Enskog-like discrete velocity models for vehicular traffic flow

Michael Herty; Lorenzo Pareschi; Mohammed Seaïd; Michael Herty; Lorenzo Pareschi; Mohammed Seaïd

doi:10.3934/nhm.2007.2.481

Networks and Heterogeneous Media

2007, Volume 2, Issue 3: 481-496. doi: 10.3934/nhm.2007.2.481

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Enskog-like discrete velocity models for vehicular traffic flow

1.
Department of Mathematics, Universität Kaiserslautern, AG Technomathematik, P.O. Box 3049, D-67663 Kaiserslautern
2.
Department of Mathematics & CMCS, University of Ferrara, I-44100 Ferrara
3.
AG Technomathematik, Fachbereich mathematik, Universität Kaiserslautern, D-67663 Kaiserslautern

Received: 01 February 2007 Revised: 01 May 2007
Primary: 65C05, 90B20; Secondary: 82B40.

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.
- Lighthill-Whitham-Richards model,
- Discrete-velocity equations,
- Monte Carlo method
Citation: Michael Herty, Lorenzo Pareschi, Mohammed Seaïd. Enskog-like discrete velocity models for vehicular traffic flow[J]. Networks and Heterogeneous Media, 2007, 2(3): 481-496. doi: 10.3934/nhm.2007.2.481

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Abstract

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.
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