Papers of the Regional Science Association

, Volume 53, Issue 1, pp 5–25 | Cite as

Linear urban models

  • Michael Batty
Twenty-Ninth North American Meetings of the Regional Science Association


A class of linear models is developed in which activities are derived from transformations of each other and exogenous activities. The models are illustrated using spatial distributions of population and employment. Reduced forms are derived and the influence of different transformations on spatial model solutions is explored in terms of the balance of exogenous and endogenous variables, and through analysis of eigenstructures. Ten model types including the traditional Lowry model and Coleman's model of social exchange, are applied to an eight zone representation of Melbourne and the analysis is used to show how model solutions can be spatially independent of their inputs.


Spatial Distribution Linear Model Model Solution Model Type Spatial Model 
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  1. Bailey, N. J. T. 1964.The elements of stochastic processes, with applications to the natural sciences. New York: John Wiley.Google Scholar
  2. Bartholomew, D. J. 1982.Stochastic models for social processes. Chichester, England: John Wiley.Google Scholar
  3. Batty, M. 1976.Urban modelling: algorithms, calibrations, predictions. Cambridge, England: Cambridge University Press.Google Scholar
  4. Batty, M. 1979. Invariant-distributional regularities and the Markov property in urban models: an extension of Schinnar's result.Environment and Planning A 11: 487–497.Google Scholar
  5. Batty, M. 1981. Symmetry and reversibility in social exchange.Journal of Mathematical Sociology 8: 1–41.Google Scholar
  6. Coleman, J. S. 1973.The mathematics of collective action. London: Heinemann Educational Books.Google Scholar
  7. Garin, R. A. 1966. A matrix formulation of the Lowry model for intra-metropolitan activity location.Journal of the American Institute of Planners 32: 361–364.Google Scholar
  8. Harris, B. 1966. Note on aspects of equilibrium in urban growth models. Philadelphia: Department of City and Regional Planning, University of Pennsylvania.Google Scholar
  9. Heal, G., Hughes, G. and Tarling, R. 1974.Linear algebra and linear economics. London: Macmillan.Google Scholar
  10. Lowry, I. S. 1964.A model of metropolis. Santa Monica, California: The Rand Corporation, RM-4035-RC.Google Scholar
  11. Massey, D. B. 1973. The basic-service categorisation in planning.Regional Studies 7: 1–15.Google Scholar
  12. Schinnar, A. P. 1978. Invariant distributional regularities of nonbasic spatial activity allocations: the Garin-Lowry model revisited.Environment and Planning A 10: 327–336.Google Scholar
  13. Wilson, A. G. 1974.Urban and regional models in geography and planning. London: John Wiley.Google Scholar
  14. Wilson, A. G., Coelho, J. D., MacGill, S. M. and Williams, H. C. W. L. 1981.Optimization in locational and transport analysis. Chichester, England: John Wiley.Google Scholar

Copyright information

© The Regional Science Association 1983

Authors and Affiliations

  • Michael Batty
    • 1
  1. 1.University of Wales Institute of Science and TechnologyCardiffWales

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