Enskog-like discrete velocity models for vehicular traffic flow

We consider an Enskog-like discrete velocity model which in the limit yields the viscous Lighthill-Whitham-Richards equation used to describe vehicular traffic flow. Consideration is given to a discrete velocity model with two speeds. Extensions to the Aw-Rascle system and more general discrete velocity models are also discussed. In particular, only positive speeds are allowed in the discrete velocity equations. To numerically solve the discrete velocity equations we implement a Monte Carlo method using the interpretation that each particle corresponds to a vehicle. Numerical results are presented for two practical situations in vehicular traffic flow. The proposed models are able to provide accurate solutions including both, forward and backward moving waves.