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Scaling of pedestrian channel flow with a bottleneck. (English) Zbl 0978.90016
Summary: Pedestrian channel flow at a bottleneck is investigated under the open boundaries by using the lattice-gas model of biased random walkers. It is shown that a dynamical phase transition occurs from the free flow to the choking flow at a critical density ${p}_{c}$ with increasing density. The flow rate saturates at higher density than the critical density. In the choking-flow region, a scaling behavior is found as follows: the saturated flow rate ${J}_{s}$ scales as ${J}_{s}\propto {d}^{0·93±0·02}$ and the critical density ${p}_{c}$ scales as ${p}_{c}\propto {\left(d/W\right)}^{1·16±0·02}$, where $d$ is the width of the bottleneck and $W$ is the width of channel. The plot of the rescaled flow rate against the rescaled density collapses onto a single curve.
##### MSC:
 90B20 Traffic problems 60G50 Sums of independent random variables; random walks