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.
