Entropy-maximizing methods of transport analysis vis-á-vis a physical system theory modeling framework

Abstract

The entropy-maximizing method suggested by A.G. Wilson (1970) for the development of the gravity model of transportation systems is examined from the physical system theory point of view. Whereas Wilson's entropy maximizing approach considers the transportation system in the aggregate as a single entity, in order to develop an expression for the system entropy, the physical system theory modeling framework as well as the systemic entropy-maximizing method discussed invoke the component-to-system construct to formulate the requisite expression for the system entropy. Both the physical system theory method and the systemic entropy-maximizing method are endowed with a property that makes it possible for relevant forms of the system-level model to be developed by hypothesizing suitable relationships among the flow-volume and level-of-service variables of the constituent transport links (viewed as components of the transport system) in a manner that is consistent in the network-theoretic sense as well as commensurate with the system model in the behavioral form. Based on this feature, a systemic interpretation of Wilson's entropy-maximizing method in the context of a few elementary conceptual configurations of a transport network is used to compare entropy-maximizing methods with systemic methods.