Scaling behaviour in discrete traffic models

We investigate the noisy, discrete, single lane highway traffic model proposed by Nagel and Schreckenberg (1992) and demonstrate by computer simulations that, as a function of the car density, there is a dynamical transition from laminar flow to jammed traffic in the system related to the divergence of the relaxation time of average car velocity. The critical 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)-dimensional percolation) transition of jammed regions can be rather far from the jamming point depending on the strength of the noise which indicates that cooperativity leading to the jamming transition can be long range in character.