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

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.