Dynamic Trip Modelling The GeoJournal Library Volume 84 Managing Editor: Max Barlow, Toronto, Canada Founding Series Editor: Wolf Tietze, Helmstedt, Germany Editorial Board: Paul Claval, France Yehuda Gradus, Israel Sam Ock Park, South Korea Herman van der Wusten, The Netherlands The titles published in this series are listed at the end of this volume. Dynamic Trip Modelling From Shopping Centres to the Internet by ROBERT G.V. BAKER School of Human and Environmental Studies, University of New England, Australia A C.I.P.Catalogue record for this book is available from the Library of Congress ISBN-10 1-4020-4345-7 (HB) ISBN-13 978-1-4020-4345-1 (HB) ISBN-10 1-4020-4346-5 (e-book) ISBN-13 978-1-4020-4346-8 (e-book) Published by Springer, P.O. 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To Sue, Kristen and Cameron Contents Preface ix Illustrations xi Chapter 1: Introduction 1 1.1 Shopping Change 1 1.2 Definitions of Retail Forms Underpinning the Model 6 1.3 The Time-space Convergence 16 1.4 A Way Forward 18 Chapter 2: An Introduction to Retail and Consumer Modelling 21 2.1 Definition 21 2.2 A Justification for Modelling 22 2.3 The Art of Modelling 23 2.4 Model-building and its Weaknesses 29 2.5 Examples of Retail and Consumer Modelling 31 2.6 A Vision for Dynamic Trip Modelling 75 Chapter 3: Dynamic Trip Modelling 77 3.1 Background to the RASTT Model 77 3.2 Space and Time-discounting Shopping Trips 79 3.3 Characteristics of Space-discounting Behaviour 84 3.4 The Time-discounting Model 97 3.5 The Fourier Transform and Aggregate Periodic Trips 116 3.6 Estimating Shopping Centre Hours 126 3.7 Two Dimensional Space-time Modelling 130 3.8 Estimating Market Penetration with an Extension of Shopping Hours 134 3.9 Stochastic Space-time Trips 138 3.10 Space-time Modelling Shopping Trips: A Summary 151 3.11 Dynamic Shopping Trip Modelling 156 viii Contents Chapter 4: Empirical Testing of the RASTT Model in Time and Space 157 4.1 Introduction 157 4.2 Background to the Research Methodology 158 4.3 The Empirical Method 161 4.4 The Sydney Project: Long Term Time Change of Shopping Trips (1980-1998) 167 4.5 Changes in Time-space Trip Behaviour in the Sydney Project 200 4.6 Application of the RASTT Model to Unplanned Shopping Centres: Armidale in Regional New South Wales, 1995 237 4.7 Application of the RASTT Model to Planned Shopping Centres: Auckland, New Zealand, 2000 247 4.8 Is there a ‘Global’ RASTT Model? 256 Chapter 5: Dynamic Modelling of the Internet 265 5.1 Introduction 265 5.2 The RASTT Model and Internet Transactions 268 5.3 Deriving the RASTT Model for Internet Transactions 273 5.4 Empirical Evidence 277 5.5 Applications to Shopping Transactions 289 5.6 Summary 290 Chapter 6: The Socio-Economic and Planning Consequences of Changes to Shopping Trips 293 6.1 The Problem of Shopping Times and Shopping Places 293 6.2 The Role of Parking and Walking 294 6.3 The Vacant Shop Problem in Australia 298 6.4 The Role of the Large Supermarket or Superstore 304 6.5 The Role of Planned Regional Shopping Centres 317 6.6 Policy Implications for Modelling Shopping Trip Change 321 6.7 Retail Planning as a ‘Wicked Problem’ 326 Chapter 7: Conclusions 327 B ib liography 339 Preface The thesis of this book is that there are one set of equations that can define any trip between an origin and destination. The idea originally came from work that I did when applying the hydrodynamic analogy to study congested traffic flows in 1981. However, I was disappointed to find out that much of the mathematical work had already been done decades earlier. When I looked for a new application, I realised that shopping centre demand could be like a longitudinal wave, governed by centre opening and closing times. Further, a solution to the differential equation was the gravity model and this suggested that time was somehow part of distance decay. This was published in 1985 and represented a different approach to spatial interaction modelling. The next step was to translate the abstract theory into something that could be tested empirically. To this end, I am grateful to my Ph.D supervisor, Professor Barry Garner who taught me that it is not sufficient just to have a theoretical model. This book is an outcome of this on-going quest to look at how the evolution of the model performs against real world data. This is a far more difficult process than numerical simulations, but the results have been more valuable to policy formulation, and closer to what I think is spatial science. The testing and application of the model required the compilation of shopping centre surveys and an Internet data set. I would like to thank the management of the shopping centres for allowing me to survey consumers. I have had to observe, in some cases, a lag period to use some of the data as part of commercial confidentiality agreements. I am indebted to David Marshall who supervised the collection and collation of the shopping centre data. The Internet data was kindly made available by Dr Les Cottrell and Dr Gerod Williams from their network at the Stanford Linear Accelerator Centre. I also appreciate the work on this project by Troy MacKay, Brett Carson and Raj Rajaratnam and their discussions over many cups of coffee. My thanks also extends to Mike Roach who undertook a huge cartographic task and Sue Baker for a difficult proofing job. I am also indebted to the Australian Research Council for grants to complete the shopping centre surveys and Internet analysis. Finally, thanks to my family, Sue, Kristen and Cameron, my brother Ross, my parents, Ellen and Douglas, and Alpha O without whose support during the good times and bad, this book would not have happened. Illustrations List of Figures Figure 1.1 Meadowhall Regional Planned Shopping Centre, Sheffield, 1999 Figure 1.2 The Macellum on the Dupondius coin (AD 65) in the reign of the Emperor Nero Figure 1.3 Market Share of Pharmaceutical Products in Australia, 1997 Figure 1.4 The Generation of an Internet Tree showing the Aspatial Connectivity from 100,000 Internet Routers and the Hierarchical Structures that develop from a few Highly Connected Nodes Figure 1.5 The Time-space Convergence Showing the Cone of Time and Space Interaction Relative to Changes in Technology Figure 2.1 A Flow Diagram Showing the Evolution of the Gravity Model in the Context of Consumer Behaviour Figure 2.2 A Process of Building Relevant, Testable and Reproducible Models Figure 2.3 The Regression of Mean Trip Frequency and the β Coefficient of the Gravity Model for Shopping Trips to the Sydney Shopping Centres 1980/82 and 1988/89 Figure 2.4 An Extension of Shopping Hours reduces the Slope of the Gravity Model (β ) where there is an Increased Propensity for Households to Travel to Planned Shopping Centre O rather than Shop Locally. Inset Photographs: (right), Vacant Shops (signed) in the Abbotsford Shopping Centre from Competition from MarketPlace Leichhardt (left), Sydney, New South Wales, May, 1999 Figure 2.5 Loschian Modifications in Christaller’s Hexagonal Trade Areas and the Northwest Retail Hierarchy for Canberra, Australian Capital Territory Figure 2.6 The Location of 24-hour Coles Supermarkets in Sydney 1996 Figure 2.7 Consumer Equilibrium Analysis for Shopping Time and Visits to a Shopping Centre xii Illustrations Figure 2.8 Impact of Price Shifts (top) and Demand Curve Formation (bottom) Figure 2.9 The Trading Hour Consumption Curve for Shopping Centre Time- Visit Allocations Figure 2.10 Percentage Composition of Socio-economic Status of Late Night Shoppers (Armidale, NSW, November, 1995) Figure 2.11 Shopping Preferences for Extended Hours by Socio-economic Groups Figure 2.12 Analogous Engel Curves Relative to the Size of the Centre (a) Percentage of HDI Respondents in the Sample Plotted with HDI Trip Frequency and (b) a Model showing Normal and Inferior Engel Lines with Centre Scale Figure 2.13 The Utility of Shopping at a Hierarchy of Malls in Sydney with Trip Distance, 1988/89 Figure 2.14 The Relative Utility Distribution with (k D)/N for Sydney Project 1988/89 and 1996/98 Figure 2.15 The Regression of the Gravity Coefficient β and U2N2/MD2 for the Aggregate Sydney Project in 1988/89 and 1996/98 (excluding the regional Bankstown Square samples) Figure 2.16 Quadratic Distributions of the Gravity Coefficient (top) and Mean Trip Frequency (bottom) with Centre Size (Sydney Project 1980/82 and 1988/89). The Point of Inflections are at N = 147 and 145 Centre Destinations, respectively, for Small (negative slope) and Large (positive slope) Centre Behaviour Figure 2.17 The Relationship between Trip Frequency and the Percentage of Multi-purpose Shopping (Sydney Project 1988/89) Figure 2.18 The Relationship between the Gravity Coefficient and the Percentage of Multi-purpose Shopping Squared Divided by the Transfer Coefficient (Sydney Project 1988/89) Figure 2.19 The Distribution of MPS changing with Centre Size (Sydney Project 1988/89).