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

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.