Equivalences Between Entropy and Network Models for Transportation Systems

Abstract

Rcprinu available dirrclly fmm lhs prinler F'hotmpying pcrmiucd by liccnr onlyTransportation systems studies have been successfully carried out by making use of both probabilistic models based on an entropy maximization principle and deterministic models based on system theory. Specifically. the cenual problem of trip or flow-distribution has k e n handled by the two methods yielding identical results. The paper establishes an equivalence between the two methodologies. This raises a basic question as to how a probIem which has been categorized as probabilistic could ever be solved by a network method which is applicable only to a deterministic system. The Dwer ~o i n l s out that such an auivalence is rendered wssible in this case be-. . . ca& the Wilson [1970jmodel for the transportation problem is c&t into the framework oithe maximum entropy principle by defining cenain proportions as probabilities. In other words. the trip disttibutioo is not an inherently random hen omen on and as such throws ooen the wssibilitv of solvine the ~roblem bv a deterministic method.-.The general implications of such an equivalence are pointed out since they are of possible relevance in many other situations when proportions are interpreted as probabilities.

The zone-size-dependent entropy formula and spatial interaction modelling: An additional note

“…Roy and Flood 1992;Slater 1992;Pooler 1992Pooler , 1993Pooler , 1994Kantorowich 1992;Gonc Ëalves and Ulyssea-Neto 1993;Mathur and Kesavan 1996) evidence that it is still alive, attractive and far from being a closed ®eld.…”