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consequently increase the time needed to reach the door, thus increase the total
time to evacuate the room. Due to the threshold on the density, however, we
observe a “freezing-by-heating” effect, see fig.4: the average effect of increasing
ξ
is to lower evacuation time. Indeed, as
λ
increases, we observe a decrease of
the number of iterations needed to evacuate all the individuals initially placed
in the room.
The somehow oscillating structure of the plot is not yet understood; among
possible explanations are the effect of the finite values of scalar product in equa-
tion (3) or an effect of sub-lattices. Such effects exist between individuals who
move in opposite way through the same link at the same time and thus do not
interact because they do not meet on a lattice site.
4 Conclusion
The model presented in this paper is a first attempt to consider a different ap-
proach at modeling crowd motion at a mesoscopic level, the main idea being the
relaxation of the exclusion principle. This in turn allows us to define an interac-
tion between individuals thereby assuming that what prevents individuals from
moving are not the conditions at the target location but the conditions at the
initial location. The non-local aspect of movement is introduced by considering
mobility at neighbor locations. The main ingredients of the rules for motion are
then: a simple propagation-collision scheme where the collision consists of a local
friction, a search for mobility and a capacity to explore alternative routes. In this
paper, we therefore show that although the exclusion principle is relaxed most
of the macroscopical phenomena occurring in a crowd are simulated. The gain
achieved is a simpler algorithm where no conflicts between individuals have to
be resolved while still qualitatively achieving the expected complex behavior of
the crowds motion. Future work should thus definitively involve a quantitative
comparison with real data.
References
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4. Bastien Chopard and Michel Droz.
Cellular Automata Modeling of Physical Systems
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