A G Wilson

A family of spatial interaction models, and associated developments

This paper shows that the gravity model is not a single model but that there is a whole family of spatial interaction models. The properties of this family are outlined in some detail. Basic concepts of such models can be developed in a variety of ways, and these are illustrated. The paper then outlines a number of other theoretical developments, and is particularly concerned with the disaggregation of such models, with the incorporation of time variables, and with the relation of spatial interaction, to more general, models. Uses of spatial interaction models are outlined briefly and the final section of the paper draws a number of conclusions and presents a summary.

Equilibrium Values and Dynamics of Attractiveness Terms in Production-Constrained Spatial-Interaction Models

A number of mechanisms are explored for modelling equilibrium values of attractiveness terms in production-constrained spatial-interaction models. They include revenue and facility-size balancing, a differential-equation representation of profit maximisation, and mathematical-programming formulations. The different methods turn out to be closely related but offer different and complementary insights. Some dynamic properties of such equilibrium points are explored, including the identification of circumstances which generate discrete changes for smooth changes in parameters. A number of possible algorithms for calculating the points are described.

Catastrophe Theory and Bifurcation-Applications to Urban and Regional Systems.

Alan Wilson surveys the range of applications currently devised that have been developed from new advances in mathematics enabling the development of models where sudden changes in equilibrium can be accounted for.

Optimization in locational and transport analysis

In a review of urban and regional modelling the authors discuss aspects of the subject based on optimisation techniques. A range of applications of these techniques in the field of locational and transport analysis is covered. Chapters of the book detail mathematical programming methods, the use of random utility theory and programming approaches to spatial interaction and activity location. Regional account-based models are generated using entropy maximising methods and it is shown how the Lowry model can be presented as an input-output model. Current perspectives of dynamical systems theory are outlined. A range of applications of the methods covered is discussed including some systematic studies of design procedures in transport planning. (TRRL)

Calibration and testing of the SELNEC transport model

Wilson A. G., Hawkins A. F., Hill G. J. and Wagon D. J. (1969) Calibrating and testing of the SELNEC transport model, Reg. Studies 3, 337–350. This paper describes the mathematical model used in the South-East Lancashire-North-East Cheshire Transportation Study. The description concentrates on the innovations which have been introduced in this particular model, with special reference to the distribution and modal split submodels. The process of calibrating and testing the model is described and some preliminary results are presented. A number of conclusions are drawn, and some directions for further research are noted.

Catastrophe theory and urban modelling: an application to modal choice

Some of the elementary ideas underlying catastrophe theory are reviewed and it is shown how the cusp catastrophe can be used in the theory of binary choice. A specific application to modal choice is presented and a number of conjectures are made about the wider application of the method in urban modelling.

The Dynamics of Urban Spatial Structure: Some Exploratory Results Using Difference Equations and Bifurcation Theory

It is demonstrated that a simple difference equation model, which exhibits complex bifurcation behaviour, can be used to represent change in urban retailing and residential systems. These submodels are combined to form a rudimentary dynamic model of urban spatial structure. A sample of exploratory results are presented for a 169-zone hypothetical system.

Modelling the city: Performance, policy and planning

This paper describes the construction of a three-dimensional computer model of the City of Bath and its development into an urban information system. The hypermedia application used to structure the underlying database is described and and the use of the system to consider issues of planning and conservation discussed.

Ecological and urban systems models: some explorations of similarities in the context of complexity theory

There are similarities of form between urban system models and models of ecosystems. These are systematically explored and a general model formulation which embraces both kinds of model is presented. Some insights are gained by using ideas from ecosystem modelling in urban modelling. The biggest gains, however, are for ecosystem modelling. It is demonstrated that urban techniques can be used for incorporating spatial competition effects into such models in novel ways, and that the complex dynamics can then be effectively interpreted. Urban systems have contributed significantly to complexity theory in the past—because they are complicated enough to be interesting but simple enough to be solvable. These insights can now be transferred to complex (spatial) ecosystems. The possibility of joint eco-urban models is explored.

Spatial Structure, Spatial Interaction, and Their Integration: A Review of Alternative Models

Models of spatial structure, spatial interaction, and integrated location-interaction models are reviewed and the nature of their contribution to the geographers understanding of patterns and change is explored. The main discussion focuses first on spatial structure and then on spatial interaction. Integrated models are explored in relation to six categories employed by Zeeman, the first of these being concerned with pattern, the rest with increasingly complicated aspects of dynamics. The categories are: equilibrium, ‘fast’ dynamics, ‘slow’ dynamics, feedbacks, noise, and diffusion. The argument is illustrated by examples at each stage.