SCALING BEHAVIOR IN DISCRETE TRAFFIC MODELS

We investigate the noisy, discrete, single lane highway traffic model proposed by Nagel and Schreckenberg and demonstrate by computer simula tions that, as a function of the car density, there is a dynamical tra nsition from laminar Row to jammed traffic in the system related to th e divergence of the relaxation time of average car velocity. The criti cal density is close to the position of the maximum in the fundamental diagram. We give estimates of the critical exponents related to this jamming transition. The critical density of the geometrical ((1 + 1)-d imensional percolation) transition of jammed regions can be rather far from the jamming point depending on the strength of the noise which i ndicates that cooperativity leading to the jamming transition can be l ong range in character.