General Kinetic Models for Vehicular Traffic Flows and Monte-Carlo Methods

In this paper we present a general derivation of kinetic models for traffic flows including different kinds of interaction rules. We show that most kinetic previously derived models can be cast in the actual formulation. The development of Monte-Carlo methods for direct simulation of kinetic models is considered as an initial step towards realistic and efficient computations of traffic phenomena. Monte-Carlo methods are developed for these kinetic models. Several numerical examples are computed and compared to the previously obtained solutions of the stationary equation.