In this paper we shall discuss a simple model for Traffic on a two-lane road. We shall assume that the road is infinitely long and that there are no Crossings. We shall investigate the mean speed of Vehicles with a given desired speed 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 with another up with another vehicle. Upon catching up it immediately assumes the speed of the slower vehicle and follows this vehicle a certain distance, depending upon the on-coming traffic and the sight conditions, before it can move into the opposing lane and pass. When passing becomes possible the passing vehicle immediately resumes its desired speed, which it maintains until it catches up with another vehicles. A distribution of desired speeds will be assumed to be given. The sight conditions and the oncoming traffic will be described in very general terms. A non-linear integral equation for the mean speed of a vehicle with given desired speed will be derived and various aspects of this equation will be investigated. The relationship of this model to other models for traffic on two-lane roads will be shortly Discussed. Finally, a few numerical examples will be given.
Abstract