The nondeterministic Nagel-Schreckenberg traffic model with open boundary conditions

We study the phases of the Nagel-Schreckenberg traffic model with open boundary conditions as a function of the randomization probability p > 0 and the maximum velocity $v_{max}>1$. Due to the existence of “buffer sites” which enhance the free flow region, the behaviour is much richer than that of the related asymmetric exclusion process (ASEP, {v}_{max} = 1$). Such sites exist for $v_{max}\ge 3$ 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 phase transitions. For p > $p_c$ an additional maximum current phase occurs like for the ASEP. The density profile decays in the maximum current phase algebraically with an exponent $\gamma \approx 2\mathrm{/}3$ for all $v_{max}\ge 2$ indicating that these models belong to another universality class than the ASEP where $\gamma =1\mathrm{/}2$.