Car accidents on a single-lane highway.

We study the occurrence of car accidents in the Nagel-Schreckenberg model. Both the effects of stochastic braking and speed limit are analyzed. An approximate scaling relation is observed with the varying of speed limit. The stochastic noise will enhance the probability for accidents in the low density region and suppress that in the high density region. The probability for car accidents to occur becomes a broadened distribution over a wide range of density.