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For fixed
µ
and varying coupling strength
k
S
a surprising result can be ob-
served (Fig. 7(b)). For
µ
= 0 the evacuation time is monotonically decreasing
with increasing
k
S
since for large coupling to the static field the pedestrians will
use the shortest way to the exit. For large
µ
,
T
(
k
S
) shows a minimum at an in-
termediate coupling strength
k
S
≈
1. This is similar to the faster-is-slower effect
described in Sec. 1: Although a larger
k
S
leads to a larger effective velocity in
the direction of the exit, it does not necessarily imply smaller evacuation times.
4 Conclusions
We have introduced a stochastic cellular automaton to simulate pedestrian be-
haviour
1
. The general idea in our model is similar to chemotaxis. However, the
pedestrians leave a virtual trace rather than a chemical one. This virtual trace
has its own dynamics (diffusion and decay) which e.g. restricts the interaction
range (in time). It is realized through a dynamic floor field which allows to give
the pedestrians only minimal intelligence and to use local interactions. Together
with the static floor field it offers the possibility to take different effects into
account in a unified way, e.g. the social forces between the pedestrians or the
geometry of the building.
The floor fields translate spatial long-ranged interactions into non-local in-
teractions in time. The latter can be implemented much more e
ciently on a
computer. Another advantage is an easier treatment of complex geometries. We
have shown that the approach is able to reproduce the fascinating collective phe-
nomena observed in pedestrian dynamics. Furthermore we have found surprising
results in a simple evacuation scenario, e.g. the nonmonotonic dependence of the
evacuation time on the coupling to the dynamic floor field. Also friction effects
(Sec. 3.3), related to the resolution of conflict situations where several individuals
want to occupy the same space, can lead to counterintuitive phenomena.
References
1. Chowdhury, D., Santen, L., Schadschneider, A.: Statistical physics of vehicular
tra
=
c and some related systems. Phys. Rep.
329
(2000) 199-329
2. Helbing, D.: Tra
=
c and related self-driven many-particle systems. Rev. Mod. Phys.
73
(2001) 1067-1141
3. Schreckenberg, M., Sharma, S.D. (Ed.):
Pedestrian and Evacuation Dynamics
,
Springer 2001
4. Helbing, D., Molnar, P.: Social force model for pedestrian dynamics. Phys. Rev.
E51
(1995) 4282-4286
5. Fukui, M., Ishibashi, Y.: Self-organized phase transitions in cellular automaton
models for pedestrians. J. Phys. Soc. Jpn.
68
(1999) 2861-2863
6. Muramatsu, M., Irie, T., Nagatani, T.: Jamming transition in pedestrian counter
flow. Physica
A267
(1999) 487-498
1
Further information and Java applets for the scenarios studied here can be found on
the webpage
http://www.thp.uni-koeln.de/
∼
as/as.html
.