  In this paper we investigate the ability of some recently introduced discrete
kinetic models of vehicular traffic to catch, in their large time behavior,
typical features of theoretical fundamental diagrams. Specifically, we address
the so-called "spatially homogeneous problem" and, in the representative case
of an exploratory model, we study the qualitative properties of its solutions
for a generic number of discrete microstates. This includes, in particular,
asymptotic trends and equilibria, whence fundamental diagrams originate.
