Nondeterministic Nagel-Schreckenberg traffic model with open boundary conditions

Abstract

We study the phases of the Nagel-Schreckenberg traffic model with open boundary conditions as a function of the randomization probabilities p>0 and the maximum velocity v(max)>1. Due to the existence of "buffer sites" which enhance the free-flow region, the behavior is much richer than that of the related, parallel updated asymmetric exclusion process [(ASEP), v(max)=1]. Such sites exist for v(max)> or =3 and p<p(c) where the phase diagram is qualitatively similar to the p=0 case: there is a free flow and a jamming phase separated by a line of first-order transitions. For p>p(c) an additional maximum current phase separated by second-order transitions occurs like for the ASEP. The density profile decays in the maximum current phase algebraically with an exponent gamma approximately 2 / 3 for all v(max)> or =2 indicating that these models belong to another universality class than the ASEP where gamma=1 / 2.