Stochastic Boundary Conditions in the Nagel-Schreckenberg Traffic Model

Abstract

We consider the generalization of the asymmetric exclusion model (ASEP) with parallel update where cars can move with velocities v ≤ w_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 ≥ 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 ≤ 2.