The Backward Looking Effect in Lattice Hydrodynamic Model of Pedestrian Flow

Abstract

Based on Li’s lattice model, a new lattice hydrodynamic model of single-file pedestrian flow is proposed by incorporating the backward looking effect at middle and high density. By applying the linear stability theory to obtain the stability conditions of the extended model, the results show that the new model can enhance the stability of the pedestrian flow when the backward looking effect is considered. Through nonlinear analysis, the modified KdV equation is derived to describe the pedestrian jam near the critical point. Moreover, numerical simulations show that the proposed model is theoretically an improvement over previous ones.