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A uni-directional two-lane road is approximated by a set of two parallel closed one-dimensional chains. Two types of car i.e. slow and fast ones are considered in the system. Based on the Nagel-Schreckenberg (Na-Sch) model of traffic flow, a set of reaction-diffusion processes are introduced to simulate the behaviour of the cars. Fast cars can pass the slow ones using the passing-lane. We write and solve the mean field rate equations for the density of slow and fast cars respectively. We also investigate the properties of the model through computer simulations and obtain the fundamental diagrams . A comparison between our results and $v_{max}=2$ version of Na-Sch model is made.
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