Modeling Isotropic Traffic Flow Under Vehicle-to-Vehicle Communication: A Kinetic Approach

Abstract

Vehicle-to-vehicle communication enables inter-vehicle interactions by sending a message or exchanging data. So a vehicle is affected not only by the ones in front but also by the ones behind. The mutual influence changes the feature of traffic flow from the anisotropy to the isotropy. In this paper, I model vehicle interactions by a stochastic game and formulate the isotropic flow in lane-based traffic by a kinetic approach. Specifically, a scalar variable, called the cooperation willingness, is introduced, which may evolve as time passes. Also, I formulate a mapping between the cooperation willingness and the cooperation probability. I embed the cooperation probability into the stochastic game. Also, a general expression of the evolution equation of cooperation willingness is derived. The equilibrium solutions for a given choice of five and seven discrete classes of the cooperation willingness are solved. Finally, the proposed kinetic model of the isotropic lane-based traffic flow is used to simulate the merging of two clusters of vehicles. The results show that the nudging of vehicles ahead can improve the efficiency of traffic flow. It also confirms the theoretical analysis results.