Pareto-optimal coupling conditions for the Aw-Rascle-Zhang traffic flow model at junctions
This work addresses the problem of modeling traffic flow at junctions for macroscopic second-order models, but the results are limited to special junction types and lack empirical validation.
The authors propose coupling conditions for the Aw-Rascle-Zhang traffic flow model at junctions that conserve both vehicle count and Lagrangian attribute mixing, and prove the Riemann solver is well-posed for 1-to-2 and 2-to-1 junctions.
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.