Dynamical Universality Class of the Nagel–Schreckenberg and Related Models

Andreas Schadschneider (), Johannes Schmidt (), Jan de Gier () and Gunter M. Schütz ()
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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

A chapter in Traffic and Granular Flow '17, 2019, pp 53-60 from Springer

Abstract: 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.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-11440-4_7

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DOI: 10.1007/978-3-030-11440-4_7

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