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Dynamical Universality Class of the Nagel–Schreckenberg and Related Models

In: Traffic and Granular Flow '17

Author

Listed:
  • Andreas Schadschneider

    (Universität zu Köln, Institut für Theoretische Physik)

  • Johannes Schmidt

    (Universität zu Köln, Institut für Theoretische Physik)

  • Jan de Gier

    (The University of Melbourne, ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS), School of Mathematics and Statistics)

  • Gunter M. Schütz

    (Forschungszentrum Jülich, Institute of Complex Systems)

Abstract

Models for vehicular traffic fall into distinct dynamical universality classes of non-equilibrium systems. Such models share model-independent aspects of their dynamics, such as current fluctuations. Up to now the universality class of the Nagel–Schreckenberg (NaSch) model was not known except for the special case v max = 1 $$v_{\max }=1$$ . In this case the model corresponds to the ASEP (asymmetric simple exclusion process) which belongs to the Kardar–Parisi–Zhang (KPZ) class characterized by the dynamical exponent z = 3∕2. We have shown that the NaSch model for general v max $$v_{\max }$$ also belongs to the KPZ class. Here we demonstrate that the universality class is not changed by extending the model to a two-lane NaSch model with dynamical lane changing rules. As an application we estimate the relaxation time to the (generally unknown) stationary state.

Suggested Citation

  • Andreas Schadschneider & Johannes Schmidt & Jan de Gier & Gunter M. Schütz, 2019. "Dynamical Universality Class of the Nagel–Schreckenberg and Related Models," Springer Books, in: Samer H. Hamdar (ed.), Traffic and Granular Flow '17, pages 53-60, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-11440-4_7
    DOI: 10.1007/978-3-030-11440-4_7
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