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A Multiparticle Lattice Gas Automata Model
for a Crowd
Stefan Marconi and Bastien Chopard
Computer Science Department
University of Geneva
1211 Geneva 4, Switzerland
marconi@cui.unige.ch
and
Bastien.Chopard@cui.unige.ch
Abstract.
We propose to study the complexmotion of a crowd with a
mesoscopic model inspired by the lattice gas method. The main idea of
the model is to relaxthe exclusion principle by which individuals are not
allowed to physically occupy the same location. The dynamics is a simple
collision-propagation scheme where the collision term contains the rules
which describe the motion of every single individual. At present, these
rules contain a friction with other individuals at the same site, a search
for mobility at neighboring sites, coupled to the capacity of exploring
neighboring sites. The model is then used to study three experiments:
lane formation, oscillations at a door and room evacuation.
1
Introduction
The problem of crowd movement has been studied in the past using various
approaches ranging from fluid dynamics [1] to coupled Langevin equations [2].
These approaches are based on the resolution of partial differential equations
which model the interaction between each pair of individuals in crowd. Lately,
however, the use of cellular automata have been introduced as a simple and in-
tuitive way of simulation [3]. Such an approach deals with a local set of rules
which describes the motion of individuals on a discrete representation of space.
The local rules are usually simple to understand while still allowing a complex
collective behavior to emerge. We propose a new model using such a mesoscopic
approach inspired by the so-called lattice gas techniques [4] which are in the
same stream of thought as cellular automatas. The main novelty of our model
consists in relaxing the exclusion principle, by which individuals in a crowd can-
not occupy the same physical location, to a probabilistic view where individuals
are in fact allowed to superpose albeit an influence on their movement. With
complete analogy to the statistical approach of transport phenomena in fluids,
more specifically the Boltzmann equation, the dynamics of the model consists
then of a succession of collisions and propagations where the emerging behavior
of the system is essentially governed by the collision term. The main motivation
for this approach arises from the fact that the discretization of space on a lattice
does not yield any specific scale. A lattice site may just as well represent 1
m
2
or 10
m
2
and may, consequently, contain a varying number of individuals. The
