Dynamical Universality Class of the Nagel–Schreckenberg and Related Models

  • Andreas SchadschneiderEmail author
  • Johannes Schmidt
  • Jan de Gier
  • Gunter M. Schütz
Conference paper


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 \(v_{\max }=1\). 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 \(v_{\max }\) 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.



Support by the German Science Foundation (Grant SCHA 636/8-2) and the Bonn-Cologne Graduate School of Physics and Astronomy (BCGS) is gratefully acknowledged. J.S. thanks the Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS) for funding that allowed him to visit The University of Melbourne where parts of this work were done.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Andreas Schadschneider
    • 1
    Email author
  • Johannes Schmidt
    • 1
  • Jan de Gier
    • 2
  • Gunter M. Schütz
    • 3
  1. 1.Institut für Theoretische PhysikUniversität zu KölnKölnGermany
  2. 2.ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS), School of Mathematics and StatisticsThe University of MelbourneMelbourneAustralia
  3. 3.Institute of Complex SystemsForschungszentrum JülichJülichGermany

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