Derivation and analysis of continuum models for crossing pedestrian traffic

TL;DR

This paper derives and analyzes continuum PDE models for crossing pedestrian traffic, capturing collision avoidance and flow dynamics, with proofs of solution existence and stability analysis, supported by numerical simulations.

Contribution

It introduces new mean-field PDE models for intersecting pedestrian flows, including existence proofs and stability analysis, advancing understanding of pedestrian traffic dynamics.

Findings

Existence of global weak solutions for the parabolic model

Stability analysis of stationary states in the 1D model

Numerical simulations illustrating complex pedestrian flow behaviors

Abstract

In this paper we study hyperbolic and parabolic nonlinear partial differential equation models, which describe the evolution of two intersecting pedestrian flows. We assume that individuals avoid collisions by sidestepping, which is encoded in the transition rates of the microscopic 2D model. We formally derive the corresponding mean-field models and prove existence of global weak solutions for the parabolic model. Moreover we discuss stability of stationary states for the corresponding one-dimensional model. Furthermore we illustrate the rich dynamics of both systems with numerical simulations.