Information Technology Reference
In-Depth Information
Panics
: In panic situations, many counter-intuitive phenomena can occur. In
the faster-is-slower effect [18]a higher desired velocity leads to a slower movement
of a large crowd. In the freezing-by-heating effect [19]increasing the fluctuations
can lead to a more ordered state. For a thorough discussion we refer to [17,18]
and references therein.
2 Definition of the Model
First we discuss some general principles applied in the development of the model
[11,12]. To allow an e
cient implementation for large-scale computer simulations
a discrete model is preferable. Therefore a two-dimensional CA is used with
stochastic dynamics taking into account the interactions between the pedestri-
ans. Similar to chemotaxis, we transform long-ranged interactions into local ones.
This is achieved by introducting so-called
floor fields
. The transition probabilities
for all pedestrians depend on the strength of the floor fields in their neighbour-
hood such that transitions in the direction of larger fields are preferred.
Interactions between pedestrians are repulsive for short distances ('private
sphere'). This is incorporated through hard-core repulsion which prevents multi-
ple occupation of the cells. For longer distances the interaction is often attractive,
e.g. in crowded areas it is usually advantageous to walk directly behind the pre-
decessor. Large crowds may be attractive due to curiosity and in panic situation
often herding behaviour can be observed [18].
The long-ranged part of the interaction is implemented through the floor
fields. We distinguish two kinds, a
static floor field
and a
dynamic floor field
.
The latter models the dynamic interactions between the pedestrians, whereas
the static field represents the constant properties of the surroundings.
The dynamic floor field corresponds to a virtual trace which is created by the
motion of the pedestrians and in turn influences the motion of other individuals.
Furthermore it has its own dynamics (diffusion and decay) which leads to a
dilution and vanishing of the trace after some time. We assume the dynamic
field to be discrete. Therefore the integer field strength
D
xy
can be interpreted
as number of bosonic particles located at (
x, y
).
The static floor field does not change with time since it only takes into account
the effects of the surroundings. It allows to model e.g. preferred areas, walls and
other obstacles. A typical example can be found in Sec. 3.2 where the evacuation
from a room with a single door is examined. Here the strength of the static field
decreases with increasing distance from the door.
The introduction of the floor fields allows for a very e
cient implementa-
tion on a computer since now all interactions are local. We have translated the
long-ranged spatial interaction
into a
local interaction with “memory”
. Therefore
the number of interaction terms grows only linearly with the number of parti-
cles. Another advantage of local interactions can be seen in the case of complex
geometries. Due to the presence of walls not all particles within the interac-
tion range interact with each other. Therefore one needs an algorithm to check
