On Cellular Automata Models of Single Lane Traffic

Abstract

The jamming transition in the stochastic cellular automaton model (Nagel-Schreckenberg model) of highway traffic is analyzed in detail, by studying the relaxation time, a mapping to surface growth problems and the investigation of correlation functions. Three different classes of behavior can be distinguished depending on the speed limit $v_{max}$. For $v_{max}=1$ the model is closely related to KPZ class of surface growth. For $1<v_{max}<\infty$ the relaxation time has a well defined peak at a density of cars $\rho$ somewhat lower than position of the maximum in the fundamental diagram: This density can be identified with the jamming point. At the jamming point the properties of the correlations also change significantly. In the $v_{max}=\infty$ limit the model undergoes a first order transition at $\rho \to 0$. It seems that in the relevant cases $1<v_{max}<\infty$ the jamming transition is under the influence of second order phase transition in the deterministic model and of the first order transition at $v_{max}=\infty$.

17 pages LaTeX, 14 PostScript figures, To appear in Phys. Rev. E

References in corpus (1)

• Car-oriented mean-field theory for traffic flow models

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• Kardar-Parisi-Zhang Universality of the Nagel-Schreckenberg Model
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