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Traffic and Granular Flow '11 pp 35–46Cite as

Stationary State Properties of a Microscopic Traffic Flow Model Mixing Stochastic Transport and Car-Following

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Abstract

We study the stationary properties of a microscopic traffic flow model related to a continuous time mass transport process. It is a stochastic collision-free mapping of a classical deterministic first order car-following model calibrated by the targeted speed function and the driver reaction time. The stationary states of the model are analytically treated for vanishing reaction time. Some approximations are calculated, assuming a product form of the invariant measure. When the reaction time is strictly positive, the process is studied by simulation. A relation between the parameters and the propagation of kinematic stop-and-go waves is identified as identical to the well-known stability condition of the car-following model. The results underline a negative impact of the driver reaction time parameter on the homogeneity of the flow in stationary state.

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Acknowledgements

A. T. acknowledges support from VINCI/ParisTech Grant 8L1142 “Éco-Conception des ensembles bâtis et des infrastructures”.

Author information

Authors and Affiliations

  1. IFSTTAR – GRETTIA, 2 rue de la Butte Verte, 93166, Noisy le Grand, France

    Sylvain Lassarre

  2. Paris-Est University – LAMA, bv. Descartes, 77454, Marne-la-Vallée, France

    Michel Roussignol

  3. Institut für Theoretische Physik, Universität zu Köln, 50937, Köln, Germany

    Andreas Schadschneider

  4. Paris-Est University – LVMT, 19 rue Alfred Nobel, 77455, Marne-la-Vallée, France

    Antoine Tordeux

Authors
  1. Sylvain Lassarre
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  2. Michel Roussignol
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  3. Andreas Schadschneider
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  4. Antoine Tordeux
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Corresponding author

Correspondence to Sylvain Lassarre .

Editor information

Editors and Affiliations

  1. Institute of Computer Science, Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

    Valery V. Kozlov

  2. Moscow State Automobile & Road Technical University, Moscow, Russia

    Alexander P. Buslaev

  3. Russian Academy of Sciences, Electronics Institute and Kotel’nikov Radioengineeering, Moscow, Russia

    Alexander S. Bugaev

  4. Mathematical Cybernetics Department, Moscow Technical University of Communications & Informatics, Moscow, Russia

    Marina V. Yashina

  5. Universität Köln, Institut Theoretische Physik, Köln, Germany

    Andreas Schadschneider

  6. und Verkehr, Universität Duisburg-Essen Physik von Transport, Duisburg, Germany

    Michael Schreckenberg

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Lassarre, S., Roussignol, M., Schadschneider, A., Tordeux, A. (2013). Stationary State Properties of a Microscopic Traffic Flow Model Mixing Stochastic Transport and Car-Following. In: Kozlov, V., Buslaev, A., Bugaev, A., Yashina, M., Schadschneider, A., Schreckenberg, M. (eds) Traffic and Granular Flow '11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39669-4_4

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