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.