In this paper, we study the probability of car accidents in the modified Nagel–Schreckenberg (mNaSch) under the periodic boundary condition. In order to understand the quality of interaction between vehicles in each phase of the mNaSch, the velocity correlation coefficients were investigated. The effect of the evacuation of damaged vehicles was also studied. The fundamental diagram of the system is constructed in both cases with and without the evacuation. We found that the synchronized phases in the mNaSch are manifested into two aspects. In the first phase, the velocity correlation coefficients are zero where all vehicles move at the same speed. Hence, in the other phase, the speed of vehicles shows a synchronization as the form of clusters of moving vehicles where two speeds predominate simultaneously and the velocity correlation coefficients are higher. In addition, the car accidents in the modified mNaSch depend strongly on the initial configuration especially, if we consider those car accidents really happening in the system. The evacuation of damaged vehicles enhances the traffic situation and qualitatively changes the traffic phases in the mNaSch.

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In this paper, we studied a two-lane cellular automaton model that considers both types of bottlenecks (i.e., moving and fixed). The slow-moving vehicles are considered as moving bottlenecks in our model. The fundamental diagram and the spacetime configuration were derived. The effect of the bottleneck induces a qualitative and quantitative change in the fundamental diagram of both lanes. Also, the system depends strongly on the length of the fixed bottleneck. Hence, for extremely low densities, vehicles are self-organized into two lanes. The probability of vehicle accidents is computed. It is found that the rear-end and lane-changing collision probabilities were reduced as the length of the fixed bottleneck increased. Furthermore, at low densities the fixed bottleneck has even less impact on the occurrence of lane-changing collisions. Moreover, the revised lane-changing rules reduces the flux at low and moderate density regions and augments it at large densities in the lane where there is a bottleneck. The results also indicate that the revised lane-changing rules maximizes the rear-end collisions and minimizes the unsafe lane changing collisions.

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