Influx ratio preserving coupling conditions for the networked Lighthill-Whitham-Richards model

TL;DR

This paper introduces a new coupling condition for the Lighthill-Whitham-Richards traffic model at merging junctions, preserving inflow ratios and providing accurate predictions in various traffic scenarios.

Contribution

It proposes a novel inflow ratio preserving coupling rule and analyzes two Riemann solvers for merging junctions within the traffic flow model.

Findings

Relaxation-based Riemann solver accurately predicts free-flow and congestion.

The new coupling rule maintains inflow ratios at junctions.

Numerical experiments validate the effectiveness of the proposed methods.

Abstract

A new coupling rule for the Lighthill-Whitham-Richards model at merging junctions is introduced that imposes the preservation of the ratio between inflow from a given road to the total inflow into the junction. This rule is considered both in the context of the original traffic flow model and a relaxation setting giving rise to two different Riemann solvers that are discussed for merging 2-to-1 junctions. Numerical experiments are shown suggesting that the relaxation based Riemann solver is capable of suitable predictions of both, free-flow and congestion scenarios without relying on flow maximization.