Qualitative behaviour and numerical approximation of solutions to conservation laws with non-local point constraints on the flux and modeling of crowd dynamics at the bottlenecks

TL;DR

This paper numerically investigates a pedestrian traffic model with non-local constraints, validating the scheme's convergence and demonstrating its ability to reproduce key phenomena like Faster Is Slower and Braess' paradox.

Contribution

It proves convergence of a finite volume scheme for the model and validates its qualitative behavior through simulations of crowd dynamics at bottlenecks.

Findings

Scheme converges and matches explicit solutions.

Model reproduces Faster Is Slower phenomenon.

Model captures Braess' paradox in crowd flow.

Abstract

In this paper we investigate numerically the model for pedestrian traffic proposed in [B.Andreianov, C.Donadello, M.D.Rosini, Crowd dynamics and conservation laws with nonlocal constraints and capacity drop, Mathematical Models and Methods in Applied Sciences 24 (13) (2014) 2685-2722]. We prove the convergence of a scheme based on a constraint finite volume method and validate it with an explicit solution obtained in the above reference. We then perform ad hoc simulations to qualitatively validate the model under consideration by proving its ability to reproduce typical phenomena at the bottlenecks, such as Faster Is Slower effect and the Braess' paradox.