Towards the modeling of vehicular traffic as complex system: a kinetic theory approach

Kinetic theory methods are applied in this paper to model the dynamics of vehicular traffic. The basic idea is to consider each vehicular-driver system as a single part, or micro-system, of a large complex system, in order to capture the heterogeneous behavior of all the micro-systems that compose the overall system. The evolution of the system is ruled by nonlinearly additive interactions described by stochastic games. A qualitative analysis for the proposed model with discrete states is developed, showing well-posedness of the related Cauchy problem for the spatially homogeneous case and for the spatially nonhomogeneous case, the latter with periodic boundary conditions. Numerical simulations are also performed, with the aim to show how the model proposed is able to reproduce empirical data and to show emerging behavior as the formation of clusters. Keywords: Traffic flow; empirical data; heterogeneity; nonlinearity; Cauchy problem. AMS Subject Classification: 35L50, 35L65, 90B20