Nonlocal Generalized Aw-Rascle-Zhang model: well-posedness and singular limit

TL;DR

This paper introduces a nonlocal version of the Generalized Aw-Rascle-Zhang traffic model, proving well-posedness and analyzing the limit as the nonlocal kernel approaches a delta function, connecting it to the classical model.

Contribution

It establishes existence, uniqueness, and a nonlocal-to-local limit for the first time in a coupled two-equation traffic flow system with nonlocal flux.

Findings

Proved well-posedness of the nonlocal model.

Established convergence to the local model with exponential kernels.

First nonlocal-to-local limit result for such coupled systems.

Abstract

We discuss a nonlocal version of the Generalized Aw-Rascle-Zhang model, a second-order vehicular traffic model where the empty road velocity is a Lagrangian marker governed by a transport equation. The evolution of the car density is described by a continuity equation where the drivers' velocity depends on both the empty road velocity and the convolution of the car density with an anisotropic kernel. We establish existence and uniqueness results. When the convolution kernel is replaced by a Dirac Delta, the nonlocal model formally boils down to the classical (local) Generalized Aw-Rascle-Zhang model, which consists of a conservation law coupled with a transport equation. In the case of exponential kernels, we establish convergence in the nonlocal-to-local limit by proving an Oleinik-type estimate for the convolution term. To the best of our knowledge, this is the first nonlocal-to-local limit result for a system of two non-decoupling equations with a nonlocal flux function.