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CA Approach to Collective Phenomena in
Pedestrian Dynamics
Andreas Schadschneider
1
, Ansgar Kirchner
1
, and Katsuhiro Nishinari
1
,
2
1
Institut fur Theoretische Physik, Universitat zu Koln, D-50937K¨oln, Germany
2
Department of Applied Mathematics and Informatics, Ryukoku University, Shiga,
Japan
Abstract.
Pedestrian dynamics exhibits a variety of fascinating and
surprising collective phenomena (lane formation, flow oscillations at
doors etc.). A 2-dimensional cellular automaton model is presented which
is able to reproduce these effects. Inspired by the principles of chemotaxis
the interactions between the pedestrians are mediated by a so-called floor
field. This field has a similar effect as the chemical trace created e.g. by
ants to guide other individuals to food places. Due to its simplicity the
model allows for faster than real time simulations of large crowds.
1
Introduction
The investigation of tra
c flow using methods from physics has attracted a
lot of interest during the last decade [1,2]. Due to their simplicity, especially
cellular automata models (CA) have been at the focus of attention. In contrast
to highway tra
c, pedestrian flow [3]is truely 2-dimensional and effects due
to counterflow become important. This gives rise to several self-organization
phenomena not observed in vehicular tra
c.
The most successful model for pedestrian dynamics so far is the so-called
social force model [4]. Here pedestrians are treated as particles subject to long-
ranged forces induced by the social behaviour of the individuals. This idea leads
to equations of motion similar to Newtonian mechanics.
Most cellular automata models for pedestrian dynamics proposed so far [5,
6,7]and can be considered as generalizations of the BML model for city tra
c
[8]. However, these models are not able to reproduce all the collective effects
observed empirically. The same is true for more sophisticated models [9,10].
In [11,12,13,14]a new kind of CA model has been introduced which - despite
its simplicity - is able to reproduce the observed collective effects. It takes its
inspiration from the process of chemotaxis as used by some insects. They create
a chemical trace to guide other individuals to food places. This is also the central
idea of active-walker models [15,16]used for the description of human and animal
trails. In the approach of [11]the pedestrians also create a trace which, in contrast
to trail formation and chemotaxis, 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
