Suppose that road trips are generated at random points on an inflnite plane, that each has the same straight-line distance from origin to destination, and that all directions from origin to destination are equally likely. Suppose also that there is a basic road system that permits travel at a speed v in a straight line between any two points. The Report is concerned with the effect on the average travel time of providing an additional network of roads, called motorways, on which travel takes place at a speed V greater than v. A motorway may be joined or left at any point and it is assumed that each trip will be made by the quickest route. The ultimate object is to find the system of motorways that minimizes the average travel time, but this Report is mainly concerned with finding the average time for certain specific types of system. A complete determination of average travel time is made for a system consisting of infinite parallel motorways spaced at regular intervals. Partial determinations are made for a network in the form of a rectangular grid, and for an n- directional system. The results show that, while a square grid may often in practice provide a good system, a rectangular grid or a multi-directional system will sometimes be better. The Report ends with brief references to actual road systems that approximate to rectangular (as distinct from square) grids or to multi-directional systems. (Author/publisher)
Samenvatting