  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.
