Enskog-like discrete velocity models for vehicular traffic flow

Michael Herty, Lorenzo Pareschi, Mohammed Seaïd

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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.

Original languageEnglish
Pages (from-to)481-496
Number of pages16
JournalNetworks and Heterogeneous Media
Issue number3
StatePublished - 2007
Externally publishedYes


  • Discrete-velocity equations
  • Lighthill-Whitham-Richards model
  • Monte Carlo method


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