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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.

MSC:

90B20 Traffic problems in operations research
60G50 Sums of independent random variables; random walks
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References:

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