A mathematical model and its solutions for traffic flow management

The study of mathematical modeling of traffic flow has become increasingly important in modern urban contexts, driven by the need to enhance the quality of life in cities, mitigate environmental pollution, and improve the efficiency of transportation systems. Over the past decades, numerous mathematical frameworks have been proposed to characterize traffic dynamics, including microscopic, macroscopic, and kinetic models. Each of these approaches exhibits distinct strengths and limitations, which are typically associated with the computational complexity required for numerical simulations and with the capability of the model, to accurately reproduce real-world traffic phenomena, specifically, capturing complex interactions—such as those between pedestrians and vehicles—as well as emergent phenomena, such as queue formation at traffic signals, poses a significant challenge. In this study, we investigated the Riemann problem associated with the non-homogeneous Aw–Rascle model. More specifically, we conducted a systematic comparison of different numerical methods for solving the Riemann problem within this framework, with the aim of evaluating their performance and reliability.