An Alternative Formulation for Spatial-Interaction Modeling

Bibliographic Data

ID4138914
AuthorsWaldo Tobler (0000-0002-0049-8502, University of California, Santa Barbara, corresponding author)
Year1983
Volume15
Issue5
Pages693-703
Publication date1983-05-01
Peer ReviewedYes
Open AccessYes
TypeARTICLE
VenueEnvironment and Planning A Economy and Space (JOURNAL)
Journal identifiersISSN: 0308-518X • E-ISSN: 1472-3409
PublisherSAGE Publications Inc (PUBLISHER)
DOI10.1068/a150693
OpenAlexW2089512773
LanguageEN
Citations received13
References cited14

Elementary geometric assumptions are used to derive a spatial-interaction model in which places are related to each other through a set of simultaneous linear equations. The system has simple properties with respect to aggregation and turnover, yet incorporates spatial competition, adjacency, and effects of geographic shadowing. The objective function satisfied by the model reduces congestion and minimizes the per capita work; solves a quadratic transportation-problem and fulfils in-sum and out-sum constraints. The associated Lagrangians can be interpreted as pushes and pulls, or as shadow prices. A spatially continuous version of the model consists of coupled elliptical partial differential equations with Neumann boundary conditions, solvable by numerical methods. With migration data from the United States of America the model yields an amazingly good fit, better than existing models and with fewer free parameters. Inversion of the model yields an estimate of distances between regions. In-movement rates are predicted from out-movement rates in the model

Adjacency list · Algorithm · Geometry · Mathematical analysis · Mathematical optimization · Quadratic equation · Computer Science · Mathematics · Regional Economics and Spatial Analysis · Transportation Planning and Optimization · Urban Transport and Accessibility · Applied Mathematics

Tools

Open DOISci-Hub