A variety of cellular automaton models have been proposed to give a discrete approximation to traffic flow. Nagel and Schreckenberg [1] have demonstrated that their model accurately describes some of the main features of real traffic. Later, multi-lane ([2]) and two-dimensional (e.g. [4][3]) CA models were proposed. This paper continues in this line by introducing a CA model in which vehicles move on two lanes, in opposite directions.
Multi-lane models require additional rules to describe lane changes, and non-trivial interactions between the lanes are observed. In the present case, two lanes in opposite directions, these interactions depend strongly on the absolute and relative densities on the two lanes. In the limit of large absolute densities, interactions can be ignored. When absolute densities are small, relative densities become important. For instance, if there are no vehicles in the on-coming lane, our model behaves (up to reflection of one lane) like an asymmetric model with two lanes in the same direction. If there are only a few vehicles in a given lane and an intermediate number in the oncoming lane, then vehicles in the oncoming lane will pass, and slow progress on the given lane. Finally, if the density on both lanes is large, then the passing is impossible, and the model is equivalent to two copies of the one-lane model.
The one-lane CA model of [1] assumes that all vehicles have the same maximum velocity. Indeed, the one-lane model does not permit a true distribution of maximum velocities. Such a model would create platoons of vehicles, each following a slow car. One motivation of [2] for introducing two (uni-directional) lanes was to avoid this effect. This consideration motivates our own work as well. We investigate routes with passing and no-passing zones; platoons form in the no-passing zones, and disperse in the following passing zone.