Stability analysis of pedestrian traffic flow in horizontal channels: A numerical simulation method

The operational state of the pedestrian flow through the horizontal passage has a direct bearing on the operational efficiency of the entire urban railway transit hub. This study aimed to build a lattice hydrodynamic model considering the overtaking effect of pedestrian traffic and the proportion of the pedestrian flow in two opposite directions. Based on the linear stability analysis, the stability condition of the model was obtained. The results showed that reducing the difference in the proportion of the pedestrian flow in two opposite directions could expand the stable region. Further, the mKdV equation describing the density wave propagation behavior near the critical point was derived based on nonlinear analysis. The kink–anti-kink wave solution was found for the mKdV equation. The results showed that when the overtaking effect was less than the threshold of 0.16, the jamming transition occurred between the uniform pedestrian flow and the kink density waves. When the overtaking constant was more than the threshold, a chaotic region appeared on the phase diagram. The anti-interference capability of the pedestrian flow decreased, and the entire system was in an unstable state. The numerical simulation verified the accuracy of the linear and nonlinear analyzes.