Pareto-optimal coupling conditions for the Aw-Rascle-Zhang traffic flow model at junctions

TL;DR

This paper develops and analyzes a new Riemann solver for the Aw-Rascle-Zhang traffic flow model at junctions, ensuring conservation and optimal coupling conditions for complex road network interactions.

Contribution

It introduces a novel Riemann solver based on assignment coefficients and multi-objective optimization, specifically designed for the Aw-Rascle-Zhang model at junctions.

Findings

The Riemann solver is well posed for 1-to-2 diverge junctions.

The Riemann solver is well posed for 2-to-1 merge junctions.

The coupling conditions conserve vehicle number and traffic attributes.

Abstract

This article deals with macroscopic traffic flow models on a road network. More precisely, we consider coupling conditions at junctions for the Aw-Rascle-Zhang second order model consisting of a hyperbolic system of two conservation laws. These coupling conditions conserve both the number of vehicles and the mixing of Lagrangian attributes of traffic through the junction. The proposed Riemann solver is based on assignment coefficients, multi-objective optimization of fluxes and priority parameters. We prove that this Riemann solver is well posed in the case of special junctions, including 1-to-2 diverge and 2-to-1 merge.