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 c1 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. (Author/publisher)
Abstract