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The nondeterministic Nagel-Schreckenberg traffic model with open boundary conditions

S. Cheybani·J. Kertesz·M. Schreckenberg
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Abstract

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

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S. Cheybani, J. Kertesz, M. Schreckenberg. 2000-06-14. The nondeterministic Nagel-Schreckenberg traffic model with open boundary conditions. https://doi.org/10.1103/physreve.63.016108

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