Chapter 80
Computational Modeling of Collective Behavior of Panicked Crowd Escaping Multi-floor Branched Building Dmitry Bratsun, Irina Dubova, Maria Krylova, and Andrey Lyushnin
Abstract The collective behavior of crowd leaving a room is modeled. The model is based on molecular dynamics approach with a mixture of socio-psychological and physical forces. The new algorithm for complicatedly branched space is proposed. It suggests that each individual develops its own plan of escape, which is stochastically transformed during the evolution. The algorithm includes also the separation of original space into rooms with possible exits selected by individuals according to their probability distribution. The model has been calibrated on the base of empirical data provided by fire case in the nightclub “Lame Horse” (Perm, 2009). The algorithm is realized as an end-user Java software. The code has been tested on a number of multi-level buildings with complicated geometry.
With the increasing size and frequency of mass events leading to more often crowd disasters, the study of collective behavior of panicked crowd has become important research area. However, even successful modeling approaches are hard to calibrate since the dynamics of crowd is sensitive to changes in the model. Probably, the only way to calibrate the model is to compare the results of computer simulations with scenarios of real events giving the most comprehensive empirical data. In this paper, it is presented the computational modeling of the crowd panicking in closed space of multi-level branched building. The model is based on molecular
D. Bratsun (B) Theoretical Physics Department, Perm State Pedagogical University, Perm, Russia e-mail:
[email protected] I. Dubova · M. Krylova · A. Lyushnin Department of Informatics, Perm State Pedagogical University, Perm, Russia I. Dubova e-mail:
[email protected] A. Lyushnin e-mail:
[email protected] T. Gilbert et al. (eds.), Proceedings of the European Conference on Complex Systems 2012, Springer Proceedings in Complexity, DOI 10.1007/978-3-319-00395-5_80, © Springer International Publishing Switzerland 2013
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Fig. 80.1 Pedestrian chooses his path randomly if there are several points of gathering
dynamics approach proposed by Helbing et al. [1]. Their model assumes a mixture of socio-psychological and physical forces influencing the behaviour in a crowd: Mi
dVi = F1i + F2im + F3im + F2W F3W ij + ij , dt i=m
i=m
j
(80.1)
j
where Vi = dri /dt is velocity of pedestrian i of mass Mi and radius Ri and F1i = Mi
Ui − Vi , ti
Dim , B F3im = Dim H (Dim ) knim + K (Vm − Vi ) · τ im τ im ,
F2im = Anim exp
W Dim , BW W W W W knim + K Vi · τ W = Dim H Dim im τ im ,
(80.2) (80.3) (80.4)
W W F2W im = A nim exp
(80.5)
F3W im
(80.6)
Dim ≡ Ri + Rm − |ri − rm |.
(80.7)
Here nim and τ im are normal and tangent unit vectors to the contact line between i and m pedestrians respectively; A, B, AW , B W , k, K are parameters. H stands for the function of Heaviside. The first force (80.2) is responsible for the state of panic of pedestrian. Each of pedestrians likes to move with a certain desired speed Ui in a certain direction, and therefore tends to correspondingly adapt his actual velocity Vi with a certain characteristic time ti . Simultaneously, he tries to keep a velocity-dependent distance from other pedestrians j (80.3) and walls (80.5). The forces (80.4) and (80.6) describe the effects of counteracting body compression and a sliding friction impeding relative tangential motion.
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Fig. 80.2 Scheme illustrating the algorithm for selecting by the pedestrian a way out of the room
Keeping in mind the modeling in multi-floor buildings with a complicated structure, we have supplemented the model proposed in [1] by two important improvements [2]. First, we divide the initial space into separate rooms and define for each room the point (or points) of the gathering of pedestrians. Entering into a room everyone tends to reach this point. In the case when the number of gathering points more than one, the pedestrian must choose his path of the movement (Fig. 80.1). However, depending on how close pedestrian to a certain gathering point and how many other pedestrians seen in that direction the probability is higher for closer point and smaller number of people. The simplest algorithm provides a random selection based on distribution: N7 P5 = , (80.8) N5 + N7 where N5 and N7 are number of pedestrians in the direction 5 and 7 respectively (Fig. 80.2). As a result, each participant of crowd develops its own plan how to get out the building. This plan may be modified over time depending on the situation. Since the final result of stochastic system may vary, it should be averaged over the realisations. The model has been calibrated using the empirical data provided by deadly Lame Horse fire [3]. The fire has occurred on December 5, 2009, around 1 a.m. in the nightclub “Lame Horse” located in Perm, Russia. A total of 282 people had reportedly been invited to the club’s party. The fire started when sparks from fireworks ignited the low ceiling and its willow twig covering. The fire quickly spread to the walls and damaged the building’s electrical wiring, causing the lights to fail. When the evacuation started, some people left via rear exits. The vast intake of oxygen turned the club’s hall into a large fire tube and boosted the spread of fire. As fumes and smoke overtook the air, panic erupted and patrons stampeded toward the exit. According to witnesses, one leaf of the club’s double doors was sealed shut, and the public was unaware of the backdoor exit behind the stage not shown by emergency lighting. Subsequent events have shown that the people had only about 60 second to escape the club. But when fumes and smoke overtook the air, the panic has erupted. It is known that 153 people have died as a result of the fire and 62 people have become disabled. And only 70 persons have escaped the club itself within first minute. In Fig. 80.3 we give an example of numerical simulation of panicked crowd of 283 pedestrians (143 men and 140 women) trying to escape the nightclub “Lame
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Fig. 80.3 Simulation of 283 pedestrians escaping the nightclub “Lame Horse”
Fig. 80.4 Dynamics of pedestrians leaving the nightclub “Lame Horse” during the fire
Horse”. The plan of the club was taken from open sources. One can see that finally it is formed arch-like blocking of the exit. All people who were not able to leave the room within 60 second can be considered as victims of the fire. Figure 80.4 illustrates dynamics of number of leaving people in time. One can notice that the normal regime of the exit from the building extends approximately to 13 seconds. Then panic starts and the rate of leave falls sharply. By calibrating force functions and simulation parameters we have obtained the same rate as it was in real event: finally only 60 people have leaved the club within 60 second (Fig. 80.4).
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The proposed algorithm has been applied to a number of multi-level buildings with complicated geometry. Such program could help to designers and architects to estimate potential dangers of internal structure of buildings for people in extraordinary situation and to minimize it on designing stage. Acknowledgements The work was supported by the Department of Science and Education of Perm region (project C26/244), the Ministry of Science and Education of Russia (project 1.3103.2011) and Perm State Pedagogical University (project 031-F).
References 1. Helbing D, Farkas I, Vicsek T (2000) Simulating dynamical features of escape panic. Nature 407:487–490 2. Aptukov AM, Bratsun DA (2009) Modelling group dynamics of crowd panicking in the closed room. Vestn Perm Univ Fiz 3:18–23 3. BBC News 05.12.2009. http://news.bbc.co.uk/2/hi/europe/8396587.stm
