Second-order traffic flow models on networks

TL;DR

This paper develops a new second-order traffic flow model on networks based on the Aw-Rascle-Zhang framework, introducing an approximation for homogenized pressure and solving it with a Godunov-type scheme, validated through numerical simulations.

Contribution

It introduces a novel approximation method for homogenized pressure in second-order traffic models on networks, enhancing model accuracy.

Findings

The new approximation effectively captures homogenized pressure.

Numerical results demonstrate the model's accuracy.

Comparison shows improvements over classical models.

Abstract

This paper deals with the Aw-Rascle-Zhang model for traffic flow on uni-directional road networks. For the conservation of the mass and the generalized momentum, we construct weak solutions for Riemann problems at the junctions. We particularly focus on a novel approximation to the homogenized pressure by introducing an additional equation for the propagation of a reference pressure. The resulting system of coupled conservation laws is then solved using an appropriate numerical scheme of Godunov type. Numerical simulations show that the proposed approximation is able to approximate the homogenized pressure sufficiently well. The difference of the new approach compared with the Lighthill-Whitham-Richards model is also illustrated.