Dynamic Trip Modelling

The GeoJournal Library

Volume 84

Managing Editor:

Founding Series Editor:Wolf Tietze, Helmstedt, Germany

Editorial Board: Paul Claval, FranceYehuda Gradus, IsraelSam Ock Park, South KoreaHerman van der Wusten, The Netherlands

The titles published in this series are listed at the end of this volume.

Max Barlow, Toronto, Canada

Dynamic Trip ModellingFrom Shopping Centres to the Internet

by

ROBERT G.V. BAKERSchool 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. Box 17, 3300 AA Dordrecht, The Netherlands.

www.springer.com

Printed on acid-free paper

All Rights Reserved© 2006 SpringerNo part of this work may be reproduced, stored in a retrieval system, or transmitted in any formor by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise,without written permission from the Publisher, with the exception of any material suppliedspecifically for the purpose of being entered and executed on a computer system, for exclusiveuse by the purchaser of the work.

Printed in the Netherlands.

To Sue, Kristen and Cameron

Contents

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

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

Preface ix

Illustrations xi

1.2 Definitions of Retail Forms Underpinning the Model 6

1.4 A Way Forward 18 1.3 The Time-space Convergence 16

1.1 Shopping Change 1

2.1 Definition 21

2.3 The Art of Modelling 23

2.5 Examples of Retail and Consumer Modelling 31

Chapter 3: Dynamic Trip Modelling

2.2 A Justification for Modelling 22

2.6 A Vision for Dynamic Trip Modelling 75

Chapter 1: Introduction 1

Chapter 2: An Introduction to Retail and Consumer Modelling 21

77

2.4 Model-building and its Weaknesses 29

3.4 The Time-discounting Model

Chapter 4: Empirical Testing of the RASTT Model in Time and Space

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

247 4.8 Is there a ‘Global’ RASTT Model? 256 Chapter 5: Dynamic Modelling of the Internet 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 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

B ib liography

157

265

293

327

339

viii Contents

4.7 Application of the RASTT Model to Planned Shopping Centres: Auckland, New Zealand, 2000

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

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.

at the Stanford Linear Accelerator Centre. I also appreciate the work on this made available by Dr Les Cottrell and Dr Gerod Williams from their network

Illustrations List of Figures

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

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 ( ) where there is an Increased Propensity for Households to Travel to

Vacant Shops (signed) in the Abbotsford Shopping Centre from Competition

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

Figure 1.1 Meadowhall Regional Planned Shopping Centre, Sheffield, 1999

a few Highly Connected Nodes

Planned Shopping Centre O rather than Shop Locally. Inset Photographs: (right),

from MarketPlace Leichhardt (left), Sydney, New South Wales, May, 1999

β

Figure 2.9 The Trading Hour Consumption Curve for Shopping Centre Time-

Figure 2.10 Percentage Composition of Socio-economic Status of Late Night

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

Figure 2.13 The Utility of Shopping at a Hierarchy of Malls in Sydney with Trip Distance, 1988/89

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,

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). The Point of Inflection is at N = 167 Centre Destinations for Small (negative slope) and Large (positive slope) Centre Behaviour Figure 2.20 The Gravity Model as a Negative Exponential Distribution away

Illustrationsxii

Visit Allocations

Figure 2.8 Impact of Price Shifts (top) and Demand Curve Formation (bottom)

Shoppers (Armidale, NSW, November, 1995)

and (b) a Model showing Normal and Inferior Engel Lines with Centre Scale

Figure 2.14 The Relative Utility Distribution with (k D)/N for Sydney Project

respectively, for Small (negative slope) and Large (positive slope) Centre

1 2from a Shopping Centre for β > β

Figure 2.21 The Trade-off between Constant Logarithmic Supply of Destinations and Constant Negative Exponential Demand for a Shopping Centre C , if Consumers Minimise Trip Distance Figure 3.1 The Fourier Transform of exp-g2t for Space-discounting Consumers Figure 3.2 Changing Market Areas for Space-discounting Behaviour for Successive Time Periods Figure 3.3 Changing Trip Distributions over a Day for Space-discounting Shopping Figure 3.4 Changing Morning and Afternoon Distributions for Westfield Burwood and Ashfield Mall for pre-Christmas Space- and Time-discounting Trip

2f, 3f to 6f ) and Post Office Distance for Westfield Burwood (Sample: 15/12/88A), Sydney Data Set, 1988/89 Figure 3.6 The Fourier Frequency Assignment Ψ(f) with Shopping Time (t) Figure 3.7 Testing the Shopping Time Hypothesis in Figure 3.6 with Distance Zones 1 and 2 in the Westfield Burwood pre-Christmas Rush Sample (15/12/88A) with Box and Whisker Plots Figure 3.8 The Relationship between Mean Shopping Duration (p) and Destinations Visited m (1988/89) showing the Shift Right towards ‘Large Centre’ Behaviour

Figure 3.9 The Regression of Intra-centre Shopping Frequency (f = p/2T) and the Mean Shopping Duration p per Trading Week T ( f = m× k /2T) showing the Shift Right towards ‘Large Centre’ Behaviour

Figure 3.10 Comparison for the Theoretical m/2T and m/4T Values with the p/T Empirical Estimates from the Sydney 1988/89 Data Set Figure 3.11 Regression showing the Relationship between Two Forms of the Intra-centre Shopping Frequency (f = mk/2T)) and (f = Mk ) for the Sydney Project 1988/89 Figure 3.12 Regression showing the Relationship between Two Forms of the Intra-centre Shopping Frequency (f =mk/2T)) and (f = Mk ) for the Sydney Project 1996/98

and 100 Trading Hours (per week) for ‘Small Centre’ Behaviour

Illustrations xiii

Behaviour, respectively: Sydney Project 1988/89

Figure 3.13 Simulation of the Space-time Shopping Distributions for 49.5, 70

Figure 3.5 The Negative Exponential Self-reciprocity between Trip Frequency ( f,

and 100 Trading Hours (per week) for ‘Large Centre’ Behaviour Figure 3.15 The Aggregation of Population Demand Waves (Sf) of Different Frequencies

3Three Equally-sized Centres (n =3) over the Trading Week

Figure 3.17 (a) The Graph of a sinc Function and the Gaussian Wave Packet

Probability Density Function for T = 1.0 (dotted line) Figure 3.18 The Probability Density of the Weekly Grocery Trip as a Gaussian Wave Packet with the Shift Towards More Frequent Trips with Extended Shopping Hours Figure 3.19 The Higher Frequency Shift with the Extension of Shopping Hours in the Sydney Project from Regulated Hours in 1988/89 to Deregulated Hours in 1996/98

Leichhardt (8/12/88A) and Bankstown Square (23/3/89M) Figure 3.21 Bessel Functions of Order Zero and One Figure 3.22 The Relationship between the Gravity Coefficient and Mean Trip

Figure 3.23 The Relationship between Retail Floorspace and the Number of Retail Destinations: Y = -0.811+ 0.313X , R 2 = 0.92 Figure 3.24 The Aggregate Household Time ‘Doughnut’ for MarketPlace

hours per week

Figure 3.26 The Shopping Trip Pattern for Space-discounting Behaviour (α = 2) compared to Non-Space-discounting Behaviour ( = 1.3)

State to n Shopping Centres

Illustrationsxiv

Figure 3.16 The Demand Wave φ showing the Equal Likelihood of Visiting

(dotted line) and; (b) the Gaussian Wave Packet for T = 0.5, 1.0 and the

Figure 3.20 The Theoretical and Empirical Frequency Distributions for MarketPlace

Figure 3.25 A Venn Diagram showing Set Relationships among Selected RandomProcesses

Figure 3.28 The Poisson Distribution for n Shopping States

α

Leichhardt 8/12/88A through an Extension of Trading Hours from 49.5 to 60

Post Office Distance in the Sydney 1980/82, 1988/89 and 1996/98 Data Sets

Figure 3.27 State Transition Flow Chart for Trip-chaining from a Residential

Figure 3.14 Simulation of the Time-space Shopping Distributions for 49.5, 70

Figure 3.29 The Erlangian Distribution for N Stops over a Distance D Figure 4.1 The Location of the Planned Shopping Centres used in the Sydney

Projects Figure 4.3 An Example of the Segmentation of One Kilometre Concentric Aggregation Bands from MarketPlace Leichhardt, Sydney Project 1996/98, where the Respondents Pointed to which Band their Residence is Located Figure 4.4 Regression between Postcode Centroid Distance and Segment Nominated Distance (Aggregate Sydney Project 1996/98) Figure 4.5 Box and Whisker Plots for Trip Distance at Bankstown Square for Equivalent Morning (top) and Afternoon Samples (bottom): 1989, 1997 and 1998 Figure 4.6 Box and Whisker Plots for Trip Frequency at the Regional PSC Bankstown Square for Equivalent Morning (top) and Afternoon (bottom) Samples: 1989, 1997 and 1998 Figure 4.7 Box and Whisker Plots for Trip Frequency at the Community PSC Ashfield Mall for Equivalent Morning 1989 and 1998 (top) and Afternoon Samples: 1989, 1997 and 1998 (bottom) Figure 4.8 Box and Whisker Plots for Total Populations Perception of the Level of Shopping Satisfaction for 1988/89 and 1996/98 Figure 4.9 Box and Whisker Plots for Equivalent Samples of the Time Spent Shopping (Duration/min/trip) at Pre-Christmas Westfield Burwood Afternoon Samples: 1988, 1996 and 1997

over the Decade from 1988/89 to 1996/98

Socio-economic Index over the Decade from 1988/89 to 1996/98 Figure 4.12 Regressions for the Time-space Convergence (β = k 2/M) for the 1980/82, 1988/89 and 1996/98 Data Sets for the Sydney Project Figure 4.13 The Stages in the Evolution of a New Definition of the Gravity Coefficient (using 1988/89 and 1996/98 data): First Approximation Regresses the Deterministic and Probabilistic Forms of the Transport Coefficient M; Second Approximation Regresses a Revised and Standardised Form of M Eliminating the

Illustrations xv

Project, Australia with the Period or Year of Sampling

Figure 4.2 Sample Questionnaire used in the Sydney, Armidale and Auckland

,

Figure 4.10 Box and Whisker Plots for Total Samples of Shops Visited per trip

Figure 4.11 Box and Whisker Plots for Total Samples of the Changes in the

Autocorrelation; Third Approximation Corrects the Double Counting in the Deterministic Form of M

Lines are the 95% Confidence Lines from the True Mean of the Regression Figure 4.15 Aggregate Transfer Mobility (M) with Centre Size (Number of Shopping Destinations) for the 1988/89 Sydney Data Set Figure 4.16 Aggregate Transfer Mobility (M) with Centre Size (Number of Shopping Destinations) for the 1996/98 Sydney Data Set Figure 4.17 The Aggregate Curve for Trading Hours Regulated (1980/82 and 1988/89; 15 samples) and Deregulated (1996/98; 17 samples) Data from the Sydney Project Figure 4.18 (top left) Quadratic Regression of Population Index and Distance Decay from Bankstown Square 3/11/80 (1km Bands); (top right) Log-Linear Regression of Population Index and Distance Decay from Bankstown Square 3/11/80 (1km bands); (bottom left) Quadratic Regression of Population Distance and Distance Decay from Bankstown Square 3/11/80 (1km bands); (bottom right) Quadratic Regression of Population Density and Distance Decay from Bankstown Square 3/11/80 (1.5km bands) Figure 4.19 The Gravity Trip Distribution for Ashfield Mall 23/3/98 (Afternoon)

Improved DW-statistic of 1.380 Figure 4.20 The Park Test Regressing the Logarithm of Frequency Variance and Trip Distance and Testing for Significance Figure 4.21 The Bankstown Square 1997 Afternoon Gravity Regression (left) Including and (right) Excluding the 13.5km Point Figure 4.22 Quadratic Regression of the Gravity Coefficient-Trading Hour Hypothesis for the Sydney Project 1988/89 Figure 4.23 Quadratic Regression of the Gravity Coefficient-Trading Hour Hypothesis for the Sydney Project 1996/98 Figure 4.24 Three Dimensional Contour Model of Changing Time-space Behaviour at the Community Centre MarketPlace Leichhardt, from the Regulated 49.5 hours in 1988 to a Supply Average of 64.7 hours in 1998

Figure 4.25 Three Dimensional Contour Model of Changing Time-space Behaviour at the Regional Centre Bankstown Square from the Regulated 49.5 hours in 1989 to a Supply Average of 61.6 hours in 1998

Illustrationsxvi

Figure 4.14 Regression between Raw (top, R^2 = 0.666) and Standardised (bottom, R^2 = 0.84 ) Probabilistic Forms of the Gravity Coefficient. The Dotted

for (left) 10 Zones with DW-statistic of 0.758 and (right) 9 Zones with an

Figure 4.26 Linear Regression between (p/2T) and (mw/2T) for (left) the 1996/98 Sydney Data Set and for (right) the Aggregate Sydney Data Set (1988/89 and 1996/98)

Figure 4.27 Linear Regression between Inter-location Trip Frequency ( f ) and Intra-centre Frequency k, ( Mkf = ), for (left) 1988/89 and (right) 1996/98 Sydney Data Sets Figure 4.28 Linear Regression for MPS and Trip Frequency, Sydney Project 1988/89, 1996/98 and Aggregate Regression Figure 4.29 Quadratic Regression for Percentage of MPS and Centre Scale (Number of Destinations), Sydney Project 1988/89, 1996/98 and Aggregate Regression Figure 4.30 The Relationship between the Percentage of MPS and HDI Respondents in the Sydney Project (1988/89 and 1996/98) Figure 4.31 The Relationship between the Percentage of MPS and HDI × Trip

Figure 4.32 The Regression of the Gravity Coefficient and U2N2/MD2 for the Sydney Project Excluding Bankstown Square Data (left) 1988/89 and (right) 1996/98 Figure 4.33 The Location of Armidale, New South Wales Figure 4.34 The Scatter Plot of the Five Armidale 1995 Samples Compared to Sydney 1980/82, 1988/89 and 1996/98 Regressions of β = k2 /M Figure 4.35 The Scatter Plot of the Five Armidale 1995 Samples Compared to Sydney 1988/89 and 1996/98 Regressions of f =± Mk Figure 4.36 The Scatter Plot of the Five Armidale 1995 Samples Compared to the Aggregated 1988/89 and 1996/98 Regression of p/2T = m × k/2T for Sydney

Sydney 1988/89 and 1996/98 Aggregate Regression of MPS = h k Figure 4.38 Quadratic Regression of MPS Percentage and Centre Destinations

Sydney 1988/89 and 1996/98 Regression of MPS = HDI k2

Illustrations xvii

Frequency Squared (per week) in the Sydney Project (1988/89 and 1996/98)

β

Figure 4.37 The Scatter Plot of the Five Armidale 1995 Samples Compared to

showing the Armidale Samples as Positive Type 2 MPS

×Figure 4.39 The Scatter Plot of the Five Armidale 1995 Samples Compared to the

Sydney 1988/89 and 1996/98 Regressions of U= D× k / N Figure 4.41 Location Map of the Three Planned Shopping Centres Sampled in the Auckland Survey, Thursday April 6, 2000

2

Figure 4.43 The Scatter Plot of the Six Auckland 2000 Samples Compared to Sydney 1988/89 and 1996/98 Regressions of f = ± Mk Figure 4.44 The Scatter Plot of the Six Auckland 2000 Samples Compared to Sydney 1988/89 and 1996/98 Regressions of p/2T = m × k/2T

Aggregate Sydney 1988/89 and 1996/98 Regressions of MPS = h k

2

Figure 4.48 The Regression of Sydney 1980/82, 1988/89 and 1996/98, Armidale

2

Sydney 1996/98 and Auckland 2000 of f = ± Mk (bottom) Post-1993 Extended

Improved R-squared Value of 0.60

and Auckland 2000 of p/2T = m × k/2T

and Auckland 2000 for MPS = h k

and Auckland 2000 for MPS = HDI k2

Figure 5.1 The Location of the hepnrc.hep.net.gif Monitoring Site (top) and the Remote Hosts (bottom)

Illustrationsxviii

Figure 4.40 The Scatter Plot of the Five Armidale 1995 Samples Compared to

Figure 4.42 The Scatter Plot of the Six Auckland 2000 Samples Compared to Sydney 1980/82, 1988/89 and 1996/98 Regressions of β = k /M

Figure 4.45 The Scatter Plot of the Six Auckland 2000 Samples Compared to the

Sydney 1988/89 and 1996/98 Regressions of MPS = HDI × kFigure 4.46 The Scatter Plot of the Six Auckland 2000 Samples Compared to

Figure 4.47 The Scatter Plot of the Six Auckland 2000 Samples Compared to Sydney 1988/89 and 1996/98 Regressions of U= D ×

Figure 4.49 (top) The Aggregate Regression of Sydney 1988/89, Armidale 1995,

Hours Data (Excluding Sydney 1988/89 Points) (28 Samples) showing an

Figure 4.50 The Regression of Sydney 1988/89, Armidale 1995, Sydney 1996/98

Figure 4.51 The Regression of Sydney 1988/89, Armidale 1995, Sydney 1996/98

Figure 4.52 The Regression of Sydney 1988/89, Armidale 1995, Sydney 1996/98 ×

Figure 4.53 The Regression of Sydney 1988/89, Armidale 1995, Sydney 1996/98

k/N

1995 and Auckland 2000 for β = k /M

and Auckland 2000 for U= D × k/N

Figure 5.2 (top) A Range of Possible Time-space Distributions that could apply 0 0 =

10,000 km and a scaled φo max

Auckland or Backwards to Perth from the ith Sydney Site defines the Underpinnings of the Type of Differential Equations in Equations (5.16) to (5.18) (Baker, 2001)

Figure 5.5 The Ping Time Distribution for Traffic in the hepnrc.hep.net.gif Network for 2000 Figure 5.6 The Internet Traffic Wave for hepnrc.hep.net.gif using Packet Loss

0 0

handle Peak Traffic Times with Small Amplitudes. This is not the Case with Connections to Europe and Asia Figure 5.7 The Cumulative Frequency of Traffic Contributions from Successive 75km Zones from the hepnrc.hep.net.gif

Figure 5.8 (top) The Gravity Model for Traffic Densities for the hepnrc.hep.net.gif Monitoring Site in 2000 for Average Ping Times for

Density Plot (bottom right) Figure 5.9 (top left) The Gravity Model for Traffic Densities for the hepnrc.hep.net.gif Monitoring Site in 2000 for Average Ping Times 5-15ms;

sin 0.208 t; and (bottom right) a Density Plot Figure 5.10 (top left) The Gravity Model for Traffic Densities for the hepnrc.hep.net.gif Monitoring Site in 2000 for Average Ping Times 15-25ms;

0.108 t; (bottom left) the Three-dimensional plot for 168 hours for φ =6.9 exp-

Illustrations xix

to Internet Demand are Simulated for β = 0.0001, T = 24 hours, x = 0 to x

(top right) the Three-dimensional Plot for 24 hours for φ =6.9 exp-0.004 D sin

0.004 D sin 0.108 t; and (bottom right) a Contour Density Plot

t; (bottom left) the Three-dimensional Plot for 168 hours for φ =58 exp-0.015 D

sin 0.12t showing Time Gaussian Behaviour over 24-hours and Two-Dimensional Latencies less than 25ms; (bottom left) the Three-dimensional of φ =A exp-0.005D

Periods 5-15ms to 75-85ms. Monitoring Site Relative to Latency

US Origin-destination Pairs (-130 W to -60 W Longitudes) show the Capacity to Averages for 2000. The Range 0 to 168 hours represents Monday to Sunday. The

0.385 (left) and a 3-Dimensional Plot (right) Figure 5.4 Contour Density Plot for a Simulation of the RASTT Model with k =

Figure 5.3 The Equal Likelihood of J umping Forwards in Time to Sites in

Wave for k= 0.1 (Baker, 2001) 1.0 (bottom). A Three-dimensional Plot Visualising a likely form of the Demand

= 10 for a Sequence of k Values where k =0.1, 0.2,...

(top right) the Three-dimensional Plot for 24 hours for φ =58 exp-0.015 D sin 0.208

Figure 5.11 The Linear Regression between Latency ∆t and Distance Range x∆ showing Time Gaussian Behaviour for the hepnrc.hep.net.gif Site Figure 5.12 The Plot of Periodic Pairs for the hepnrc.hep.net.gifthe Phase Line Standardised to the Earth’s Rotation

right) Total Walking Distance (compared to a normal distribution); (bottom left) Maximum Walking Distance (compared to a normal distribution); and (bottom

Figure 6.2 Log-linear Regression of Total Walking Distance from Carparks in the Tracking Armidale 1995 Data Set Figure 6.3 The Location of Sample Centres in the New South Wales Retail Hierarchy Figure 6.4 The Regression of UCL 1996 Population and Population Change

Figure 6.5 Main Street Mayfield showing a Vacant Shop, Financial Planner and Pawnbroker forming a Sequence of Shops in what was Prime Retail Space a

Figure 6.6 The Redeveloped Supermarket Site in the Centre of Main Street Mayfield showing the Current Tenants as the Salvation Army Second Hand Shop and a $2 Shop Figure 6.7 Extra Employees per One Hundred Thousand Dollars of Turnover, NSW Figure 6.8 The Collapse of Rental Income from Prime Retail Properties surrounding Regional Shopping Centres (1990 to 1995)

Meadowhall Regional Shopping Centre Figure 6.10 Vacant Shops in Morley, Leeds in 1999, 12 months after the Opening of the White Rose Centre, 3km away

Illustrationsxx

Site Relative to

Figure 6.1 (top left) Frequency Distributions for Number of Shops Visited; (top

right) Time Spent Shopping (compared to a normal distribution)

(1996-2001) for the Selected Case Studies

Decade earlier. The former Cake Shop, now Vacant, offers the First Three MonthsRent Free (notice on the door)

Figure 6.9 Vacant Shops in Sheffield in 1999, nine years after the Opening of the

List of Tables Table 1.1 Classification of Planned Shopping Centres Table 1.2 Proposed Floorspace Assignments for the Proposed Woolworths Supermarket, Inverell, New South Wales 2000 Table 1.3 Change in Independent Supermarkets and Food Specialty Stores in Australia 1992-1999 Table 2.1 Survey of Tenancy Changes in Local Centres, Canberra, 1998 Table 2.2 Shopping Centres used in the Canberra Household Shopping Preference Survey 1996, 1997

Consumer Behaviour Table 2.4 An Individual’s Assessment of their Level of Shopping Satisfaction (Utility) Table 2.5 Characteristics of ‘Small’ and ‘Large’ Centre Behaviour

Table 3.1 A Classification of Relevant Equations using Space-Time Operators

Set

in the Sydney 1988/89 Data Set Table 3.4 SE and FA Estimates of Mean Trading Hours for the 1988/89 Sydney Data Set Table 4.1 Occupation Weighting for the Index of Disposable Income (IDI) Table 4.2 Number of Retail Outlets for Sampled PSCs Sydney Project 1980/82, 1988/89 and 1996/98 Table 4.3 Sample Sizes, Sydney Project, Equivalent Time Samples (shaded) for 1988/89 and 1996/98 Table 4.4 Trip Distance Comparison, Sydney Project, Equivalent Samples (shaded) for 1988/89 and 1996/98

Table 2.3 A Review of the Important Attributes Considered in Studies of

Table 3.2 Time-space Characteristics of Three Malls in the Sydney 1988/89 Data

Table 3.3 Various Estimates of the Intra-centre Shopping Frequency (per week)

Table 2.6 Source Matrix of Literature Associations for Multi-purpose Shopping

Table 4.5 Mean Trip Frequency Comparison, Sydney Project, Equivalent Samples (shaded) and Pre-Christmas Samples (bold) for 1988/89 and 1996/98 Table 4.6 Comparison in the Mean Level of Shopping Satisfaction, Sydney Project, Equivalent Samples (shaded) and Pre-Christmas Samples (bold) for 1988/89 and 1996/98 Table 4.7 The Percentage of Samples in the 1988/89 and 1996/98 Data Sets (The Westfield Chatswood Sample in 1989 of 17.61 is included in the Mean Shopping Satisfaction, but not in 1996/98 because of refurbishment.) Table 4.8 Comparison in the Mean Shopping Time, Sydney Project for Equivalent Samples (shaded) and Pre-Christmas Samples (bold) for 1988/89 and 1996/98. The Total Time Spent Shopping (Frequency × Time Spent Shopping per

Table 4.9 Comparison in the Mean Shops Visited for 1988/89 and 1996/98 in the Sydney Project, Equivalent Samples (shaded) and Pre-Christmas Samples (bold) Table 4.10 Comparison in the Socio-economic Index for 1988/89 and 1996/98 in the Sydney Project, Equivalent Samples (shaded) and Pre-Christmas Samples (bold)

and 1998 Samples)

and 1998 Samples)

Index of Disposable Income)

Sample

Table 4.11 A Summary of Occupational Types from Respondents from Sydney

Table 4.12 Summary of Nature of Trip Purpose from Respondents from Sydney

Table 4.13 Changing Behaviour from Particular Trip Purpose and Socio-

Table 4.15 The Estimation of the Gravity Coefficient for Bankstown Square

Bankstown Square Morning Sample, BSA- Bankstown Square Afternoon

xxii Illustrations

trip) per week is in brackets (the asterisk describes the Mann-Whitney Significanceat the 0.05 Level)

Project (Ordinary Font, 1988/89; Bold Font 1996 or 1997; Bold Italic Font 1997

Project (Ordinary Font, 1988/89; Bold Font 1996 or 1997; Bold Italic Font 1997

economic Groups from 1988/89 to 1996/98 (1988/89 Samples, Normal Font; 1996/98 Samples, Bold Font) (HI High Income; LI Low Income, according to the

Square Morning Sample, 3/11/1980

using Two Assignment Procedures (DW = Durban-Watson Statistic); BSM-

Table 4.14 Population Index and Density Assignments for 1km Bands: Bankstown

1996/98 Data Set

Christmas Samples (bold)

(shaded) and Pre-Christmas Samples (bold) Table 4.19 The Sample Sizes in the Armidale Survey, November 1995

Table 4.21 Population Change in Armidale and Region 1991–1996 Table 4.22 Numbers of Students Enrolled at Armidale Campus of UNE Table 4.23 Full-time Equivalent Staff Numbers at UNE, Armidale

Compared to the Sydney Project 1996/98 Table 4.25 Sample Sizes of Centre Surveys, Auckland, April 6, 2000

to the Sydney Project 1996/98 Table 4.27 Comparison between Auckland Samples with Selected Sydney Samples in 1997/98 taken on the Thursday before Easter Table 6.1 Walking Distance Statistics from Armidale Carparks

Main Streets only

Table 6.4 Changes in Landuse of Retail Establishments in Oberon

1995-1997

Table 4.16 Mean Trip Frequency and Variance per Concentric Band: Sydney

Table 4.17 Comparison in Variance in Trip Frequency for 1988/89 and 1996/98

Table 4.18 Comparison in the Spatial and Time-based (in brackets) Gravity Coefficients for 1988/89 and 1996/98 in the Sydney Project, Equivalent Samples

Table 4.20 Comparison between Armidale LGA, Primary Trade Area and NSW

Table 4.24 Summary of Statistics of Armidale Surveys (bold), November 1995,

Table 6.2 Selected Case Studies of Retail Vacant Shops in Non-metropolitan New South Wales. All Elements not stated as CBD Values are

Table 6.3 Multi-purpose Retail Functions within Oberon Retail Establishments

Major Supermarket Re-locating to an Edge-of-centre Site, Mayfield NSW

xxiiiIllustrations

Samples in the Sydney Project for Equivalent Samples (shaded) and Pre-

LGA Averages for Selected Socio-economic Groups, 1991

Table 4.26 Summary Statistics of Auckland Surveys, November 1995, Compared

Table 6.5 List of Shop Closures and New Businesses within 18 Months of the

1995-2000

1980 and 1992 Table 6.8 NSW Employment and Retail Structural Ratios

1992-95 Table 6.10 Changes in Employment Structures at Coles, Armidale

Queensland

Table 6.7 Ratio of Full-time to Part-time Employment for NSW and WA,

Table 6.9 Changes in Employment Structure at Coles Supermarkets, ACT

Table 6.11 Floorspace Equivalent per Person Employed for NSW and

xxiv Illustrations

Table 6.6 Comparison in Retail Employment Statistics between Australian States

trading) and Westfield Miranda and Parramatta, Sydney (deregulated hours) for 1999 and 2001

compared to Westfield Carindale, Brisbane (both regulated hours and no Sunday Table 6.12 Westfield Marion, Adelaide Floorspace and Turnover Statistics