Abstract
Entropy maximising models are well established within the field of urban modelling as a method for predicting flows of people or material within an urban system. The dynamic urban retail model (Harris and Wilson, Environ Plan A 10:371–388, 1978) is one of the most well known applications of this technique and is an example of a BLV (Boltzmann-Lotka-Volterra) model. We define an agent-based model (ABM) of urban retail and explore whether it can be made equivalent to a BLV model. Application of both models to the metropolitan county of South Yorkshire in the UK indicates that both models produce similar outputs. This direct comparison provides some insights into the differences and similarities of each approach, as well as highlighting the relative strengths and weaknesses. The ABM has the potential to be easier to disaggregate, while the entropy maximising model is more computationally efficient.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
For simplicity we are only modeling independent retailers. An interesting extension of the model might be to include chain stores with one retailer owning multiple shops.
- 2.
We use a neighborhood size of 10.
References
Clarke, M., & Wilson, A. G. (1985). The dynamics of urban spatial structure: The progress of a research programme. Transactions of the Institute of British Geographers, 10, 427–451.
Clarke, G.P. & Wilson, A.G. (1986). Combining theoretical and empirical research in retail location analysis (Working Paper 468). Leeds: School of Geography, University of Leeds.
Clarke, G. P., Clarke, M., & Wilson, A. G. (1986). Multiple bifurcation effects with a logistic attractiveness function in the supply side of a service system. Systemi Urbani, 7, 43–76.
Epstein, J. M., & Axtell, R. (1996). Growing artificial societies. Cambridge: MIT Press.
Hagen-Zanker, A., Engelen, G., Hurkens, J., Vanhout, R., & Uljee, I. (2006). Map comparison kit 3: User manual. Maastricht: Research Institute for Knowledge Systems.
Harris, B., & Wilson, A. G. (1978). Equilibrium values and dynamics of attractiveness terms in production-constrained spatial-interaction models. Environment and Planning A, 10, 371–388.
Holland, J. H. (1995). Hidden order: How adaptation builds complexity. Reading: Addison Wesley.
Lombardo, S. R. (1986). New developments of a dynamic urban retail model with reference to consumers’ mobility and costs for developers. In D. A. Griffith & R. J. Haining (Eds.), Transformations through space and time. Dordrecht: Martinus Nijhoff.
Lowry, I. S. (1964). A model of metropolis (Memorandum RM.4035-RC). Santa Monica: Rand Corporation.
Wilson, A. G. (1967). A statistical theory of spatial distribution models. Transportation Research, 1, 253–269.
Wilson, A. G. (1970). Entropy in urban and regional modelling. London: Pion.
Wilson, A. G. (2006). A generalised representation for a comprehensive urban and regional model. Computers, Environment and Urban Systems, 31, 148–161.
Wilson, A. G. (2008). Boltzmann, Lotka and Volterra and spatial structural evolution: An integrated methodology for some dynamical systems. Journal of the Royal Society, Interface, 5, 865–871.
Wilson, A. G., & Dearden, J. (2011). Phase transitions and path dependence in urban evolution. Journal of Geographical Systems, 13(1), 1–16.
Wilson, A. G., & Oulton, M. (1983). The corner shop to supermarket transition in retailing: The beginnings of empirical evidence. Environment and Planning A, 15(2), 265–274.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Appendices
Appendix 1: An Algorithm for Calculating the Boundary and Membership of Emergent Retail Zones
Pseudo code is given here for calculating the emergent retail zones that appear in the model.
-
Setup an empty list of shops called processedList
-
While there are still shops not in processedList
-
Choose a shop s that is not in processedList
-
Setup an empty list called shopList
-
Call function findClosedGroup with s, shopList and processedList as parameters
-
shopList now contains all the shops in one retail zone
-
The recursive function findClosedGroup does the following:
-
For each shop t nearby
-
If t is not already in shopList
-
Add t to shopList
-
Add t to processedList
-
Call function findClosedGroup with t, shopList and processedList as parameters
-
-
Appendix 2: Data Sources
The retail data comes from the Town Centres project 2004. We use the total retail floor space attribute from each town centre area to:
-
For the BLV model: set the floor space of each retail zone.
-
For the ABM: determine the number of retailer agents we need to generate inside the town centre area. We do this by dividing the total retail floor space by an average shop size of ∼2,800 m2, which produced about 500 retailer agents for the region.
The average shop size was chosen to reduce the computational load but could obviously be reduced given more time.
The population data are from the 2001 UK Census. We use the All people field from the KS001 Usual resident population table for the CAS Ward boundaries. Then:
-
For the BLV model: the centroid of each CAS Ward is the location of each residential zone and the Pi value is set to the All people value.
-
For the ABM: the All people value, divided by an aggregation factor, decides the number of consumer agents we generate at random positions inside the CAS Ward boundary. In this case the aggregation factor was set to 24 (meaning that each consumer agent represents 24 people) and produced ∼50,000 consumer agents in the model. Again this was done to allow for reasonable computation times.
The average income data are from the CACI Paycheck data for 1999 at postcode area level. We aggregate these data up to CAS Ward level and then use the aggregate value for each CAS Ward to:
-
For the BLV model: set the ei value for the corresponding residential zone.
-
For the ABM: set the spending money available to each agent living inside the CAS Ward.
For simplicity, all travel costs were calculated from the Euclidean distance between two points.
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Dearden, J., Wilson, A. (2012). The Relationship of Dynamic Entropy Maximising and Agent-Based Approaches in Urban Modelling. In: Heppenstall, A., Crooks, A., See, L., Batty, M. (eds) Agent-Based Models of Geographical Systems. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-8927-4_35
Download citation
DOI: https://doi.org/10.1007/978-90-481-8927-4_35
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-8926-7
Online ISBN: 978-90-481-8927-4
eBook Packages: Humanities, Social Sciences and LawSocial Sciences (R0)