The Nagel-Schreckenberg model revisited

TL;DR

This paper revisits the Nagel-Schreckenberg traffic model, analyzing its stationary states for different maximum velocities using analytical approximations and simulations, with a focus on the braking parameter's influence.

Contribution

It provides a comparative study of analytical approximations and simulations for the Nagel-Schreckenberg model with v_max > 1, highlighting the role of the braking parameter p.

Findings

Stationary state properties depend on the braking parameter p.

Analytical approximations align with simulation results for certain parameters.

Local structure varies significantly with p.

Abstract

The Nagel-Schreckenberg model is a simple cellular automaton for a realistic description of single-lane traffic on highways. For the case $v_{max}=1$ the properties of the stationary state can be obtained exactly. For the more relevant case $v_{max}>1$, however, one has to rely on Monte Carlo simulations or approximative methods. Here we study several analytical approximations and compare with the results of computer simulations. The role of the braking parameter $p$ is emphasized. It is shown how the local structure of the stationary state depends on the value of $p$. This is done by combining the results of computer simulations with those of the approximative methods.