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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 d 0·93±0·02 and the critical density p c scales as p c (d/W) 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:
90B20Traffic problems
60G50Sums of independent random variables; random walks