  We develop a discrete Boltzmann-type model that uses dynamics in phase space
to describe the behavior of traffic flows. Firstly, we model the traffic flow
at mesoscopic scale using dynamics in phase space, which is considered as an
evolution model in a graph, and we demonstrate the existence of phase
transition phenomena through theoretical analysis. Secondly, we assumed the
density of vehicles in geometric space to be homogeneous and single-peaked,
respectively, and performed numerical simulations to obtain the results
consistent with experience. According to this model, we can perform effective
simulations on the effects played by multiple parameters on the traffic flow.
