Mean-field theory for car accidents

Effects of a type of quenched randomness on car accidents in a cellular automaton model

In this paper we numerically study the probability Pac of the occurrence of car accidents in the Nagel-Schreckenberg (NS) model with a defect. In the deterministic NS model, numerical results show that there exists a critical value of car density below which no car accident happens. The critical density Pc1 is not related only to the maximum speed of cars, but also to the braking probability at the defect. The braking probability at a defect can enhance, not suppress, the occurrence of car accidents when its value is small. Only the braking probability at the defect is very large, car accidents can be reduced by the bottleneck. In the nondeterministic NS model, the probability Pac exhibits the same behaviors with that in the deterministic model except the case of vmax=1 under which the probability Pac is only reduced by the defect. The defect also induces the inhomogeneous distribution of car accidents over the whole road. Theoretical analyses give an agreement with numerical results in the deterministic NS model and in the nondeterministic NS model with vmax=1 in the case of large defect braking probability.

Effects of quenched randomness induced by car accidents on traffic flow in a cellular automata model

In this paper we numerically study the impact of quenched disorder induced by car accidents on traffic flow in the Nagel-Schreckenberg (NS) model. Car accidents occur when the necessary conditions proposed by [J. Phys. A 30, 3329 (1997)]] are satisfied. Two realistic situations of cars involved in car accidents have been considered. Model A is presented to consider that the accident cars become temporarily stuck. Our studies exhibit the "inverse- lambda form" or the metastable state for traffic flow in the fundamental diagram and wide-moving waves of jams in the space-time pattern. Model B is proposed to take into account that the "wrecked" cars stay there forever and the cars behind will pass through the sites occupied by the "wrecked" cars with a transmission rate. Four-stage transitions from a maximum flow through a sharp decrease phase and a density-independent phase to a high-density jamming phase for traffic flow have been observed. The density profiles and the effects of transmission rate and probability of the occurrence of car accidents in model B are also discussed.

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.