Car accidents in cellular automata models for one-lane traffic flow

Conditions for the occurrence of car accidents are introduced in the Nagel-Schreckenberg model. These conditions are based on the thought that a real accident depends on several parameters: an unexpected action of the car ahead (sudden stop or abrupt deceleration), the gap between the two cars, the velocity of the successor car and its delayed reaction time. We discuss then the effect of this delayed reaction time on the probability of traffic accidents. We find that these conditions for the occurrence of car accidents are necessary for modeling realistic accidents.