Comparison study of the reactive and predictive dynamic models for pedestrian flow

• Two higher-order dynamic models, i.e. reactive vs. predictive, for pedestrian flow are formulated and compared.
• The algorithm used to solve the two dynamic models is designed.
• Numerical results show that the two models are able to reproduce the formation of stop-and-go waves and the blocking effect at bottlenecks.
• The patterns of the local structured clusters are distinctly different at bottlenecks due to different path-choice behaviors of pedestrians.
• The strong anticipation consciousness of pedestrians to compression can avoid congestion and thereby reduce accidents in pedestrian traffic.

This paper formulates the reactive and predictive dynamic models for pedestrian flow and presents a comparison of the two models. The path-choice behavior of pedestrians in the reactive dynamic model is described that pedestrians tend to walk along a path with the lowest instantaneous cost. The desired walking direction of pedestrians in the predictive dynamic model is chosen to minimize the actual cost based on predictive traffic conditions. An algorithm used to solve the two models encompasses a cell-centered finite volume method for a hyperbolic system of conservation laws and a time-dependent Hamilton–Jacobi equation, a fast sweeping method for an Eikonal-type equation, and a self-adaptive method of successive averages for an arisen discrete fixed point problem. The two models and their algorithm are applied to investigate the spatio-temporal patterns of flux or density and path-choice behaviors of pedestrian flow marching in a facility scattered with an obstacle. Numerical results show that the two models are able to capture macroscopic features of pedestrian flow, traffic instability and other complex nonlinear phenomena in pedestrian traffic, such as the formation of stop-and-go waves and clogging at bottlenecks. Different path-choice strategies of pedestrians cause different spatial distributions of pedestrian density specially in the high-density regions (near the obstacle and exits).