N(t)\rangle=\frac{\mu-1}{(\mu-2)^2}\cdot\nonumber\\
&&\ \ \ \left(\mu(1+t)-2t-\frac{(\mu-2)(\mu-1)^t\mu(1+t)}{(\mu-1)^{t+1}-1}
\right).
\label{exactN}\end{aligned}$$ Asymptotically, (\[exactN\]) implies for large times $$\langle N(t)\rangle\sim \frac{1-\mu}{2-\mu}\cdot t
\,\,\,\quad{\rm as}\,\,\,t\to\infty\;,
\label{grad}$$ i.e. a linear behaviour as observed in simulations for the ordered regime. This expression is also consistent with the fact that $T\to\infty$ for $\mu\to 1$.

![Evacuated persons in dependence of time for the ordered regime; comparison of the numerical results with the analytical approximation (\[grad\]) for the density $\rho=0.3$.[]{data-label="plot_10"}](\DIR/fig17.eps){width="0.8\columnwidth"}

![Time-dependence of the number of evacuated persons for the ordered regime; comparison of the numerical results with the analytical approximation (\[grad\]) for the density $\rho=0.003$.[]{data-label="plot_10b"}](\DIR/fig18.eps){width="0.8\columnwidth"}

From fig. \[plot\_10\] we see that the analytical approximation (\[grad\]) for $\langle N(t)\rangle$ is very good for high densities ($\rho=0.3$) and friction parameter values $\mu\leq 0.6$. However, for very high parameter values ($\mu\geq 0.8$) the agreement is not satsifactory. Here the assumption that a typical local configuration looks like that in fig. \[plot\_8\] no longer holds. The observed flow is underestimated since the large friction parameter $\mu$ is responsible for a flow reduction through conflicts occuring away from the door. Therefore particles are not so dense-packed at the exit (compared to the situation at smaller $\mu$-values) which leads to an effective reduction of conflicts.

In the 