of the update procedure. Such situations will be called [*conflicts*]{}. At first it appears that conflicts are undesirable effects which reduce the efficiency of simulations and should therefore be avoided by choosing a different update scheme. We will show in the following that this is not the case and that conflicts are important for a correct description of the physics of crowd dynamics.

Conflicts without friction {#confnofric}
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In [@ourpaper; @aki0] conflicts between pedestrians were solved in the following way: whenever $m>1$ particles share the same target cell, one ($l\in\{1,\ldots,m\}$) is chosen to move while its rivals for the same target keep their position. There are two main ways to decide which particle $l$ is allowed to move:

1.  According to the relative probabilities with which each particle chooses its target cell, i.e. the probability for particle $l$ to move is ${p_{ij}^{(l)}}/{\sum_{s=1}^{m}p_{ij}^{(s)}}$.

2.  All particles move with the same probability $\frac{1}{m}$.

The observed behaviour has been shown to be quite robust and does not depend on the details of the conflict resolution [@ourpaper].

Introduction of the friction parameter $\mu$
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We now extend the basic model by a new friction parameter $\mu \in [0,1]$, in order to describe clogging and 