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 $\gamma = 1/2$. 
S. Cheybani, J. Kertesz, M. Schreckenberg