A Lattice Hydrodynamic Model of Bidirectional Pedestrian Traffic Considering the Cumulative Effect of Delay Time

A two-dimensional lattice hydrodynamic model with bidirectional flow is proposed with consideration of the continuous cumulative effect of delayed-time. The stability condition is obtained by linear analysis. Nonlinear analysis derived the mKdV equation to depict density wave of pedestrian congestion. The phase diagram shows the coexistence curve and the neutral stability curve. The neutral stability curve reveals the stable region and unstable region. The unstable region is shrunken with the increase of fraction c of east-bound and west-bound pedestrian from all pedestrians (c <= 0.5). Moreover, the increase of delay time can reduce the unstable region too. It indicates that the cumulative effect of delay time can effectively improve the stability of pedestrian traffic. In numerical simulation and analysis, we discuss the impacts of delay time and strength coefficient on pedestrian traffic. Results indicate that the cumulative effect of delayed-time and the increase of strength coefficient lambda can improve the stability of pedestrian traffic under a certain conditions.