the two floor fields. The values of the fields $D$ and $S$ are weighted with two sensitivity parameters $k_S\in [0,\infty[$ and $k_D\in [0,\infty[$. This yields $$\label{formula}
      p_{ij} = N\exp{\left(k_D D_{ij}\right)}
      \exp{\left(k_S S_{ij}\right)}(1-n_{ij})\xi_{ij}\,,$$ with the occupation number $n_{ij} = 0,1$, the obstacle number $$\xi_{ij} = \begin{cases} 
    0 & \quad \mbox{for forbidden cells (e.g.\ walls)}\\
    1 & \quad \mbox{else} \\
    \end{cases}$$ and the normalization $$N = \left[\sum_{(i,j)}
    e^{k_D D_{ij}} e^{k_S S_{ij}}(1-n_{ij})\xi_{ij}\right]^{-1}\,.$$

3.  Each pedestrian chooses randomly a target cell based on the transition probabilities $p_{ij}$ determined by (\[formula\]).

4.  Conflicts arising by any two or more pedestrians attempting to move to the same target cell are resolved by a probabilistic method. The pedestrians which are allowed to move execute their step. The explicit procedure of conflict resolution will be described in detail in section \[conflicts\].

5.  $D$ at the origin cell $(i,j)$ of each [*moving*]{} particle is increased by one: $D_{ij}\to D_{ij}+1$.

The above rules are applied to all pedestrians at the same time (parallel update). This introduces a timescale of about $0.3~$sec/timestep [@ourpaper].

Resolution of Conflicts {#conflicts}
=======================

Due to the use of parallel dynamics it is possible that two or more particles choose the same destination cell in Step 3 