Macroscopic modeling of pedestrian flow based on a second-order predictive dynamic model

摘要

This work presents a second-order predictive dynamic model for pedestrian flow to investigate movement patterns and non-equilibrium phenomena in pedestrian traffic. This model is described as a system of nonlinear hyperbolic conservation laws with relaxation under the hypothesis that a group of pedestrians are regarded as a continuous anisotropic medium. The desired or preferred walking direction of pedestrians is assumed to minimize the total actual walking cost based on predictive traffic conditions, which satisfies the predictive dynamic user-equilibrium assignment. To solve this model, a cell-centered finite volume method for hyperbolic conservation laws coupled with a self-adaptive method of successive averages for an arisen discrete fixed point problem is adopted. The proposed model and algorithm are validated by comparing the results carried out by the model with experimental observations under non-congested conditions. Numerical examples are designed to investigate macroscopic features and path-choice behaviors of pedestrian flow. Numerical results indicate that the proposed model is able to reproduce some complex nonlinear phenomena in pedestrian traffic, such as the formation of congestions and stop-and-go waves.