On the modeling of granular traffic flow by the kinetic theory for active particles trend to equilibrium and macroscopic behavior

The modeling of vehicular traffic flow is developed by methods of the discrete mathematical kinetic theory for active particles. The discretization refers to the velocity variable in the case of spatially homogeneity. The discretization overcomes, at least in part, some technical difficulties related to the selection of the correct representation scale. Moreover, the modeling approach includes in the state equation of the vehicle an activity variable suitable to model the quality (low or high) of the vehicle–driver system. This paper aims to be the first of a project concerning traffic flow by active particles methods.