An approach to optimal allocation of transportation facilities on expressway

摘要

The present study deals with a mathematical model for the optimal allocation of transportation facilities or interchange-exits on an expressway network in Japan, all of which has been evaluated empirically from the engineering point of view. Consequently, it is important for the present mathematical model to include socio-economical constraints rationally from practical statistics, which includes constrained parameters in terms of demography, industrial output, geography, environment load, and political requirements at times inconsistently to each other. These constraints should be evaluated rationally, and for practical simplification an equivalent density distribution is proposed to be triaged by the maximum entropy criterion that provides each ratio of attribution based upon Frobenius characteristic equation. An effective width along a given route can be assumed, which evaluates these effective parameters into a single equivalent density distribution function in terms of distance. Consequently, the present problem is described as minimization of total sum of weighted distance coordinate to any exit for the optimal allocation. An example optimal allocation is compared to the actual expressway under construction in Japan.