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    The study of cities is one of the grand challenges of twenty-first-century science, and mathematical modelling—in this case, urban modelling—provides a crucial contribution to scholarly and practical projects fully to comprehend their workings, evolution, and associated planning problems. There have been significant developments in urban modelling over the last fifty years or so (though foundational work dates back to the nineteenth century and beyond), and it remains a highly active and flourishing field of research and study.

    Urban modelling draws on population demography and economics. It seeks to represent the activities and structures associated with employment, residential location, and housing, the use of services such as retail, education, or health and associated transport and telecommunications interactions. The history of urban modelling can be seen as the development of submodels which, in more ambitious projects, are then combined into comprehensive models. These models can then be deployed as ‘What if?’ forecasting tools to test plans for future urban development. The retail model, for example, is extensively applied commercially.

    In five volumes, this new Routledge collection—edited by the scholar whose work in urban and regional modelling established the research agenda for the field from the 1970s onwards—answers the need for an authoritative reference work to map the vast body of published literature and to make sense of the continuing explosion in research output. Much of scholarly literature generated by this multidisciplinary enterprise remains inaccessible or is highly specialized and compartmentalized, so that it is hard for many of those who are interested to obtain an informed and comprehensive overview. Bringing together the very best canonical and cutting-edge contributions, this collection offers an invaluable, one-stop resource.

    Volume I captures the early history of modelling up to the early 1960s. Volume II demonstrates the development of the comprehensive model, building on Lowry’s 1964 work and the foundations of transport modelling, enhanced by the introduction of entropy-maximizing methods in 1967. Volume III covers the 1970s and 1980s, which in part demonstrated the power of mathematical programming and also the introduction of effective dynamic analysis. The final volumes collect the best scholarship from the 1990s to the present day, focusing particularly on applications of modelling and the areas where the dynamic urban model still remains incomplete.

    Urban Modelling is fully indexed with a comprehensive introduction, newly written by the learned editor, which places the gathered materials in their historical and intellectual context. The collection is certain to be recognized as an indispensable reference work.

    draft cONTENTS

    Volume I: The foundations

    Part 1: Populations: Demography, Ecology, Epidemiology, and Warfare

    1. T. R. Malthus, An Essay on the Principle of Population (J. Johnson, 1798).

    2. P. F. Verhulst, ‘Notice sur la loi que la population poursuit dans son accroissement’, Correspondance mathématique et physique, 1838, 10, 113–21.

    3. F. W. Lanchester, Aircraft in Warfare: The Dawn of the Fourth Arm (Constable, 1916), pp. 39–53.

    4. A. J. Lotka, Elements of Physical Biology (Williams and Wilkins, 1924).

    5. W. O. Kermak and A. G. McKendrick, ‘A Contribution to the Mathematical Theory of Epidemics’, Proceedings, Royal Society of London, A, 1927, 115, 700–21.

    6. V. Volterra, ‘Population Growth, Equilibria and Extinction Under Specified Breeding Conditions: A Development and Extension of the Theory of the Logistic Curve’, Human Biology, 1938, 10.

    7. L. F. Richardson, ‘Generalized Foreign Politics’ [1939], from L. F. Richardson, Arms and Insecurity (Boxwood Press, 1960), pp. 12–36.

    8. P. H. Leslie, ‘On the Use of Matrices in Certain Population Mathematics’, Biometrika, 1945, 23, 183–212.

    Part 2: Economics

    9. J. H. von Thunen, Der isolierte staat in beziehung auf landwirtschaft und nationalokonomie (Gustav Fisher, 1826), trans. C. M. Wartenburg, The Isolated State (Oxford University Press, 1966).

    10. A. Weber, Uber den standort der industrien (Tubingen, 1909), trans. C. J. Friedrich, Theory of the Location of Industries, University of Chicago Press, Chicago. (10, 138)

    11. R. M. Haig, ‘Towards an Understanding of the Metropolis’, Quarterly Journal of Economics, 1926, 40, 197–208.

    12. H. Hotelling, ‘Stability in Competition’, Economic Journal, 1929, 39, 41–57.

    13. E. M. Hoover, ‘Some Programmed Models of Industry Location’, Land Economics, 1967, 43, 303–11.

    14. W. Leontief, The Structure of the American Economy, 1919–1939 (Oxford University Press, 1951).

    15. P. A. Samuelson, ‘Thunen at 200’, Journal of Economic Literature, 1983, 21, 1468–88.

    Part 3: Spatial Interaction

    16. E. G. Ravenstein, ‘The Laws of Migration’, Journal of the Royal Statistical Society, 1885, 48, 167–227.

    17. W. J. Reilly, The Law of Retail Gravitation (G. P. Putman and Sons, 1931).

    18. J. H. S. Bossard, ‘Residential Propinquity as a Factor in Marriage Selection’, American Journal of Sociology, 1932, 38, 219–44.

    19. S. A. Stouffer, ‘Intervening Opportunities: A Theory Relating Mobility and Distance’, American Sociological Review, 1940, 5, 845–67.

    20. J. Q. Stewart, ‘A Measure of the Influence of Population at a Distance’, Sociometry, 1942, 5, 63–71.

    21. G. K. Zipf, ‘The P1P2/D Hypothesis on the Inter-City Movement of Persons’, American Sociological Review, 1946, 11, 677–86.

    22. J. G. Wardrop, ‘Some Theoretical Aspects of Road Traffic Research’, Proceedings, Institution of Civil Engineers, Part II, 1952, 1, 325–78, 344–8.

    23. R. B. Mitchell and C. Rapkin, Urban Traffic: A Function of Land Use (Columbia University Press, 1954).

    Part 4: Urban Morphology and Dynamics

    24. E. W. Burgess, ‘The Determinants of Gradients in the Growth of a City’, Publications, American Sociological Society, 1927, 21, 178–84.

    25. W. Christaller, Die centralen Orte in Suddeutschland (Gustav Fischer, 1933), trans. C. W. Baskin, Central Places in Southern Germany (Prentice Hall, 1933).

    26. H. Hoyt, ‘The Structure and Growth of Residential Neighbourhoods in American Cities’ (Federal Housing Administration, Washington, D.C., 1939).

    27. A. Losch, Die raumliche ordnung der wirtschaft (Gustav Fischer, 1940), trans. W. H. Woglam and W. F. Stolper, The Economics of Location, Yale University Press, 1954).

    28. E. Ullman, ‘A Theory of Location for Cities’, American Journal of Sociology, 1940–1, 46, 853–64.

    29. C. D. Harris and E. L. Ullman, ‘The Nature of Cities’, Annals, American Academy of Political and Social Sciences, 1945, 242, 7–17.

    Volume II: Towards large-scale models

    Part 5: Large-Scale Transport and Land-Use Models

    30. J. D. Carroll, ‘Spatial Interaction and the Urban-Metropolitan Regional Description’, Papers, Regional Science Association, 1955, 1, 1–14.

    31. A. M. Voorhees, ‘A General Theory of Traffic Movement’, Proceedings, Institute of Traffic Engineers, 1955, 46–56.

    32. B. Harris, ‘Some Problems in the Theory of Intra-Urban Location’, Operations Research, 1961, 9, 695–721.

    33. I. S. Lowry, ‘A Model of Metropolis, RM-4035-RC’ (The Rand Corporation, 1964).

    34. K. J. Schlager, ‘A Land Use Plan Design Model’, Journal of the American Institute of Planners, 1965, 31, 103–11.

    35. A. G. Wilson, A. F. Hawkins, G. J. Hill, and D. J. Wagon, ‘Calibrating and Testing the SELNEC Transport Model’, Regional Studies, 1969, 2, 337–50.

    Part 6: Spatial Interaction-1: Retail

    36. G. A. P. Carrothers, ‘An Historical Review of the Gravity and Potential Concepts of Human Interaction’, Journal of the American Institute of Planners, 1956, 22, 94–102

    37. W. G. Hansen, ‘How Accessibility Shapes Land Use’, Journal of the American Institute of Planners, 1959, 25, 73–6.

    38. B. Harris, ‘A Model of Locational Equilibrium for the Retail Trade’ (Penn-Jersey Transportation Study, Philadelphia, 1964).

    39. D. L. Huff, ‘Defining and Estimating a Trading Area’, Journal of Marketing, 1964, 28, 34–8.

    40. T. R. Lakshmanan and W. G. Hansen, ‘A Retail Market Potential Model’, Journal of the American Institute of Planners, 1965, 31, 134–43.

    Part 7: Spatial Interaction-2: Transport

    41. T. J. Fratar, ‘Vehicular Trip Distribution by Successive Approximation’, Traffic Quarterly, 1954, 8, 53–65.

    42. A. G. Wilson, ‘A Statistical Theory of Spatial Distribution Models’, Transportation Research, 1967, 1, 253–69.

    43. H. J. Wootton and G. W. Pick, ‘A Model for Trips Generated by Households’, Journal of Transport Economics and Policy, 1967, 1, 137–53.

    Part 8: Spatial Interaction-3: Residential Location

    44. W. Alonso, ‘A Theory of the Urban Land Market’, Papers, Regional Science Association, 1960, 6, 149–57.

    45. D. J. Herbert and B. H. Stevens, ‘A Model for the Distribution of Residential Activity in an Urban Area’, Journal of Regional Science, 1960, 2, 21–36.

    Part 9: Economics

    46. M. Beckmann, C. B. McGuire, and C. B. Winsten, Studies in the Economics of Transportation (Yale University Press, 1956), pp. 46–79.

    47. W. Isard, Location and the Space-Economy (MIT Press, 1956), pp. 200–6.

    48. W. Leontief and A. Strout, ‘Multi-Regional Input-Output Analysis’, in T. Barna (ed.), Structural Interdependence and Economic Development (Macmillan, 1963), pp. 119–50.

    49. R. Artle, The Structure of the Stockholm Economy (Cornell University Press, 1965), pp. xvii–xlii.

    50. G. S. Becker, ‘A Theory of the Allocation of Time’, Economic Journal, 1965, 75, 488–517.

    51. R. E. Quandt and W. J. Baumol, ‘The Demand for Abstract Modes’, Journal of Regional Science, 1966, 9, 129–62.

    Part 10: Micro-Simulation, Network Analysis, Urban Dynamics

    52. G. H. Orcutt, ‘A New Type of Socio-Economic System’, Review of Economic Statistics, 1957, 58, 773–97.

    53. J. D. Nysten and M. F. Dacey, ‘A Graph Theory Interpretation of Nodal Regions’, Papers, Regional Science Association, 1961, 6, 29–42.

    54. J. W. Forrester, Urban Dynamics (MIT Press, 1969).

    Volume III: Integration and innovation: the 1970s

    Part 11: Post-Lowry Comprehensive Models

    55. W. Goldner, ‘The Lowry Model Heritage’, Journal of the American Institute of Planners, 1971, 37, 100–10.

    56. D. B. Lee, ‘Requiem for Large-Scale Models’, Journal of the American Institute of Planners, 1973, 39, 163–78.

    57. R. L. Mackett, ‘A Dynamic Activity Allocation Transportation Model’, in P. Bonsall, Q. Dalvi, and P. J. Hills (eds.), Urban Transportation Planning (Abacus Press, 1977), pp. 95–109.

    Part 12: Spatial Interaction Theory-1: Elaborating and Integrating the Transport Model

    58. M. Batty and S. Mackie, ‘The Calibration of Gravity, Entropy and Related Models of Spatial Interaction’, Environment and Planning, 1972, 4, 205–33.

    59. S. P. Evans, ‘Derivation and Analysis of Some Models for Combining Trip Distribution and Assignment’, Transportation Research, B, 1976, 10, 105–22.

    60. M. Florian and S. Nguyen, ‘A Combined Trip Distribution Modal Split and Assignment Model’, Transportation Research, 1978, 12, 241–6.

    Part 13: Spatial Interaction Theory-2: Mathematical Programming and Consumers’ Surplus

    61. S. P. Evans, ‘A Relationship Between the Gravity Model for Trip Distribution and the Transportation Model of Linear Programming’, Transportation Research, 1973, 7, 39–61.

    62. M. L. Senior and A. G. Wilson, ‘Explorations and Syntheses of Linear Programming and Spatial Interaction Models of Residential Location’, Geographical Analysis, 1974, 6, 209–38.

    63. S. Erlander, ‘Accessibility, Entropy and the Distribution and Assignment of Traffic’, Transportation Research, 1977, 11, 149–53.

    64. H. C. W. L. Williams, ‘On the Formation of Travel Demand Models and Economic Evaluation Measures of User Benefit’, Environment and Planning, A, 1977, 9, 285–344.

    65. D. E. Boyce, ‘Equilibrium Solution to Combined Urban Residential Location, Modal Choice and Trip Assignment Models’, in W. Buhr and P. Freidrich (eds.), Congestion Among Small Regions (Nomos, 1978).

    Part 14: Spatial Interaction Theory-3: A Continuous Space Model

    66. S. Angel and G. M. Hyman, ‘Urban Spatial Interaction’, Environment and Planning, 1972, 4, 99–118.

    Part 15: Spatial Interaction Theory-4: The Rise of the Logit Model

    67. M. E. Ben-Akiva, ‘Structure of Passenger Travel Demand Models’, Transportation Research Record, 1974, 526, 26–42.

    Part 16: Dynamics

    68. T. Poston and A. G. Wilson, ‘Facility Size Versus Distance Travelled: Urban Services and the Fold Catastrophe’, Environment and Planning, A, 1977, 9, 681–6.

    69. B. Harris and A. G. Wilson, ‘Equilibrium Values and Dynamics of Attractiveness Terms in Production-Constrained Spatial-Interaction Models’, Environment and Planning, A, 1978, 10, 371–88.

    70. D. E. Boyce and F. Southworth, ‘Quasi-Dynamic Urban Location Models with Endogenously Determined Travel Costs’, Environment and Planning, A, 1979, 11, 575–84.

    Part 17: Account-Based Models

    71. G. J. D. Hewings, ‘Regional Input-Output Models in the UK: Some Problems and Prospects for the Use of Non-Survey Techniques’, Regional Studies, 1971, 5, 11–22.

    72. T. A. Broadbent, ‘Activity Analysis of Spatial-Allocation Models’, EPA, 1973, 5, 6, 673–91.

    73. A. Rogers, ‘The Mathematics of Multiregional Demographic Growth’, Environment and Planning, 1973, 5, 3–29.

    74. A. G. Wilson and P. H. Rees, ‘Population Statistics and Spatial Demographic Accounts’, The Statistician, 1974, 23, 229–57.

    75. S. M. Macgill, ‘Simple Hybrid Input-Output Models: A Graphical Approach’, EPA, 1977, 9, 9, 1033–42.

    Part 18: Microsimulation

    76. A. G. Wilson and C. M. Pownall, ‘A New Representation of the Urban System for Modelling and for the Study of Micro-Level Interdependence’, Area, 1976, 8, 256–64.

    Volume IV: Integration and dynamics—the 1980s and 1990s

    Part 19: The Comprehensive Urban Model

    77. A. Anas, ‘Discrete Choice Theory and the General Equilibrium of Employment, Housing and Travel Networks in a Lowry-Type Model of the Urban Economy’, Environment and Planning, A, 1984, 16, 11, 1489–502.

    78. M. Wegener, ‘Integrated Forecasting Models of Urban and Regional Systems’, London Papers in Regional Science, 1986, 15, 9–24.

    79. M. Echenique, A. D. J. Flowerdew, J. D. Hunt, T. R. Mayo, I. J. Skidmore, and D. C. Simmonds, ‘The MEPLAN Models of Bilbao, Leeds and Dortmund’, Transport Reviews, 1990, 10, 309–22.

    Part 20: Spatial Interaction Theory

    80. M. Clarke, P. Keys, and H. C. W. L. Williams, ‘Micro-Analysis and Simulation of Socio-Economic Systems: Progress and Prospects’, in N. Wrigley and R. J. Bennett (eds.), Quantitative Geography: A British View (Routledge and Kegan Paul, 1981).

    81. G. Leonardi, ‘A Unifying Framework for Public Facility Location Problems – Part 1: A Critical Overview and Some Unsolved Problems’, Environment and Planning, A, 1981, 13, 1001–28.

    82. G. Leonardi, A Unifying Framework for Public Facility Location Problems – Part 2: Some New Models and Extensions’, Environment and Planning, A, 1981, 13, 1085–108.

    83. A. S. Fotheringham, ‘A New Set of Spatial Interaction Models: The Theory of Competing Destinations’, Environment and Planning, A, 1983, 15, 1121–32.

    84. D. E. Boyce, ‘Urban Transportation Network-Equilibrium and Design Models: Recent Achievements and Future Prospects’, Environment and Planning, 1984, 16, 1446–74.

    85. R. Kitamura, ‘An Evaluation of Activity-Based Travel Analysis’, Transportation, 1988, 15, 9–34.

    86. S. Openshaw, ‘Building an Automated Modelling System to Explore a Universe of Spatial Interaction Models’, Geographical Analysis, 1988, 20, 31–6.

    87. G. Leonardi, ‘Conceptual Foundations of Spatial Choice Models’, Environment and Planning, A, 1992, 24, 1393–408.

    88. D. A. Hensher, ‘Stated Preference Analysis of Travel Choices: The State of Practice’, Transportation, 1994, 21, 107–33.

    89. M. Patriksson, The Traffic Assignment Problem, Models and Methods (VSP, 1994).

    Part 21: Dynamics

    90. P. M. Allen and M. Sanglier, ‘Urban Evolution, Self-Organisation and Decision Making’, Environment and Planning, 1981, 13, 167–83.

    91. F. J. A. Rijk and A. C. F. Vorst, ‘On the Uniqueness and Existence of Equilibrium Points in an Urban Retail Model’, Environment and Planning, A, 1983, 15, 475–82.

    92. A. G. Wilson, ‘Transport and the Evolution of Urban Spatial Structure’, in Atti delle Giornate di Lavoro (Guida Editori, 1983), pp. 17–27.

    93. A. G. Wilson and M. J. Oulton, ‘The Corner Shop to Supermarket Transition in Retailing: The Beginnings of Empirical Evidence’, Environment and Planning, A, 1983, 15, 265–74.

    94. N. Oppenheim, ‘Dynamic Forecasting of Urban Shopping Travel’, Transportation Research B, 1986, 20, 391–402.

    95. P. Nijkamp and A. Reggiani, ‘Analysis of Dynamic Spatial Interaction Models by Means of Optimal Control’, Geographical Analysis, 1988, 20, 18–30.

    96. R. G. V. Baker, ‘An Assessment of the Space-Time Differential Model for Aggregate Trip Behaviour to Planned Suburban Shopping Centres’, Geographical Analysis, 1994, 26, 341–62.

    Part 22: Account-Based Models

    97. P. W. J. Batey and M. Madden, ‘Demographic-Economic Forecasting Within an Activity-Commodity Framework: Some Theoretical Considerations and Empirical Results’, Environment and Planning, A, 1981, 13, 1067–83.

    98. G. J. D. Hewings, ‘Regional and Interregional Interdependencies: Alternative Accounting Systems’, Environment and Planning, A, 1982, 14, 1587–600.

    99. T. J. Kim, D. E. Boyce, and G. J. D. Hewings, ‘Combined Input-Output and Commodity Flow Models for Inter-Regional Development Planning’, Geographical Analysis, 1983, 15, 330–42.

    100. S. M. Macgill, ‘Structural Analysis of Social Data: A Guide to Ho’s Galois Lattice Approach and a Partial Respecification of Q-Analysis’, EPA, 1985, 17, 8, 1089–109.

    Volume V: New models and challenges

    Part 23: Comprehensive Models

    101. M. Batty, ‘A Chronicle of Scientific Planning: The Anglo-American Modelling Experience’, Journal of the American Institute of Planners, 1994, 60, 7–16.

    102. B. Harris, ‘The Real Issues Concerning Lee’s "Requiem"’, Journal of the American Institute of Planners, 1994, 60, 31–4.

    103. M. Wegener, ‘Overview of Land-Use Transport Models’, in D. A. Hensher, K. J. Button, K. E. Haynes, and P. R. Stopher (eds.), Handbook of Transport Geography and Spatial Systems (2004), pp. 127–46.

    Part 24: Spatial Interaction Theory

    104. T. Garling, M. Kwan, and R. Golledge, ‘Computational Process Modelling of Household Activity Scheduling’, Transportation Research, 1994, 28B, 355–64.

    105. J. Pooler, ‘An Extended Family of Spatial Interaction Models’, Progress in Human Geography, 1994, 18, 17–39.

    Part 25: Dynamics

    106. A. G. Wilson, ‘Ecological and Urban Systems Models: Some Explorations of Similarities in the Context of Complexity Theory’, Environment and Planning, A, 2006, 38, 633–46.

    107. F. Medda, P. Nijkamp, and P. Reitveld, ‘A Morphogenetic Perspective on Spatial Complexity: Transport Costs and Urban Shapes’, in A. Reggiani and P. Nijkamp (eds.), Complexity and Spatial Networks (Springer, 2009), pp. 51–60.

    Part 26: New Models

    108. G. Haag, ‘Master Equations’, in C. S. Bertuglia, G. Leonardi, and A. G. Wilson (eds.), Urban Dynamics: Designing an Integrated Model (Routledge, 1990), pp. 69–83.

    109. N. Gilbert, ‘Using Computer Simulation to Study Social Phenomena’ (1995).

    110. W. D. Macmillan, ‘SimCity Meets CGE: Serious Toys for City Modelling’ (1996).

    111. M. M. Fischer, ‘Computational Neural Networks: An Attractive Class of Mathematical Models for Transportation Research, in A. Reggiani and P. Nijkamp (eds.), Complexity and Spatial Networks (Springer, 2009), pp. 2–20.

    112. S. Lombardo, M. Petri, and D. Zotta, ‘Intelligent GIS and Retail Location Dynamics: A Multi-Agent System Integrated with ArcGis: Computational Science and its Applications—Iccsa 2004’, Lecture Notes in Computer Science, 2004, 3044, 1046–56.

    113. N. Gilbert, J. C. Hawksworth, and P. A. Swinney, ‘An Agent-Based Model of the English Housing Market’, Association for the Advancement of Artificial Intelligence, Spring Symposia, 2009, 30–5.

    114. J. Dearden and A. G. Wilson, ‘A Framework for Exploring Urban Retail Discontinuities’, Geographical Analysis, 2011.

    Part 27: Applications-1: Practice

    115. M. Clarke and A. G. Wilson, ‘A Model-Based Approach to Planning in the National Health Service’, Environment and Planning, B, 1985, 12, 287–302.

    116. C. Duley and P. H. Rees, ‘Incorporating Migration into Simulation Models’, in J. C. H. Stillwell and P. Congdon, Modelling Internal Migration (Belhaven Press, 1991).

    117. M. Birkin, G. P. Clarke, M. Clarke, and A. G. Wilson, ‘Intelligent GIS: Location Decisions and Strategic Planning’, Geoinformation International (Cambridge, 1996), pp. 81–111.

    118. A. Rogers, ‘Demographic Modelling of Migration and Population: A Multiregional Perspective’, Geographical Analysis, 2008, 40, 276–96.

    119. A. D. Singleton, A. G. Wilson, and O. O’Brien, ‘Geodemographics and Spatial Interaction: An Integrated Model for Higher Education’, Journal of Geographical Systems, 2011.

    Part 28: Applications-2: Theory

    120. M. Birkin and A. G. Wilson, ‘Industrial Location Models II: Weber, Palander, Hotelling and Extensions in a New Framework’, Environment and Planning, A, 1986, 18, 293–306.

    121. M. Birkin and A. G. Wilson, ‘Dynamic Models of Agricultural Location in A Spatial Interaction Context’, Geographical Analysis, 1987, 19, 1.

    122. G. P. Clarke and A. G. Wilson, ‘Performance Indicators and Model-Based Planning II: Model-Based Approaches’, Sistemi Urbani, 1987, 9, 138–65.

    123. T. E. Rihll and A. G. Wilson, ‘Spatial Interaction and Structural Models in Historical Analysis: Some Possibilities and an Example’, Histoire et Mesure II-1, 1987, 5–32.