The purpose of this paper is to formulate a simple two-lane model for vehicular traffic which takes into account the important effect of lane-changing and passing manoeuvres. Experimental evidence indicates that a two-lane road does not have the same characteristics as two one-lane roads placed side by side, operating independently of one other. In this paper we are concerned with those cases where both lanes travel in the same direction. The mathematical model rests upon one basic principle that the total number of vehicles are conserved and upon a specific assumption: that lane-changes are functionally related to the densities in each lane. The nonlinear differential equations which we obtain with these assumptions result from a simple accounting system that keep track of changes of flow rates and densitities within a differential element of time and road length. Our model does not take into account a detailed picture of merging and overtaking rules or of the geometry and motion of individual vehicles it suggests that dominant flow patterns in each lane can be described by assigning lane-changing functions which depend on the traffic stream in each lane.
Abstract