American Institute of Mathematical Sciences

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September  2007, 2(3): 481-496. doi: 10.3934/nhm.2007.2.481

Enskog-like discrete velocity models for vehicular traffic flow

Michael Herty 1, , Lorenzo Pareschi 2, and  Mohammed Seaïd 3,

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, Italy
3. 

AG Technomathematik, Fachbereich mathematik, Universität Kaiserslautern, D-67663 Kaiserslautern, Germany

Received  February 2007 Revised  May 2007 Published  June 2007

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.
Keywords: Monte Carlo method, Lighthill-Whitham-Richards model, Discrete-velocity equations.
Mathematics Subject Classification: Primary: 65C05, 90B20; Secondary: 82B4.
Citation: Michael Herty, Lorenzo Pareschi, Mohammed Seaïd. Enskog-like discrete velocity models for vehicular traffic flow. Networks & Heterogeneous Media, 2007, 2 (3) : 481-496. doi: 10.3934/nhm.2007.2.481
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