARCH ON PEDESTRIAN FLOWS MODELLING IN RUSSIA AND PERSPECTIVES OF ITS DEVELOPMENT

V. V. Kholshevnikov1, T. J. Shields2, D. A. Samoshyn3, M. M. Galushka4

1State Moscow University of Civil Engineering, Yaroslavskoe Highway, Moscow, 127337, Russia2FireSERT Centre, University of Ulster, Newtownabbey, BT37 0QB, UK

3Fire SERT Centre, University of Ulster/Academy of State Fire Service of Russia, bldg. 4, B.Galushkin str., 129366, Moscow, Russia.

4 Faculty of Engineering, University of Ulster

ABSTRACT

This paper presents further pedestrian flow research based on the work of Predtechenskii and Milinskii [1] with the focus on pedestrian flow modelling. The results of 69 series of actual observations and experiments with 24,000 values of travel speed against density obtained in Russia, were used for analysis. Based upon new methodological principles, the general expression is derived and introduced which governs pedestrian flow speeds for all considered pathways, ie, horizontal and inclined and different psychological condition. The general expression is encapsulated in a computer based pedestrian flow simulation model ADLPV, able to calculate all parameters of human flow at different levels of psychological stress at any point in the building at any step in time. New advanced algorithm for crowd movement simulation is outlined.

INTRODUCTION

By the end of 1970, various investigations including numerous observations of pedestrian flows movement in buildings of different purpose were conducted in the Russia by the team headed by Prof. Predtechenskii [1]. The obtained relationships derived a qualitative view of the interaction between pedestrian flow speed and density, ie, as the density increases the pedestrian flow speed decreases. In quantitative terms however, different researchers use different functions approximating the empirical data with respect to pedestrian flow speed and density. This approach does not lead to the establishment of any theoretical basis for the relationship between pedestrian flow speed and density. The source data which was obtained from 69 experiments conducted in public and industrial buildings, subway stations and large pedestrian areas in urban settings, (series for horizontal planes are summarised and presented in Figure 1) was used for further analysis.

To develop the function, which describes the relationships between parameters of pedestrian flows, the principles of psychophysiological theory of functional systems, theory of coordinated optimum, game theory, physiology’s laws and special statistical methods were used [13-19]. Eventually, the relationships between travel speed, density of flow and pedestrian emotional state were established [20-21]:

(1)

- is the average travel speed of pedestrians in a flow, m/min;

- is the average travel speed of pedestrians on a route without

the influence of density, m/min;

aJ - is an empirical constant for each type of pathway;

Di - is the prevailing density of the flow, persons/m2 (or m2/m2);

Doj - is a threshold value of flow density on the j-the pathway, persons/m2 (or m2/m2 if pedestrians are measured based on their horizontal projection).

E - is an indicator of the emotional state of the pedestrian (the category of movement);

J - is an indicator of the type of route traversed;

Figure 1. Empirical relations between travel speed and density of pedestrian flow [20,21]. Horizontal ways (№ of the series; reference [ ] ):

Buildings: theatres, cinemas 1- [2], 5- [3]; universities 2- [2]; industrial 3- [2]; transport structures 4- [2], 13, 14 - [4]; sports 6- [5]; other 7- [2]; trade 8- [6]; schools: senior group 9 - [7], middle 10 - [7], young 11- [7]; Streets: shopping centre 12- [6]; transport junction 15 - [4], 16 - [8], 18- [9], Industrial unit: 19- [9]; Underground stations: 20 - [10], 21- [11]; Experiment: 22, 23 - [12].

D, person/m2

V, m/min

The values of Doj and aJ are given in a Table 1. The categories of movement and the corresponding values of free travel speed along the routes are given in a Table 2.

Route type aj Do,

person/m2

Horizontal outdoorsHorizontal indoorsDoor apertureStair downwardsStair upwards

0.4070.2950.2950.4000.305

0.690.510.650.890.67

Table 1. Values of ai and Doj for each route type [20,21].

Categories of movement

Unimpeded travel speed , m/min

Horizontal plane, door aperture, stairs downward: Stairs upward:

Comfortable Quiet Active Of increased activity

<49.049.0 – 66.066.0 – 90.090.0 – 120.0

<27.027.0 – 38.038.0 – 55.055.0 – 75.0

Table 2. Categories of movement, emotional state and unimpeded travel speed [20,21].

Obviously, different categories of movement (corresponding to particular emotional state of people in a flow) should be used for different purpose. For example, category “of increased activity” is used for evacuation computations in Russian Fire Prevention Building Codes, which was justified in [20,21]. In

particular, for deterministic calculations, the values of =100 m/min is accepted for horizontal plane,

door aperture, stairs downward, and =60m/min for stairs upward. The graphs plotted based on the

formula (1) for evacuation calculation are given on the Figure 2. Explanations of some formulas on the Figure 2b are given further in the text. Based on established relations, the algorithms for pedestrian flow modelling were developed.

ALGORITHMS FOR PEDESTRIAN FLOW MODELLING

For built environments to function as required it is necessary to provide integrated circulation routes. In buildings circulation routes can take up to between 30% and 40% of available floor space [20]. For normal use they should be unobstructed and comfortable to use. In emergency conditions such as evacuation in the event of a fire they should similarly be unobstructed, easy to use and lead naturally to places of relative safety, ie, the flow patterns induced through usage under normal conditions should not mitigate against usage under emergency conditions.

To meet these requirements, circulation routes should be precisely computed and different methods may be used for this pupose. It is possible to calculate pedestrian flows manually. In 1958 Predtecenskii and Milinskii completed the g

raph-analytical method of pedestrian flow traffic computation [1]. This method has some limitations. However, it is possible to use it for egress calculation and it is being used for engineering calculations in Russia.

Figure 2. The relationships between parameters of pedestrian flow, applied in Russian Fire Prevention Building Codes: a) average travel speed and b) intensity of movement against density of flow.

Obviously, modelling is more powerful tool and the model ADLPV (from Russin - Analysis of Foot Traffic Flow, Probability) was developed [20, 22]. In this model the entire building is sub-divided into elements of floor space with the lenths equal to 0.5m – 1.0 m and with the width of the route. At timeo

the number of people in the first elementary section is determined: . If the width of the pathway section is bi the density of flow is:

Figure 3. Model of pedestrian flow states fluctuations at consecutive moments of time [20,21].

(2)

a b

Time t0

A

A

B

B

C C

Time t=t0+t

A

A

B

B

C C

i-1 i+1i

Sector:

i-1 i+1i

Sector:

Sector: j Sector: j

These go along the elementary sector i with travel speed V. Analogical statements are on previous i-1, on the next i+1 sector and on the elemental sector j adjoining to the i.

After the lapse of in the instance of time occupants move from sector i to a next sector i+1,

Figure 3. These occupants will be designated as . From of people placed in a sector i at the

instant t0, this sector will contain only - persons after the lapse of , but this number will be

added by the people passed from the previous sectors i-1 and j during this time , and respectively. That the flow density at the sector i can be written as following:

(3)

The travel speed of the occupants of sector i at time t1 is then a function of the density of the flow in sector i is calculated according to (1).

This process is repeated for all of the occupied sectors. Variations in the density of the flow in different sectors of the route at different times reflects the process of flow adjustment including flow spread. As shown, the variation in flow density is a result of the different numbers of occupants passing through the connected sectors of the route. In general, the number of occupants moving from sectors i to sector i+1 is:

(4)

Where Vpass is the speed of the occupants passing through the sector bounded, eg, by A-A, B-B, C-C (VA,VB and VC respectively), Figure 3. If occupants enter a narrower elementary sector, eg, a door opening a width correction is necessary. From field observations deviations in flow trajectory were established, ie, pedestrians on the outer fringes of the flow altered their trajectories when forced to diverge and converge by 30o and 45o respectively, Figure 4.

Conceptually for the purposes of modelling pedestrian flow it is reasonable to assume a wedge shaped flow moving forwards into the adjacent sector with a flow speed of . If the density of the flow in the sector ahead is above certain limits the flow of the migrating occupants will decelerate. Thus the speed Vpass of passing through the boundary of adjacent sectors can be taken as:

(5)

is the value of density corresponding to the maximum intensity of the flow [1]. is approximately equal to 0.5 m2/m2, Figure 2.

If Vpass = the number of occupants remaining in sector i increases while the number moving to sector i from sectors i-1 and j remains the same.

Under this condition the flow density for sector i will increase and thus flow density will quickly (5-7s according to [12]), approach . When there is congestion in the flow. If at some instant of time tk the flow density reaches its maximum value such that it cannot increase further there will be

congestion of and people, who cannot move from one sector to the next.

During a next time step , some people will leave sector i. It means, that and

people from sectors i-1 and j will be able to move to sector i. Their contributions with

respect to flow into sector i at is proportional to the width of the sectors i-1 and j. For the general case the ratio of their contributions can be expressed as:

(6)

The core of the model is described above. Special cases of pedestrian flows, which are briefly discussed below, were investigated and encapsulated in the model.

If a flow enters a route with unlimited width (i.e foyer or vestibule), it does not spread itself in width infinitely and its density is still higher then at Do,j. The density of the flow is a 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-shaped: ie, the entering the sector, it spreads at 300 angle, and at exiting the sector, it converges at 450 angle. The width of a flow (b) depends on a number of people within and length of the route (l): b=4 m, if N (number of people in a flow) <100 and , and b =6m in all the rest cases, Figure 4. It was established during an analysis of actual observations data [23].

Figure 4. The scheme of pedestrian flow traffic along a route with unlimited width [23].

Movement through door aperture is the most crucial during the evacuation movement (and consequently modeling), 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 study [12] the adjustment coefficients, presented earlier in Fig. 2b, were established. One of them m is multiplied on V counted according to (1) if density of flow D near a door is higher 0.5 m2/ m2. It is consider phenomenon called “false aperture”:

m=1.25-0.5D (7)

The “false aperture” phenomenon is that if density of flow is higher 0.5 m2/ m2, then the people passing an aperture on the edge of flow are driven to a doorpost by the dense flow. So, they try to push themselves from the doorpost 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, obtained during actual observations. If door width

l

b

300

450

450

300

is more or equal to 1.6m, then intensity is constant and equal to 8.5 m2/m min, if the width of a door is less, intensity depends on a door width b:

q=2.5+3.75b m2/ m min (8)

Further, normally at evacuation condition, one-way flows are generated, but for instance in traffic structures, such as underground subway stations, cross flows and contrary flows exists. These special cases of pedestrian’s flows were investigated, and valid models were developed [24].

The set of expressions above describes completely pedestrian flow on elementary sectors and their respective transitions for the deterministic V = f(D). However, probability could be introduced in the calculations, because flow traffic is a random process. For each value of pedestrian flow density at each time interval the corresponding flow speed distribution is generated from which a value of flow speed is randomly chosen.

Obviously, different people could have various travel speeds at current value of flow density. But ability to chose preferable travel speed is physically restricted by the density of flow. So, average travel speed might be calculated by (1), standard deviation of the travel speed – by the formula:

= (9)

where, - standard deviation from the . According to actual observations, distribution obeys

Gauss law. So, is taken as 1/6 from the travel speed range, which depends on emotional state of people, Table 2. Graph on travel speed fluctuation depending on density of flow for people in high active emotional state along the horizontal plane is given on Figure 5.

Figure 5. Graph of travel speed range fluctuations depends on flow density for category of movement “of increased activity” and horizontal plane [20,21].

The main difficulty for flow modelling is the density impact, which required complicated algorithms and high computer power. At the low density of flow, Di D0, while density does not affect travel speed, travel

time is route length divide on travel speed. Such kind of situations happened quite frequent outdoors, on city streets, where physical limiters for flow traffic are absent. Complicated cases (many flow sources, different source egress time, travel speed diversity etc) required computer attraction as well. To automate these routines, SDLP model (from Russian – Free Foot Traffic Flow) was develop [20, 22].

In the case, where the researcher needs to calculate evacuation of large residential area (e.g. several thousand occupants along several kilometers length routes), but it is supposed that the density would exceed D0, SDLP might be used in a following way. For example, the ADLPV model calculates certain parameters of pedestrian flow. Mostly, these are sources’ (e.g. building etc) flow egress distribution time and travel speed values on the routes following the sources. These data could be used as input parameters for SDLP.

NEW APPROACH TO PEDESTRIAN FLOW MODELLING

The model ADLPV was developed more that 20 years ago, and its algorithm was restricted by the power of computing machines of those time. The ability to model the movement of individuals in pedestrian flow is a great achievement of the modern computer science. The most important issue here is a development of a correct technique. The most simple and quite reliable criteria for crowd movement modeling is the inter-person distance, and this approach is widely used today [e.g. 25-27].

Taking the formulae, connecting the density of flow in person/m2 with linear density in m/person [12, 28], 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 [29]:

(10)

- inter-person distance at Di, m

- inter-person distance at D0, m

с – average body width (taken 0,5 m).

In the formula (10) l is a distance between geometrical body centres. That is why, at high density of flow, where the physical compression takes place [12], the distance is 20 cm only.

Moreover, relatively high values of distance l0 are because it is the distance for furthest person ahead, because person just ahead is not an obstruction, so they may be overtaken easily. The overtake possibility is restricted by a density of flow equal 0.15 - 0.20 m2/ m2. If overtaking is impossible, l should be considered as a distance to the closest person ahead.

From analysis of field observations data it can be concluded, that for evacuation computations, the category “of increased activity” should be used. Free travel speed range for this interval is 90 - 120 m/min (1.5 to 2.0 m/s). If we turn to Table 3, which is used for forensic road accidents analysis [30], 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 differentiation for gender and age. For people who walk with hurried steps with a speed lower than 1.5 m/s (90m/min), 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 (10) could be taken from Table 3, with

the exception for movement along stair upward, because there is no data available. A

ge g

roup

, ye

ars

Gen

der

Num

ber o

f co

unts

Wal

k w

ith

hurri

ed

steps

, m/s

Ave

rage

sp

eed,

m/s

Age

gro

up,

year

s

Gen

der

Num

ber o

f co

unts

Wal

k w

ith

hurri

ed

steps

, m/s

Ave

rage

sp

eed,

m/s

1 2 3 4 5 1 2 3 4 5

7 – 8 MF

2329

1,50 – 1,811,39 – 1,72

1,631,47 60 - 70 M

F3342

1,25 – 1,671,25 – 1,56

1,421,36

8 – 10 MF

5654

1,56 – 1,861,44 – 1,78

1,671,53 Over 70 M

F1971

1,00 – 1,391,00 – 1,33

1,171,14

10 - 12 MF

4348

1,58 – 1,921,50 – 1,83

1,721,61 Amputees М 10 1,11 - 1,47 1,25

12 - 15 MF

7678

1,64 – 1,971,56 – 1,89

1,811,69 Drunk М 19 1,39 – 1,78 1,5

15 - 20MF

3820

1,67 – 2,171,58 – 1,92

1,891,75

Child led by adult by hand

F 28 1,31 – 1,53 1,44

20 - 30

MF

5772

1,75 – 2,171,67 – 2,06

1,921,83 Adult

carrying a child

MF

618

1,39 – 1,531,33 – 1,56

1,471,42

30 - 40 MF

5153

1,75 – 2,171,64 – 2,00

1,891,81

With large package

MF

94

1,5 – 1,751,47 – 1,67

1,611,53

40 – 50 MF

5574

1,67 – 2,001,53 – 2,00

1,861,69

With baby carriage

F 5 1,31 – 1,58 1,44

50 - 60MF

4650

1,50 – 1,891,44 – 1,81

1,671,56

Walking hand in hand

- 22 1,53 – 1,86 1,67

Table 3. Pedestrians’ travel speed depend on pace [30].

For foot traffic modelling in other emotional states (e.g. in “quiet” category of movement), the reducing coefficient k should be used. It is equal to ratio of average unimpeded travel speed of considered emotional state (e.g. “quiet” category - 57.5 m/min, Table 2) to average travel speed “of increased activity” category (equal to 105 m/min, Table 2). So, for the given case k=57.5/105=0.55. However, it needs further validation.

Thus, approach provides an ability to model the movement of each pedestrian in a flow, considering their age, gender, emotional state, type of egress route and density of flow (expressed as inter-person distance).

THE DERIVED LAWS AND MODELS VALIDATION

The underlying theory of pedestrian flows, relationship and models presented in this paper are distilled from much experimental work. In order to use the foregoing with confidence it was necessary to conduct some validation studies. These included observations of pedestrian flows in “The Hermitage”, a world famous museum, in one of the largest trade complexes in Russia “Children’s World”, during unannounced evacuations of multi-storey office buildings [31], analysis of pedestrian flows in the

Moscow Underground System [24] and in industrial/manufacturing complexes [32]. As an illustration, the comparison of data obtained during actual observations and modeling is given on Figure 6.

Figure 6. The result of actual observation in Moscow underground station and modelling by the model ADLPV [31]: curves show number of people (from arrived trains) passing control line (close to exit

station) at particular time instants since the first person from the trains passed the line.

The validation studies confirmed the soundness of the pedestrian flow theory, relations and models presented in this paper, ie, the actual flow patterns observed could be modelled and predicted with high levels of confidence.

CONCLUSIONS

Based on rich empirical data and on up-to-date methodologies, ie, principles of psychophysiological theory of functional systems, theory of coordinated optimum, game theory, physiology’s laws and special statistical methods, the theory describing relations between parameters of pedestrian flows (travel speed, density and emotional state level) were developed. On the basis of the theory, the simulation models, which reflect the nature of pedestrian flows, were also developed. Wide-scale research validated the established relations and developed models. The concepts described in this paper have been used in a very practical sense in Russian Fire Prevention Buildings Codes for over two decades. According to the scientific trend in the field of evacuation modelling [25-27], the core of new advanced algorithms for crowd simulation modelling has been developed.

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