The Nagel-Schreckenberg model revisited

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.