low density regime $\rho=0.03$ (not shown in the figure) the approximation again gives satisfactory agreement for $\mu\leq 0.6$. Only in the region of very low densities (e.g. $\rho=0.003$, see fig. \[plot\_10b\]) strong deviations can be observed for all $\mu$ values. In this case there are only very few particles in the system, not hindering each other. In most cases they reach the exit independently and the evacuation time essentially depends on the diameter of the room (or the average walking length) rather than on the number of particles in the system.

Number of conflicts during evacuation {#sec_number}
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![Number of conflicts in dependence of time $t$ for all three regimes ($\rho=0.3$ and $\mu=0$).[]{data-label="plot_11"}](\DIR/fig19.eps){width="0.8\columnwidth"}

![Number of conflicts in dependence of time for all three regimes ($\rho=0.3$, $\mu=0.9$).[]{data-label="plot_11b"}](\DIR/fig20.eps){width="0.8\columnwidth"}

Next we investigate the time evolution of the number of conflicts arising during an evacuation process. Figs. \[plot\_11\] and \[plot\_11b\] show the number of conflicts in dependence of time for all three regimes in the high density case $\rho=0.3$. The maximal number of conflicts occurs for all regimes and $\mu$ values shortly after the beginning of the evacuation. The number of conflicts is always largest in the disordered regime. As argued earlier here the 