The traffic movement and the demand by public or private transport are problems of present days. All cities in the world suffer with traffic jammed, air and noise pollution, affecting our life quality. With this in mind, simulation systems have arose as solution to understand traffic phenomenas and help us to design vehicular traffic efficiently. These simulation systems are based on mathematic models so that they can describe the traffic behavior. Among mathematic models employed, Cellular Automaton (CA) are able to mimic the basic characteristics of vehicular traffic. CA models, that take into account different driving style, demand more computation between two consecutive simulation time steps and also require more neighbors to calculate the correct velocity of each vehicle, which implies more memory access. This work proposes a new parallel CA model which includes new policies of acceleration and distance perception based on continuous probability function to describe the unpredictable behavior of driving styles. This model is presented in parallel platform approach in order to evaluate its performance in execution of the proposed model in simulating traffic big cities. The model herein illustrates qualitative and quantitative results similar to those suggested by the literature. Besides, we conducted tests in order to evaluate the parallel execute of the proposed model.