The Modelling of Urban Population Density: A Survey

This paper presents a state-of-the-art review of the principal models of urban population density, including the seven members of the quadratic gamma family and Amson's equilibrium models. A historical introduction is followed by a review of basic assumptions, and then each model is analysed individually, with separate discussions of principal theoretical findings and experimental results.

[1]  J. Amson.  Equilibrium Models of Cities: 2. Single-Species Cities , 1973 .

[2]  C. Kilmister.  Population in cities , 1976, The Mathematical Gazette.

[3]  J. Kau,et al.  A random coefficient model to estimate a stochastic density gradient , 1977 .

[4]  J. Q. Stewart.  Empirical Mathematical Rules concerning the Distribution and Equilibrium of Population , 1947 .

[5]  Alan Wilson,et al.  A statistical theory of spatial distribution models , 1967 .

[6]  C. Clark.  Urban Population Densities , 1951 .

[7]  Bruce E. Newling.  The Spatial Variation of Urban Population Densities , 1969 .

[8]  J. Amson.  The Dependence of Population Distribution on Location Costs , 1972 .

[9]  Jay Wright Forrester,et al.  Urban Dynamics , 1969 .

[10]  Marcial Echenique,et al.  Urban systems : towards an explorative model , 1969 .

[11]  Ye. S. Aynvarg.  Zones of Influence of Middle-Size Cities, Their Boundaries and Passenger Flows , 1969 .

[12]  J. Amson,et al.  Equilibrium Models of Cities: 1. An Axiomatic Theory , 1972 .

[13]  Brian J. L. Berry,et al.  Urban Population Densities: Structure and Change , 1963 .

[14]  F. Auerbach.  Das Gesetz der Bevölkerungskonzentration. , 1913 .

[15]  Shlomo Angel,et al.  Urban Spatial Interaction , 1972 .

[16]  R. Smeed.  THE EFFECT OF SOME KINDS OF ROUTEING SYSTEMS ON THE AMOUNT OF TRAFFIC IN THE CENTRAL AREAS OF TOWNS: (WITH PARTICULAR REFERENCE TO JOURNEYS INTO AND OUT OF THE CENTRAL AREAS) , 1962 .

[17]  L. J. Comrie,et al.  Mathematical Tables and Other Aids to Computation. , 1946 .

[18]  J. Amson.  A Note on Civic State Equations , 1977 .

[19]  Elliott W. Montroll,et al.  Introduction to Quantitative Aspects of Social Phenomena , 1975 .

[20]  D. J. White,et al.  The Use of the Concept of Entropy in System Modelling , 1970 .

[21]  F. Snickars,et al.  Derivation of the Negative Exponential Model by an Entropy Maximising Method , 1970 .