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A Note on the Entropy Solutions of the Hydrodynamic Model of Traffic Flow

Author

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  • Shane Velan

    (Centre for Research on Transportation, Université de Montréal, C.P. 6128 succursale Centre-ville, Montréal, Québec H3C 3J7)

  • Michael Florian

    (Centre for Research on Transportation, Université de Montréal, C.P. 6128 succursale Centre-ville, Montréal, Québec H3C 3J7)

Abstract

This paper describes the hydrodynamic model of traffic flow, which is used to derive the future density and flow along a roadway with known initial density. The complete model is a first-order partial differential equation, complemented by the entropy condition. The contributions from fluid dynamics and traffic flow theory are integrated. The entropy condition is proven to be equivalent to driver's ride impulse. It is shown that multiple weak solutions are possible for initial value problems with certain density discontinuities. In addition,the implications of nonsmooth equilibrium flow-density relationships are explored.

Suggested Citation

  • Shane Velan & Michael Florian, 2002. "A Note on the Entropy Solutions of the Hydrodynamic Model of Traffic Flow," Transportation Science, INFORMS, vol. 36(4), pages 435-446, November.
    • Handle: RePEc:inm:ortrsc:v:36:y:2002:i:4:p:435-446
    DOI: 10.1287/trsc.36.4.435.548
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    References listed on IDEAS

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    1. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
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    Citations

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    Cited by:

    1. Duret, Aurélien & Yuan, Yufei, 2017. "Traffic state estimation based on Eulerian and Lagrangian observations in a mesoscopic modeling framework," Transportation Research Part B: Methodological, Elsevier, vol. 101(C), pages 51-71.
    2. Yadong Lu & S. C. Wong & Mengping Zhang & Chi-Wang Shu, 2009. "The Entropy Solutions for the Lighthill-Whitham-Richards Traffic Flow Model with a Discontinuous Flow-Density Relationship," Transportation Science, INFORMS, vol. 43(4), pages 511-530, November.
    3. Raphaèle Herbin & Ludovic Leclercq, 2011. "“A Note on the Entropy Solutions of the Hydrodynamic Model of Traffic Flow” Revisited," Transportation Science, INFORMS, vol. 45(1), pages 138-142, February.
    4. Hilmi Berk Celikoglu & Mehmet Ali Silgu, 2016. "Extension of Traffic Flow Pattern Dynamic Classification by a Macroscopic Model Using Multivariate Clustering," Transportation Science, INFORMS, vol. 50(3), pages 966-981, August.
    5. Lu, Yadong & Wong, S.C. & Zhang, Mengping & Shu, Chi-Wang & Chen, Wenqin, 2008. "Explicit construction of entropy solutions for the Lighthill-Whitham-Richards traffic flow model with a piecewise quadratic flow-density relationship," Transportation Research Part B: Methodological, Elsevier, vol. 42(4), pages 355-372, May.

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