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movement of the crowd is by definition only the flow of individuals from site to
site. The main advantage of such a point of view is to completely suppress the
need to resolve any conflict between individuals competing for the same physical
location and thus simplify the algorithm without suppressing the richness of the
phenomena.
In the following sections, we formally introduce the model and then illustrate
three common experiments namely the formation of lanes in two crowds moving
in opposite directions, the alternating flow at a door of a two crowds moving
in opposite directions and finally the evacuation from a room of a single crowd
through a door [3]. The purpose of these experiments is not serve as much to
validate our choice of rules nor to outperform other approaches than to show
that the exclusion principle and the conflict management it engenders can be
avoided when simulating complex behavior of a crowd.
2 Model Description
The crowd is modeled by the collection of a number N of individuals distributed
on a 2-dimensional regular lattice with z + 1 directions c i , i =0 ..z . The total
number of individuals ρ = i =0 n i ( r ,t ) at each lattice site r is arbitrary. In
agreement with lattice gas formalism, n i ( r ,t ) denotes the number of individuals
entering site r at time t along direction c i . Each individual is locally charac-
terized by its favorite direction of motion c F . The movement of an individual
is considered to be at v max = | c i | towards the site pointed at by the lattice
direction c i .
The direction labelled c 0 = 0 points onto the site itself. It is used to model
the rest direction i.e the case when there is no actual movement.
As is the case in lattice gas systems, the dynamics of the crowd movement
is described by two steps: collision and propagation. The propagation consists
in nothing more than moving an individual to the site pointed at by the lattice
direction determined during the collision process.
The collision consists in determining the direction imposed on each individual
due to the interaction with other individuals occupying the same site. Depending
on the strength of the interaction, this imposed direction may or may not corre-
spond to the favorite direction c F of the the individual. Note that the favorite
direction is typically a constant or the lattice direction which best corresponds
to the shortest path to a given final position.
In a real crowd, there is no first principle which dictates how the individuals
are going to interact when they meet. In what follows we propose a new set of
rules which are based on common observations. First we assume that the crowd
motion is subject to some friction which occurs when density is too high. This
will slow down the local average velocity of the crowd by reducing the number
of individuals allowed to move to a nearest lattice site. Second, the individuals
are confronted with the choices of moving in their favorite direction or to move
in the direction where flow exists. Finally, each individual can consider only a
 
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