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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.

    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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    [8] Helge Holden, Nils Henrik Risebro . Follow-the-Leader models can be viewed as a numerical approximation to the Lighthill-Whitham-Richards model for traffic flow. Networks and Heterogeneous Media, 2018, 13(3): 409-421. doi: 10.3934/nhm.2018018
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  • 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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    3. R. Borsche, A. Klar, A Nonlinear Discrete Velocity Relaxation Model For Traffic Flow, 2018, 78, 0036-1399, 2891, 10.1137/17M1152681
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    8. Giacomo Dimarco, Andrea Tosin, The Aw–Rascle Traffic Model: Enskog-Type Kinetic Derivation and Generalisations, 2020, 178, 0022-4715, 178, 10.1007/s10955-019-02426-w
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    12. G. Albi, N. Bellomo, L. Fermo, S.-Y. Ha, J. Kim, L. Pareschi, D. Poyato, J. Soler, Vehicular traffic, crowds, and swarms: From kinetic theory and multiscale methods to applications and research perspectives, 2019, 29, 0218-2025, 1901, 10.1142/S0218202519500374
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  • © 2007 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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