Simulation of evacuation processes using a bionics-inspired cellular automaton model for pedestrian dynamics

https://doi.org/10.1016/S0378-4371(02)00857-9Get rights and content

Abstract

We present simulations of evacuation processes using a recently introduced cellular automaton model for pedestrian dynamics. This model applies a bionics approach to describe the interaction between the pedestrians using ideas from chemotaxis. Here we study a rather simple situation, namely the evacuation from a large room with one or two doors. It is shown that the variation of the model parameters allows to describe different types of behaviour, from regular to panic. We find a non-monotonic dependence of the evacuation times on the coupling constants. These times depend on the strength of the herding behaviour, with minimal evacuation times for some intermediate values of the couplings, i.e., a proper combination of herding and use of knowledge about the shortest way to the exit.

Introduction

Methods from physics have been successfully used for the investigation of vehicular traffic for a long time [1], [2]. On the other hand, pedestrian dynamics has not been studied as extensively [3]. Due to its generically two-dimensional nature, pedestrian motion is more difficult to describe in terms of simple models. However, many interesting collective effects and self-organisation phenomena have been observed (see [2], [4] for an overview and a comprehensive list of references), e.g. jamming and clogging, lane formation and oscillations at bottlenecks in counterflow or collective patterns of motion at intersections. These phenomena will be discussed in Section 2.4.

The model takes its inspiration1 from the process of chemotaxis (see Ref. [5] for a review). Some insects create a chemical trace to guide other individuals to food places. This is also the central idea of the active-walker models used for the simulation of trail formation. In the approach of [6] the pedestrians also create a trace. In contrast to trail formation and chemotaxis, however, this trace is only virtual although one could assume that it corresponds to some abstract representation of the path in the mind of the pedestrians. Its main purpose is to transform effects of long-ranged interactions (e.g. following people walking some distance ahead) into a local interaction (with the “trace”). This allows for a much more efficient simulation on a computer.

The basic idea of our approach might be used for studying a variety of problems, especially from biology [6], [7], [8]. Here we want to apply this model to a simple evacuation process with people trying to escape from a large room. Such a situation can lead to a panic where individuals apparently act irrationally. A nice discussion of empirical results can be found in Ref. [4]. Our motivation here is rather the determination and classification of the different types of behaviour exhibited by the model than a realistic application.

The phenomena observed during panics can be quite different from those found in “normal” situations. Nevertheless, it is desirable to have a model which is able to describe the whole spectrum of possible pedestrian behaviour in a unified way. So far mainly the social-force model [9] has been used which allows to reproduce the observed behaviour [2], [4], [10] quite accurately. In this continuum model the pedestrians interact by a repulsive (social) force which decays exponentially with the distance between them. This means that in each step of a simulation of N individuals O(N2) interaction terms have to be evaluated. Furthermore, in complex geometries it occurs quite frequently that two pedestrians are rather close to each other but do not interact since they are separated by a wall. Therefore, in principle, one has to check for all pairs of individuals whether an interaction is possible or not. For large crowds this becomes very time consuming. In contrast, in the model used here pedestrians only interact with the floor field in their immediate neighbourhood. Therefore, one has only O(N) interaction terms. A further advantage is the discreteness of the model which allows for a very efficient implementation for large-scale computer simulations.

We start with a short summary of the models basic concepts.

Section snippets

Basic principles of the model

In the model the space is discretised into small cells which can either be empty or occupied by exactly one pedestrian. Each of these pedestrians can move to one of its unoccupied neighbour cells at each discrete time step tt+1 according to certain transition probabilities (see Fig. 1). The probabilities are given by the interaction with two floor fields [6]. These two fields S and D determine the transition probabilities in such a way that a particle movement is more likely in direction of

Evacuation simulations

In the following, we describe results of simulations of a typical situation, i.e., the evacuation of a large room (e.g. in case of fire). At this, we focus on the influence of the sensitivity parameters kD and kS on the evacuation times in order to identify the different classes of behaviour exhibited by the model. As we will see interesting collective phenomena between the pedestrians lead to a non-trivial dependence of the evacuation times on KD and kS. In Section 3.2 we investigate possible

Conclusions

We have studied simple evacuation processes using a recently introduced stochastic cellular automaton for pedestrian dynamics which implements interactions between individuals using an idea similar to chemotaxis. Due to its simplicity, the model allows very high simulation speeds and is very well suited for the optimisation of evacuation procedures even in complex situations.

We have focussed on studying evacuation times in a very simple evacuation scenario. The main purpose was to elucidate the

Acknowledgements

We like to thank K. Nishinari, C. Burstedde, F. Zielen and D. Helbing for useful discussions.

References (23)

  • D. Chowdhury et al.

    Phys. Rep.

    (2000)
  • C. Burstedde et al.

    Physica A

    (2001)
  • Y. Tajima et al.

    Physica A

    (2001)
  • M. Muramatsu et al.

    Physica A

    (1999)
  • M. Muramatsu et al.

    Physica A

    (2000)
  • D. Helbing

    Rev. Mod. Phys.

    (2001)
  • M. Schreckenberg, S.D. Sharma (Eds.), Pedestrian and Evacuation Dynamics, Springer, Berlin,...
  • D. Helbing et al.
  • E. Ben-Jacob

    Contemp. Phys.

    (1997)
  • A. Kirchner, Dissertation, Universität zu Köln, 2002; available for download soon at...
  • D. Chowdhury, G. Vishwesha, A. Schadschneider,...
  • Cited by (857)

    • A multi-grid evacuation model considering the effects of different turning types

      2024, Physica A: Statistical Mechanics and its Applications
    View all citing articles on Scopus
    View full text