Dynamical transition and scaling in a mean-field model of pedestrian flow at a bottleneck

A mean-field model is presented to mimic the pedestrian channel flow with a bottleneck. The pedestrian flow is described by the mean-field rate equation on the square lattice. The dynamical transition from the free flow to the choking flow is studied by carrying out a numerical simulation for the mean-field rate equation under open boundary conditions. The phase diagram is found numerically and analytically. The scaling behavior is investigated for the transition point and the saturated flow rate in the choking-flow region. It is shown that the transition point does not depend on the strength of drift. The transition point and saturated flow rate agree with those obtained by a one-dimensional approximation.