Basic principles of the model

In the model the space is discretized into small cells which can either be empty or occupied by exactly one pedestrian. Each of this pedestrians can move to one of its unoccupied neighbour cells at each discrete time step t to t+1 according to certain transition probabilities.
The probabilities are given by the interaction with two floor fields. The two fields determine the transition probability in that way, that the particle movement is more likly in direction of higher fields. These two fields shall be regarded shortly in the following and the basic update rules of the model are summarized.

The static floor field S

The static floor field S does not evolve with time and is not changed by the presence of the pedestrians.
Such a field can be used to specify regions of space which are more attractive, e.g an emergency exit or shop windows.
In case of the here considered evacuation processes, the static floor field describes the shortest distance to a an exit door, lying at the middle of the top wall of the room. The picture below shows graphical represantations of S for different geometries.

S is calculated due to a certain distance metric for each lattice site so that the field values are increased in the direction to the door. The field values are highest for the door cells.

The dynamic floor field D

The dynamic floor field D is a virtual trace left by the pedestrians and has its own dynamics, i.e. diffusion and decay. It is used to model an attractive interaction between the particles. The picture below shows 3-dimensional plots of D for three stages during evacuation process.

At t=0 for all sites (i,j) of the lattice the dynamic field is zero, i.e. D(i,j)=0. Whenever a particle jumps from site (i,j) to one of the neighbouring cells, D of the starting place is increased by one.
Therefore D has only non negative integer values and can be compared to a bosonic field, i.e. the bosons dropped by the pedestrians during their movement create the virtual trace. Thus the field value D(i,j) corresponds to D(i,j) bosons. The dynamic floor field is time dependent, it has diffusion and decay controlled by two parameters alpha in [0,1] and delta in [0,1], which means broadening and dilution of the trace.
In each time step of the simulation each single boson of the whole dynamic field D decays with the probability delta and diffuses with the probability alpha to one of its neighbouring cells. Finally this yields to D=D(t, delta, alpha ).
Note that the dynamic floor field D is only altered by moving particles and therefore it corresponds more to a virtual velocity density field, then a particle density field.