Traffic flow in a 1D cellular automaton model with open boundaries

We have studied the open boundary cellular automaton models for the highway one-line traffic flow by using the mean field approximation and simulations. Our contribution focuses on the effect of braking probability (P) and a maximum velocity (nu (max)) on the density, flow and average velocity of cars moving in the middle of the road. The phase diagram is presented for nu (max) = 1 and nu (max) > 1. The maximal flow phase does not occur for nu (max) > 1. in contrast with the case nu (max) = 1 where this phase appears for p not equal 0. The first-order transition arises at alpha = beta(alpha < beta) for nu (max) = 1 (nu (max) > 1), where alpha and beta denote, respectively, the inside rate and the outside rate. The mean field approximation gives a good results in comparison with simulations for nu (max) > 1, while for nu (max) = 1, the phase diagram obtained from the simulations is predicted by the mean field approximation when p --> 1.