Macroscopic modeling of multi-lane motorways using a two-dimensional second-order model of traffic flow

TL;DR

This paper introduces a two-dimensional macroscopic traffic flow model that incorporates lane-changing behavior on motorways, extending existing one-dimensional models and ensuring consistency when lane-changing ceases.

Contribution

It develops a novel 2D macroscopic model for traffic flow that accounts for lane changes, based on a microscopic follow-the-leader approach, and analyzes its discretization and solutions.

Findings

Model captures lane-changing dynamics effectively.

Discretization and Riemann problem solutions are analyzed.

Numerical experiments demonstrate model features.

Abstract

Lane changing is one of the most common maneuvers on motorways. Although, macroscopic traffic models are well known for their suitability to describe fast moving crowded traffic, most of these models are generally developed in one dimensional framework, henceforth lane changing behavior is somehow neglected. In this paper, we propose a macroscopic model, which accounts for lane-changing behavior on motorway, based on a two-dimensional extension of the Aw and Rascle [Aw and Rascle, SIAM J.Appl.Math., 2000] and Zhang [Zhang, Transport.Res.B-Meth., 2002] macroscopic model for traffic flow. Under conditions, when lane changing maneuvers are no longer possible, the model "relaxes" to the one-dimensional Aw-Rascle-Zhang model. Following the same approach as in [Aw, Klar, Materne and Rascle, SIAM J.Appl.Math., 2002], we derive the two-dimensional macroscopic model through scaling of time discretization of a microscopic follow-the-leader model with driving direction. We provide a detailed analysis of the space-time discretization of the proposed macroscopic as well as an approximation of the solution to the associated Riemann problem. Furthermore, we illustrate some features of the proposed model through some numerical experiments.