Stochastic boundary conditions in the Nagel-Schreckenberg traffic model

We consider the generalization of the asymmetric exclusion model (ASEP) with parallel update where cars can move with velocities v less than or equal to v(max) and v(max) > 1. For stochastic open boundary conditions we find a line of a first-order transition separating the free flow phase from the jammed phase. For maximum velocities v(max) greater than or equal to 3 so-called "buffers" develop due to the hindrance an injected car feels from the front car at the beginning of the system. As a consequence, the phase diagram qualitatively differs from that for v(max) less than or equal to 2.