Modeling and Simulation of Macroscopic Pedestrian Flow Models

TL;DR

This paper compares macroscopic pedestrian flow models, specifically Hughes' model and a mean field game approach with nonlinear mobilities, through numerical simulations in one and two dimensions.

Contribution

It introduces a numerical analysis linking Hughes' model with a mean field game framework for pedestrian dynamics, highlighting their relationship and differences.

Findings

Numerical results demonstrate the connection between the two models.

The models effectively simulate fast exit scenarios in pedestrian crowds.

The mean field game approach provides a new perspective on pedestrian flow modeling.

Abstract

We analyze numerically some macroscopic models of pedestrian motion such as Hughes model [1] and mean field game with nonlinear mobilities [2] modeling fast exit scenarios in pedestrian crowds. A model introduced by Hughes consisting of a non-linear conservation law for the density of pedestrians coupled with an Eikonal equation for a potential modeling the common sense of the task. Mean field game with nonlinear mobilities is obtained by an optimal control approach, where the motion of every pedestrian is determined by minimizing a cost functional, which depends on the position, velocity, exit time and the overall density of people. We consider a parabolic optimal control problem of nonlinear mobility in pedestrian dynamics, which leads to a mean field game structure. We show how optimal control problem related to the Hughes model for pedestrian motion. Furthermore we provide several numerical results which relate both models in one and two dimensions. References [1] Hughes R.L.: A continuum theory for the flow of pedestrians, Transportation Research Part B: Methodological, 36, 507-535 (2000) [2] Burger M., Di Francesco M., Markowich P.A., Wolfram M-T.: Mean field games with nonlinear mobilities in pedestrian dynamics, Discrete and Continuous Dynamical Systems. Series B. A Journal Bridging Mathematics and Sciences, 19, 1311-1333 (2014)