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k
S
allow to vary the coupling strengths to each field individually. Their actual
values depend on the situation and will be discussed in Sec. 3.2.
The update rules of the full model including the interaction with the floor
fields then have the following structure [11,12]:
1. The dynamic floor field
D
is modified according to its diffusion and decay
rules: Each boson of the dynamic field
D
decays with probability
δ
and
diffuses with probability
α
to one of the neighbouring cells.
2. From (1), for each pedestrian the transition probabilities
p
ij
are determined.
3. Each pedestrian chooses a target cell based on the probabilities
p
ij
.
4. The conflicts arising by
m>
1 pedestrians attempting to move to the same
target cell are resolved. To avoid multiple occupancies of cells only one par-
ticle is allowed to move while the others keep their position. In the simplest
case the moving particle is chosen randomly with probability 1
/m
[11].
5. The pedestrians which are allowed to move execute their step.
6. The pedestrians alter the dynamic floor field
D
xy
of the cell (
x, y
) they
occupied before the move. The field
D
xy
at the origin cell is increased by
one (
D
xy
→ D
xy
+ 1).
These rules are applied to all pedestrians at the same time (parallel dynamics).
This introduces a timescale which corresponds to approximately 0
.
3
sec
of real
time [11]by identifying the maximal walking speed of 1 cell per timestep with
the empirically observed value 1
.
3
m/s
for the average velocity of a pedestrian
[20]. The existence of a timescale allows to translate evacuation times measured
in computer simulations into real times.
One detail is worth mentioning. If a particle has moved in the previous
timestep the boson created then is not taken into account in the determina-
tion of the transition probability. This prevents that pedestrians get confused by
their own trace. One can even go a step further and introduce 'inertia' [11]which
enhances the transition probability in the previous direction of motion. This can
be incorporated easily by an additional factor
d
ij
in eq. (1) such that
d
ij
>
1
if the pedestrian has moved in the
same
direction in the previous timestep and
d
ij
= 1 else.
3 Results
3.1 Collective Phenomena
As most prominent example of self-organization phenomena we discuss lane for-
mation out of a randomly distributed group of pedestrians. Fig. 4 shows a sim-
ulation of a corridor which is populated by two species of pedestrians moving in
opposite directions. Parallel to the direction of motion the existence of walls is
assumed. Both species interact with their own dynamic floor field only. Lanes
have already formed in the lower part of the corridor and can be spotted easily,
both in the main window showing the positions of the pedestrians and the small
windows on the right showing the floor field intensity for the two species. Sim-
ulations show that an even as well as an odd number of lanes may be formed,
