Cellular automata models of single-lane traffic

Abstract

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