Reaction-diffusion models describing a two-lane traffic flow

A unidirectional two-lane road is approximated by a set of two parallel closed one-dimensional chains. Two types of cars, i.e., slow and fast ones are considered in the system. Based on the Nagel-Schreckenberg model of traffic flow [K. Nagel and M. Schreckenberg, J. Phys. 2, 2221 (1992)], a set of reaction-diffusion processes is introduced to simulate the behavior of the cars. Fast cars can pass the slow ones using the passing lane. We write and solve the mean-held 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 the v(max) = 2 version of the Nagel-Schreckenberg model is made.