Memory’s effect on bidirectional pedestrian flow based on lattice hydrodynamic model

Abstract

In this paper, an extended lattice hydrodynamic model for bidirectional pedestrian flow is proposed to analyze the effect of pedestrian’s memory during a period of time on the pedestrian flow. The effect of pedestrian’s memory during a period of time is investigated by using analytical and numerical methods. The linear stability analysis indicates that the time length of pedestrian’s memory has an important effect on the stability of pedestrian flow. With increasing of the time length of pedestrian’s memory, pedestrian flow will become unstable and pedestrian congestion appear. By the use of nonlinear analysis method, three typical nonlinear wave equations including Burgers, Korteweg–de Vries (KdV) and modified Korteweg–de Vries (MKdV) equations are derived to describe the evolutions of pedestrian flow with a small amplitude disturbance in the stable, meta-stable and unstable regions, respectively. The theoretical results show that jams may be aggravated by considering the effect of pedestrian’s memory with a time length. Numerical simulations are carried out in order to clarify the theoretical results.