Stability of heterogeneous linear and nonlinear car-following models

Stop-and-go waves in congested road traffic are complex collective phenomena with significant implications for traffic engineering, road safety and the environment. Despite decades of research, understanding and controlling these oscillatory 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 that we apply to specific models and illustrate by simulation. The study provides insight into the role of individual heterogeneity in vehicle behaviour and its influence on traffic stability. • Formulation of two classes of car-following models with quenched disorder. • Derivation of general linear stability conditions for multi-vehicle periodic systems. • Application of the conditions to linear and nonlinear car-following models. • Proportional heterogeneity affects all models; additive heterogeneity affects only nonlinear models. • Results shed new light on stop-and-go wave formation, demonstrated with simulations.