This paper discusses a simple model for traffic on a 2-lane road. It is assumed that the road is infinitely long and that there are no crossings. The mean speed of vehicles with a given desired speed is investigated, assuming that the traffic conditions along the road are homogeneous. Vehicles are not allowed to leave or enter the road. Every vehicle is assumed to travel at its desired speed until it catches up to another vehicle. At this point, it immediately assumes the speed of the slower vehicle and follows this vehicle a certain distance, depending on traffic conditions, before it can move into the opposing lane and pass. When passing becomes possible, the passing vehicle resumes its desired speed, which it maintains until it catches up with another vehicle. A distribution of desired speeds is assumed to be given. Sight conditions and the oncoming traffic are described in very general terms. A nonlinear integral equation for the mean speed of a vehicle with given desired speed is derived, and various aspects of this equation are investigated. The relationship of this model to other models for traffic on 2-lane roads is briefly discussed, and numerical examples are provided.
Samenvatting