  This paper presents a new approach to the modeling of vehicular traffic flows
on road networks based on kinetic equations. While in the literature the
problem has been extensively studied by means of macroscopic hydrodynamic
models, to date there are still not, to the authors' knowledge, contributions
tackling it from a genuine statistical mechanics point of view. Probably one of
the reasons is the higher technical complexity of kinetic traffic models,
further increased in case of several interconnected roads. Here such
difficulties of the theory are overcome by taking advantage of a discrete
structure of the space of microscopic states of the vehicles, which is also
significant in view of including the intrinsic microscopic granularity of the
system in the mesoscopic representation.
