Given a set o origin-destination pairs and a road network connecting them, various sets of routes linking origins to destinations may be considered. Each set of routes has a a certain total lenght and a certain number of crossings of one route by another. it is of some interest to know how few crossings may be obtained with routes of a given total length. This question is examined theoretically by using a mathematical model with continuous distributions of trip- ends and a rule specifying a route from any origin to any destination. It is shown that if origins and destinations are distributed independently, the average number of intersections per pair of routes cannot be less than 1-8.As an example, a square town with a closely spaced grid network of roads and independent uniform origins and destinations is considered. Attention is confined to the two possible minimum-length routes with a single change of direction. Five routing systems are investigated and the average number of crossings per pair of routes is obtained in each case.
Abstract