Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research of the Institute of Mathematics and Computer Science, Czestochowa University of Technology

In developing countries, the quality of driving infrastructure, specifically road conditions, is often suboptimal, presenting challenges and limitations for motorists. However, current traffic flow models have limitations in addressing problems caused by poor road networks. To address this issue, a new macroscopic traffic flow model has been proposed in this study that considers mean-field velocity differences on roads with suboptimal conditions. A thorough model derivation of this new macroscopic traffic flow model is presented. The study establishes crucial stability conditions, providing profound insights into traffic dynamics across diverse scenarios. Numerical simulations are presented to demonstrate the model's ability to capture shock waves, rarefaction waves, and local cluster effects. The study results offer new insights into traffic dynamics in adverse road conditions and enforce the need to enhance road infrastructure to alleviate congestion and enhance road safety.

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.