Modeling and numerical simulations of multilane vehicular traffic by active particles methods

This paper deals with the modeling and numerical simulations of multilane vehicular traffic according to the kinetic theory of active particles methods. The main idea of this theory is to consider each driver-vehicle system as a micro-system, where the microscopic state of particles is described by position, velocity, and activity which is an appropriate variable for modeling the quality of the driver-vehicle. The interactions between micro-systems are modeled by stochastic game theory. This leads to the derivation of a mathematical model within the framework of the approach of kinetic theory. The well-posedness of the related Cauchy problem for the spatially homogeneous case is established. Numerical simulations are carried out to show the ability of the proposed model to reproduce the empirical data such as the asymptotic property in time and the emerging behavior of clusters with a particular focus on the road environment conditions.

Automated summary

This paper focuses on modeling and numerically simulating multilane vehicular traffic using the kinetic theory of active particles methods. The approach considers each driver-vehicle system as a micro-system and describes the microscopic state using position, velocity, and activity variables. The interactions between micro-systems are modeled using stochastic game theory, leading to a mathematical model within the framework of kinetic theory. The paper establishes the well-posedness of the related Cauchy problem for the spatially homogeneous case and demonstrates the model's ability to reproduce empirical data through numerical simulations, specifically addressing the road environment conditions.