  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.
