Two-way multi-lane traffic model for pedestrians in corridors

TL;DR

This paper extends a macroscopic traffic model to two-way multi-lane pedestrian flow, addressing congestion constraints, flow transitions, and stability issues with a focus on mathematical properties and corrections.

Contribution

It introduces a novel two-way multi-lane pedestrian traffic model with congestion handling and analyzes flow transitions and stability characteristics.

Findings

Abrupt transitions between flow regimes are demonstrated.

The model can lose hyperbolicity under certain conditions.

A diffusive correction is proposed to address instability.

Abstract

We extend the Aw-Rascle macroscopic model of car traffic into a two-way multi-lane model of pedestrian traffic. Within this model, we propose a technique for the handling of the congestion constraint, i.e. the fact that the pedestrian density cannot exceed a maximal density corresponding to contact between pedestrians. In a first step, we propose a singularly perturbed pressure relation which models the fact that the pedestrian velocity is considerably reduced, if not blocked, at congestion. In a second step, we carry over the singular limit into the model and show that abrupt transitions between compressible flow (in the uncongested regions) to incompressible flow (in congested regions) occur. We also investigate the hyperbolicity of the two-way models and show that they can lose their hyperbolicity in some cases. We study a diffusive correction of these models and discuss the characteristic time and length scales of the instability.