In order to evaluate the keep-right-except-to-pass traffic rule, which is in effect in most countries, a suitable mathematical model is necessary. With the help the following model, analysts can objectively evaluate the effects and benefits of various driving regulations and rules. We formalize the situation in which automobiles are being driven on a multi-lane freeway as a process of cellular automata (CA). Following the methods used in the studies of Kerner and Barlovic and using the NaSch model, we formalize the keep-right-except-to-pass rule into mathematical form. We set the driving strategy by adopting the Velocity-Dependent-Randomization (VDR) model, considering the driver’s psychological state with respect to his desire to slow down behind, or to pass, another automobile. Adding stochastic factors during the analysis of the driving process, we examined mathematically the effects of traffic flow, the utilization of lanes, and transportation safety which mostly depends on the frequency of lane changes, to evaluate the keep-right rule.