Spatial Interaction Network Flow Models

Abstract

The gravity models (see e.g. Wilson (1), the single perhaps most important class of spatial interaction models, will be looked at in this paper as convex network flow models. The arc characteristics of gravity type flow networks are such that the equilibrium potentials can be calculated by solving Kirchhoff’s nodal equations of flow conservation. A standard iterative procedure for doing this — in Regional Science sometimes named after K.P. Furness (2) — will be shown to be a coordinate descent method for calculating the minimum of an appropriate convex function. In fact, it is what in network flow theory is called a dual method for calculating optimal flows. As such, it is easily recognized to be applicable to more general spatial interaction network flow models, as presented e.g. in Sections III and IV. In these more general cases one might speak of implicit Furness iteration as opposed to the explicit procedure in use for the classical gravity models (see Section III).