Minimum-Cost Distances in Spatial Analysis

An axiomatic approach to distance is developed which focuses on those behavioral concepts of distance related to movement in space. In particular, spatial movement by behaving units is postulated to involve a choice from among some set of abstract trips in space, and implicitly, to involve the minimization of some relevant notion of trip costs. In this context, the relevant behavioral notion of distance in space is taken to be the minimum-cost distance generated by this choice process. These trip-cost concepts extend the classical notions of paths, path lengths, and shortest paths in metric spaces. Hence many of the analytical results of the paper involve extensions of classical shortest-path distance properties to minimum-cost distances. In addition to these extensions, a characterization theorem is given which specifies the possible functional relationships between trip costs and their associated path lengths. These relationships include most functional forms which are commonly employed in the literature.     

THE PROVENANCE OF DONKEY MILLS FROM ROMAN BRITAIN

Pompeiian-style (hourglass) grain mills are common at many Roman sites within the circum-Mediterranean countries. Three examples are known from Corfe Mullen, London and Hamworthy in southern Britain. Petrographic examination, chemical and microprobe analyses indicate that the Corfe Mullen millstone and the London donkey mill were imported from central France into southern Britain. The Hamworthy mill should be designated a ‘flat donkey mill’, and represents a recent (post-Roman) import from a volcanic source in Sardinia. There is no evidence of importation of Roman donkey mills from Germany or for transportation of such mills (or stylistic derivatives) north of London.     

NETWORK EQUILIBRIUM MODELS OF URBAN LOCATION AND TRAVEL CHOICES: A RETROSPECTIVE SURVEY*

ABSTRACT The origins and development of the network equilibrium problem are traced and interrelated. Two principal formulations are considered the network equilibrium problem with variable travel demand, and the combined model of trip distribution and traffic assignment. The relation of these models to subsequent developments concerning mode choice, residential location, estimation of origin-destination tables from link flows and stochastic route choice are then reviewed.     

Incorporating the effects of spatial structure in discrete choice models of migration

Discrete-choice theory and logit models are evaluated for their usefulness in analyzing migration patterns in a zonal system. The authors "argue that spatial effects and more specifically the relative location of zones are not taken into account in such analyses. We, therefore, introduce a measure of spatial structure and advocate its usage as a predictor of migration in such models. In an example of intrametropolitan migration in Toronto [Canada], we demonstrate that this variable is not only significant but also it improves the performance of all the other variables with the greatest impact on the distance between zones. In addition, inclusion of this variable improves the overall performance of the model in terms of residuals."     

A dynamic model of regional population growth and decline

"This paper presents a two-sector dynamic model of regional population change. The model contains a migration equation, an earnings equation, and an amenity equation for each region. In the context of this model, migration is seen as a disequilibrium process through which the regional populations move towards equilibrium positions. Migration occurs when one region is perceived to be superior to the other on the basis of its earnings and amenity levels. Equilibrium is achieved when population movements between the regions eliminate any differences in their relative attractiveness. A comparative-static analysis of the model is presented to analyze the effects of policy changes and exogenous shocks on the distribution of population among the regions." The geographical focus is on the United States.