CELLULAR-AUTOMATA MODELS OF SINGLE-LANE TRAFFIC

The jamming transition in the stochastic cellular automation model (Na gel-Schreckenberg model [J. Phys. (France) I 2, 2221 (1992)]) of highw ay traffic is analyzed in detail by studying the relaxation time, a ma pping to surface growth problems, and the investigation of correlation functions. Three different classes of behavior can be distinguished d epending on the speed limit nu(max). For nu(max) = 1 the model is clos ely related to the Kardar-Parisi-Zhang class of surface growth. For 1 < nu(max) < infinity the relaxation time has a well-defined peak at a density of cars rho somewhat lower than the position of the maximum in the fundamental diagram: This density can be identified with the jamm ing point. At the jamming point the properties of the correlations als o change significantly. In the nu(max) = infinity limit the model unde rgoes a first-order transition at rho --> 0. It seems that in the rele vant cases 1 < nu(max) < infinity the jamming transition is under the influence of a second-order phase transition in the deterministic mode l and a first-order transition for nu(max) = infinity.