Stability of heterogeneous linear and nonlinear car-following models

TL;DR

This paper investigates how different types of heterogeneity in vehicle behavior influence traffic stability and the emergence of stop-and-go waves, using linear stability analysis and simulations.

Contribution

It introduces and analyzes two heterogeneity models affecting the stability of linear and nonlinear car-following models, providing new insights into traffic instability mechanisms.

Findings

Heterogeneity impacts traffic stability differently in linear and nonlinear models.

Derived general linear stability conditions for heterogeneous models.

Simulations illustrate the influence of individual vehicle differences on traffic dynamics.

Abstract

Stop-and-go waves in road traffic are complex collective phenomena with significant implications for traffic engineering, safety and the environment. Despite decades of research, understanding and controlling these dynamics remains challenging. This article examines two classes of heterogeneous car-following models with quenched disorder to shed light on the underlying mechanisms that drive traffic instability and stop-and-go dynamics. Specifically, a scaled heterogeneity model and an additive heterogeneity model are investigated, each of which affects the stability of linear and nonlinear car-following models differently. We derive general linear stability conditions which we apply to specific models and illustrate by simulation. The study provides insights into the role of individual heterogeneity in vehicle behaviour and its influence on traffic stability.