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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 $J_s\propto d^{0.93\pm 0.02}$ and the critical density $p_c$ scales as $p_c\propto(d/W)^{1.16\pm 0.02}$, 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.

90B20Traffic problems
60G50Sums of independent random variables; random walks
Full Text: DOI
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