A mathematical solution is presented to the problem of computing the theoretical usage in terms of mean trip density, of certain high speed facilities that are placed in a given region containing trip origins and destinations. The basic types of expressway networks considered are: (1) an isolated expressway with unlimited access, (2) a sheaf of parallel expressways with unlimited access, (3) an isolated pair of parallel expressways with unlimited access, and (4) an isolated expressway with limited access. The usage of these types of expressways is established rigorously under the following assumptions: (1) the given region is of constant (vehicle) trip density, (2) a constant speed is allowed on the expressways, (3) unfettered movement at a constant speed is allowed throughout the remainder of the region, except that trip distance is measured as right-angle distance and all movement is at right angles, (4) a trip will follow the most economical route at all times, and (5) trip length is presented as random variable with joint density function. There are several parameters on which the volumes for all expressway networks depend: expressway speed, arterial speed, average trip length for the region, density for the region, value of time, and operating and accident costs at expressway and arterial speeds. There are special parameters on which the volumes for some of the special types of networks depend. Tables have been generated which display the various volumes. Data from these tables are presented in graphical form accompanied by a discussion. Results are described and the application of the results to certain phases of the transportation planning process are discussed.
Abstract