The Aw-Rascle traffic model with locally constrained flow

TL;DR

This paper investigates the Aw-Rascle traffic model with a local flow constraint at a point, proposing two solution types, analyzing their properties, and developing numerical schemes to compute them.

Contribution

It introduces two novel solution frameworks for the constrained Aw-Rascle model and compares their properties and numerical implementations.

Findings

Both solution types preserve different physical quantities.

The invariant domains for solutions are characterized.

Numerical schemes effectively compute the proposed solutions.

Abstract

We consider solutions of the Aw-Rascle model for traffic flow fulfilling a constraint on the flux at $x=0$. Two different kinds of solutions are proposed: at $x=0$ the first one conserves both the number of vehicles and the generalized momentum, while the second one conserves only the number of cars. We study the invariant domains for these solutions and we compare the two Riemann solvers in terms of total variation of relevant quantities. Finally we construct ad hoc finite volume numerical schemes to compute these solutions.