Derivation and stability analysis of macroscopic multi-lane models for vehicular traffic flow

TL;DR

This paper develops a new macroscopic multi-lane traffic flow model derived from microscopic dynamics, analyzes its stability, and confirms findings through numerical tests, advancing understanding of traffic behavior at a large scale.

Contribution

The paper introduces a novel first order macroscopic model for multi-lane traffic derived directly from microscopic lane-changing dynamics, with stability analysis and numerical validation.

Findings

The model accurately captures multi-lane traffic dynamics.

Stability analysis identifies conditions for equilibrium stability.

Numerical tests confirm theoretical stability results.

Abstract

The mathematical modeling and the stability analysis of multi-lane traffic in the macroscopic scale is considered. We propose a new first order model derived from microscopic dynamics with lane changing, leading to a coupled system of hyperbolic balance laws. The macroscopic limit is derived without assuming ad hoc space and time scalings. The analysis of the stability of the equilibria of the model is discussed. The proposed numerical tests confirm the theoretical findings between the macroscopic and microscopic modeling, and the results of the stability analysis.