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 2/3$for all${v}_{max} \ge 2$indicating that these models belong to another universality class than the ASEP where$\gamma = 1/2$.