Modeling Vehicular Traffic Flow With Taillight Effect on Deteriorated Roads

This study addresses a critical gap in traffic flow modeling by developing a macroscopic framework that simultaneously accounts for taillight signaling effects and deteriorated road conditions—a common but understudied scenario in developing regions. Building on the observation that reduced road quality and limited visibility significantly alter driver behavior, particularly in response to preceding vehicles’ taillights, we formulate a model that captures these complex interactions neglected by classical approaches. Through systematic mathematical analysis, we first demonstrate that the vector–matrix formulation yields a strictly hyperbolic and anisotropic system, characterized by finite-speed wave propagation along distinct characteristic fields. We then establish the model’s theoretical foundations by conducting a linear stability analysis that quantitatively links traffic stability to key parameters including driver sensitivity, headway, and road condition factors. Numerical simulations validate our analytical framework, revealing how small initial density perturbations evolve into characteristic traffic wave phenomena: shock formations, rarefaction waves, and stop-and-go clusters. These results not only confirm the model’s ability to reproduce realistic traffic patterns under infrastructure constraints but also provide mechanistic insights into the emergence of congestion in poor road conditions. By integrating taillight dynamics with road quality effects, this work advances macroscopic traffic theory while offering practical tools for traffic management in low-maintenance road networks.