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Summary of last decades research
“Foot traffic flows: actual observations, experiments and theory”
Prof. Valery V. Kholshevnikov
Fire Bridge meeting in University of Ulster , Northern Ireland , 2-6 September 2000
Along the centuries a city demonstrates that foot traffic flows in buildings, engineering structures and on adjacent territories are ones among the main functional processes, which provide its liveability.
However, systematic study of this process began only in fourth decade of our century.
That’s why we are the witnesses of the development of these studies along the traditional path of scientific knowledge: from empiric to the first generalizations and theoretical structures and later on to the theory itself.
In Russia these stages can be emphasized very clearly either by time periods or by scientific works of well-known experts, whose names are now the symbols of these studies. But today it is more important to summarize the results of this collective investigations but, due to the shortage of time, it’s better to list the main principles, which became understandable in this difficult scientific field during the last 70 years.
Foot traffic flow is a mass of people which is moving simultaneously and unidirectional along a mutual route. This easy and traditional definition, however, needs to be clarified, because of the broad sense of different terms in it, which leads sometimes to incorrect understanding of the real process of “foot traffic flows”. Different types of movement, the content of the people’s mass, psychological and physical state, different types of routes etc, create the zone of correct implementation of the above-mentioned term (indicated by solid line on figure 1).
The main way to obtain basic data about qualitative and quantitative characteristics of foot traffic flows, about their phenomenology etc remain actual observations and experiments. These are also valid in checking of theoretical assumptions and hypotheses. An experiment is based on aimed regulation of different characteristics of a foot traffic flow or of a route of its movement in order to learn out the degree of affectation of different factors on the process. Such an regulation is impossible in actual life, because in reality the experiment is conducted by the Nature itself, and the rules of this experiment frequently are not known to an observer. The methods of gaining initial data are common for either actual observations or experiments, i.e.: visual method; film-and-camera method (movie or photo method); video-recording method (figure 2).
Historically the visual method was the first one. This method was fully described in scientific works of A.I. Milinnsky  and V.A. Kopylov . The demerits of this method are obvious: the accuracy depends on the subjective qualities of observers; limited practical utilisation (with low density of a flow and with relatively small width of a route’ sections); impossibility to reproduce the “pictures” of people’ motion in a flow in order to make an accurate analysis, etc. That’s why in 1962 the movie (photo) method was firstly adopted , which became the main one for all future investigations. This method was described in details in the number of scientific works [4, 2]. However, the implementation of the described methods is limited due to the limited area of visible zone because of the vertical lens’ position of a camera. Other angles of lens’ axis also can’t be used, because it’s impossible to determine visual distortions, due to the perspective.
The utilisation of some special methods  helps to get rid of these limitations and to make the area of implementation of movie-photo method wider , especially on long parts of routes or video-recording of foot traffic flows in restricted areas while conducting actual observations .
The utilisation of modern video-recording devices helps to reduce the cost of actual observations due to lowering the expenses on buying and developing the miles of high-sensitive movie film.
From the scientific research’ point of view, the fixation of an observed “picture” of a foot traffic flow gives a possibility to obtain quite objective results, to increase accuracy and details of situations under analysis, because it is possible to repeat a desired number of times either the general dynamics of a foot traffic flow or individual behaviour of people in it. With such a techniques until the time being obtained about 10 times more results about parameters of foot traffic flows under actual observations in buildings of different types and on pedestrian routes of city territories, as compared with visual observations. Exact numbers are 35,000 versus 3,600; the latter number was obtained mainly during the researches led by professor A.I. Milinsky in 1946-1948.
Classical example of an experimental survey is an imitation of a forced foot traffic flow of a maximum density in a specially-constructed transformed hall, conducted by V.A. Kopylov in 1972 . The necessity of this experimental sto was explained by impossibility to make such a survey in reality with full recording of specific phenomena of force foot traffic flows, which are possible in extraordinary (alarm) situations in buildings. The transformation of the experimental hall made possible to change the width of corridors and openings from 0.8 to 3.0 meters with gradation of 0.2 m. Due to the possibility of the transformation a great number or planning schemes with different combinations of their geometrical parameters were obtained (figure 3). The foot traffic flows were formed with servicemen of fire Guard Troops Aged 25 to 30 and with students of Higher Fire Engineering School of Ministry of Home Affairs of the USSR aged 18 to 25. The physical stressing of the traffic process under the high density of the flows was additionally made by special “retaining” groups of people in the ends of passages. They produced a physical pressure on people, who moved along the passages in foot traffic flows with given density. The construction of the transforming hall made possible to place a special overhead co-ordinate grid and to place a special marks with 1 meter spacing, which helps to determine the exact position of a movie-camera. All the observations were doubled with aid of eight independent observers, equipped with chronometers and with counting machines.
To increase the accuracy of filming each participant of the experiment was supplied with numbering tags, fixed to their uniform hats. During this experimental study more than 1970 measuring of foot traffic flow’ density and of people’s velocity in it were obtained.
To compare the information obtained with the possible ones with actually-existed foot traffic flows, more than 3,000 data were obtained. These were received as results of actual experimental observations in situations of stable foot traffic flows with increased psychological and physical stressing: on subway stations during morning rush house, hear huge Moscow department stores, where more than 1.000 people used to gather near the entrance just before the time of opening and on Moscow’ stadiums after foot-ball competitions.
Unannounced evacuations from buildings  and observations of foot traffic flows with artificially taken content of participants (like school pupils during research on sub-way station) could also be considered as experimental researches.
From other hand, the study of foot traffic flows of different age groups of pupils in school buildings  is an actual experimental observation, because these flows fully conjunct to the functional processes and maintenance’ terms of the building.
However, the empiric data, obtained with different techniques during actual observations or experimental studies illustrate dependencies and rules, which are existing in any foot traffic flow and ruling the behaviour of participants and the main parameters of the motion.
The determination and description of these parameters is the task for the theory, the results of scientific researchers’ abilities to generalise, to evaluate to think heuristically and due to their intellectuality. Due to this different researchers differently interpret and model even the same phenomena.
In this relation the history of description of the foot traffic flow’ structure and its parameters is very interesting. Nearly all give the identify description: “ … The position of people in a foot traffic flow (along or across it) every ime is uneven and frequently is occasional. The distance between people constantly changes and it causes local squeezing, which later on disappear and appear again …”; “… A foot traffic flow usually has a longitudinal cigar-like shape. Avant-garde and arriere-garde parts of a foot traffic flow have few people, which are moving faster or slower, as compared with majority of people in a foot traffic flow …”; “… That’s why for an ALARM situations it is necessary to take in to account so called “spreading” of a flow and, therefore gradual changing of it density” .
But, from other hand, S.V. Beyaev  gave a model a flow’ structure in the form of “elementary foot traffic flows” i.e. people, moving one after another in longitudinal rows. He was the first who established the dependence between a velocity and density of a foot traffic flow , which he measured as a length of a space, occupied by a single person in an “elementary foot traffic flow” (metre/ person). For a design calculations he recommended constant minimum velocities of motion: along the horizontal routes 16 metre/minute, along a stair downwards 10 metre/minute, along a stair upwards 8 metre/minute.
V.M. Predtechensky and A.I. Milinsky  assumed in the design calculations to treat foot traffic flow as a rectangle with uniform density and uniform velocity of people in it. They gave the determined mathematical relationship in the form of a polynomial of 4-th degree between a velocity and density of a foot traffic flow. On the other hand, they were the first to offer the special histograms to determine movement due to different densities of a foot traffic flow.
According to this model an unique grapho-analytical method of foot traffic flow’ design calculations was elaborated. This method was based on a low, invented by V.M. Predtechensky  which showed the change of foot traffic flows’ parameters along the limits of adjacent sections of a route and formation of conglomeration of people near the limits of a route’ sections with lower passing capacity than the preceding one. Mathematical expressions of these relationships are given on figure 4.
These relationships are well known either for Russian, or for English-speaking scientific researchers due to the book of V.M. Predtechensky and A.I. Milinsky, which have been translated in English.
For the time being the understanding of foot traffic flow as an occasional process has been formed [6, 7, 8, 12, 13]. The according description of relationships between a velocity and density of a foot traffic flow was also given in a form of occasional elementary functions. It’s obvious, that this model of a foot traffic flow is mostly adequate to the given description of it actual structure. The history of creation of this model was explained by the fact, that for Building codes and Regulations a newly-elaborated Charter “Fire standards and regulations for buildings’ and structures’ design” (SNiP II-2.80) a calculative method for egress design and standards was firstly adopted. It was also necessary to learn out the calculative relationships along foot traffic flows’parameters. The numerous data of actual observations and experimental studies in buildings and engineering structures with different functions, which had been received until the time considered, gave identical by quality, but completely by quantity descriptions of the V= j (D) relationship (figure 5).
At the same time in second (post-mortal) edition of the book , “the scientific bible” for researchers of foot traffic flows, who actual obtained these relationships, it is stated, that “…latter researches, carried out in MCEI and in Higher School of Ministry of Ministry of Home Affairs of the USSR, does not show the sufficient differences as compared with formerly established relationships V= j (D), which are taken as basic ones , published in ”.
From mathematical statistics it is know, that to consider statistical set of data to differ negligibly, they must be homogeneous, and for this their mean values and dispersions must differ negligibly from statistical hypotheses’ point of view.
That’s why the statistical analysis of homogeneity of chosen data’ sets for velocity’ values at each range of density in all 69 series of actual observations and experimental studies carried out until that time, was firstly elaborated [12, 13].
This analysis showed the validity of differences between the results of former and latter sets of actual observations.
Moreover, it was found, that the series of actual observations for horizontal routes carried out under the leadership of A.I. Milinsky could not be united for establishing a mutual relationship between a velocity and density of a foot traffic flows.
Incorrectly established basic relationship determines the incorrection of all the methodics in general and factors of “motion duty” m , factor of “route type” m, factors of “ foot traffic flow structure” h in particular .
This fact shows once again the false character of the methodical attitude, which is based on dividing relationships V=f(D), obtained in different series of actual observations on main and secondary ones, or based on unification of these on spontaneous basis.
All these are separate realisation of the basic relationship, which determines their qualitative identity. But affection of numerous factors (sometimes negligible or difficultly recorded and, therefore, considered as spontaneous) which are joining to the conducting of every series of observations, determines spontaneous quantitative variances of this basic relationship.
But, among all these factors, which join a method of the relationship V= j (D) creation, a factor of “motion duty” everytime presents, which determines any basic in, phycho-emotional condition of the participants of a foot traffic flow, determined in this or that series of the observations or experiment. That’s why, when obtaining relationship of a foot traffic flow’ velocity due to it density, the affection of this factor should be excluded somehow. Actually this is impossible. But to evaluate and count this affection is quite possible, because under free (unobstructed) motion of people in a foot traffic flow with densities from 0 to 1 person/metre 2 (or 0,1 metre 2/ metre 2) the density of a flow does not affect it velocity. Hence, with motion on any type of a route (j) the factor of respond (R j) of people in a flow to an increase of density (D) shows the change of their mean velocity ( ) as regards the mean velocity under free motion ( ):
This respond is a reflection of a person’ increase of feeling’ intensity due to increase in affect of a provocative stimulus factor, that is in this case a density of a foot traffic flow. It is well-know that the quantitative relationships between physical characteristics of stimulus and intensity of feeling, which arises as a respond to this stimulus, is studied by psychophysics.
The analysis of the areas of correct utilisation of psychophysical laws showed, that relation of the R j=f(D ) relationship must be described by the Weber-Fehner law:
The determination of actual values of empirical factors “ a j” and “threshold” values of density “D 0 , j ”, on achieving of which, the density of a foot traffic flow starts affecting on motion velocity of people in it, was made in accordance with data of actual observations’ series, where density ranges density of a foot traffic flow from 0 to 1 person/metre 2 and higher were studied .
Correlating relationship R j=f(D ), obtained with high degree of accuracy for any type of a route (fig. 6-a) have values of “correlating links’ compaction factor – i.e. theoretical correlating relationships more than 0.98. Such a high degrees of correlating links compaction help to evaluate obtained relationships as functional ones and prove the truth of the adopted hypothesis about casual-corollary connection between velocity and density of a foot traffic flows to Weber-Fehner law.
Now the relationship between velocity and density with any level of psychologically – stressed situation under which a motion of people takes place, can be described with the following elementary occasional function:
This function is a multiplication of an occasional value of a velocity of a free motion to an unoccasional function, (which is put in brackets). The character of this function shows, the affect of a degree of a psychological stress of a situation (i.e. circumstances of a motion) to an occasional velocity of a flow can be evaluated by a dependence of change of mean velocity of free motion of people’ due to their emotional state under different circumstances.
For establishing this relationship, the general concepts of psycho-psychological theory of functional systems  were adopted. Apart from these, the following were used:
As a result [13, 14, 19], the logically-based relationship of velocity change due to the level of emotional condition of people in a foot traffic flow was obtained. On it’s ground a classification of motion’ categories was offered, and corresponding ranges of values of V 0 , j were established (fig. 6-b).
Putting these margins over empirical curves of V =fD ) relationships shows quite satisfactory distribution of these curves as regards the categories of motion, to which, according to the survey description, could correspond actual conditions of observations.
The occasional nature of a foot traffic flow requires a new model of its motion along sections of a route. Newly-elaborated imitating model [13, 20] analyses a motion of people in a foot traffic flow in discrete moments of time along the discrete parts of a route, to which a route is divided (fig. 7). For a implementation this model, the programme “Versions of the analysis of foot traffic flows’ motion” (“ADLPV”), and also its determinated variation “ADLP” were created. With aid of these the design relationships among parameters of foot traffic flows in egress situations were established .
For the case of free (unobstructed) motion of people in a foot traffic flow the analytic model for calculative design of people distribution along the length of a route and distribution of time of their arrival in a given section of a route (“input”) was elaborated (fig. 8). This model is realised through programmes “Free motion of foot traffic flows” (”SDLP”)  and “Drain” .
This model is the best demonstration of difference in results of “determinated” and “occasional” description of a foot traffic flow. The high degree of modelling adequacy of a people foot traffic flow as an occasional actual process is quite obvious and it allows to look upon this approach as the most perspective in all future investigations with actual observations, experimental surveys and theoretical concepts.
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If you have any questions, please do not hesitate to contact me:
Dr Dmitry Samoshin
Academy of State Fire Service of Russia
Tel.: +7 916 2999924; E-mail: info@FireEvacuation.ru