From generalized kinetic theory to discrete velocity modeling of vehicular traffic. A stochastic game approach.

This paper reports about vehicular traffic modeling by methods of the discrete kinetic theory. The purpose is to detail a reference mathematical framework for some discrete velocity kinetic models recently introduced in the literature, which proved capable to reproduce interesting traffic phenomena without using experimental information as modeling assumptions. To this aim, we firstly derive a general discrete velocity kinetic framework with binary nonlocal interactions. Then, resorting to some ideas on the stochastic game theory, we outline specific modeling guidelines for vehicular traffic, and finally we discuss the derivation of the above-mentioned vehicular traffic models from these mathematical structures.