Some contribution toward Spatial Urban Dynamics
From Relative Attractiveness point of view
Akira UCHINO*, Tetsuma FURIHATA**, Nobuhide TANAKA***,
Yutaka TAKAHASHI*
**University of Shimane, ***Gakushuin University,
*School of Commerce, Senshu University
2-1-1 Higashimita Tamaku
Kawasaki JAPAN 214-8580
Tel. +81-44-900-7953 FAX +81-44-900-7849
uchino@isc.senshu-u.ac.jp
Abstract:
There was an interesting presentation at ISDC 2004 in Oxford. The title was “Spatial
urban dynamics” presented by Peter Sanders and Frank Sanders. They expanded
Forrester s original urban dynamics model in terms of spatial point of view. While one
of us has been studying Geographic Information Systems (GIS) and applying GIS to
consumer spatial behavior. Recently we have got some research results, one of which
explains how retailers agglomerate in a city, the other one shows one of the method of
calculating relative attractiveness of retail areas. We have been developing a basic SD
model treating two shopping areas in Niigata city in Japan, but we are still struggling to
make a few modifications on the model in order to turn it into the applied one.
In this paper, we make some contribution toward spatial urban dynamics, firstly
discussing the importance of the concept of “attractiveness” in social sciences,
secondly showing latest research result on “the attractiveness” outside of system
dynamics field and how to take it into spatial urban dynamics, thirdly making
constructive comments on Sanders’ approach, finally referring to a strong possibility of
expanding spatial urban dynamics toward national models and world models.
1. “Attractiveness”
Demand and supply are adjusted by price in market mechanism. But it is true that
human being cannot gather all the information about demand and supply in real world
and that goods and services in market are not always homogeneous. When we buy a
product in a market, we evaluate competitive products, on which differences we put
prices. And we sometimes chose a more expensive product because of its better
performance. Or we chose a more expensive one because the brand of the product is
more powerful, even competitive products are all the same in performance.
When I wanted to buy a brand-new video camera made in S Company, I
visited in a big retail store. Unhappily the video camera was sold out there.
But they had another brand-new video camera sold by K Company. S
Company was original equipment manufacture so that the video was just
same as S Company’s. The difference is only the brand name, S Company
and K. And the price of K Company’s was 50 dollar less than S Company’s.
In case you chose K’s video camera instead of S’s? At that time I did not buy
K’s and went to another shop to find S’s.
In this case, the performance of the video cameras are same, the name of them are only
the difference. If retail prices are not same, brand power between two companies exists.
If S Company is well known international company, can fifty dollar compensate it, or
not? In reality it depends on own customer.
Where does a customer buy goods? Shopping style is different from country to country.
But we think not only prices but also distance and familiarity of the shops to buy
perishables and to satisfy daily needs. How to choose a specialty store, a department
store, a shopping mall, or an agglomerated retail area, when we go shopping to get some
special goods or to enjoy shopping with our family or a friend? Which area and which
shop? When we need some sort of goods, how to choose shops and the shopping route?
Where do we live? Where do we get jobs? Development of a city or a stagnation of it
highly depends on migratory flow of population into a city or outside of it, especially
high the mobile countries on of living and job changing. In Japan people are relatively
stable on working and living, and only a few cases changing both job and house at the
same time. It is popular in USA that moving house to adjacent school districts or
neighboring cities when kids attain school age to get better educational environment
without changing a job, though it is exceptional in Japan.
Prices of goods and services, drawing power of shops and agglomerated retail area“
on shopping, population increases in a city along economic development; there is a
similarity between them. We can hypothesize the concept of “attractiveness” that draws
a person’s attention, attracts a person when making a decision or choosing something.
When we think about products, services, companies, brands, tourist spots, holiday
resorts, contents or titles of audio and visual, development and stagnation of cities or
areas, immigration between countries, we make a definition of “attractiveness”. And if
we can treat the concept of “attractiveness” commonly, we have a clear understanding
of developing models in social systems. The “attractiveness is one of key concept in
social sciences. This is a basic consensus of our joint research. Our first step is focusing
on the latest research on “attractiveness” and discussing from system dynamics point of
view.
We sometimes use the “quality of life” in social system modeling. We only value it not
by quantity measure but by quality measure. The “attractiveness” as well as “quality of
life” composes of many factors or elements, changing in every situation. So we define
that the “attractiveness” is a power of products, services, and cities or nations that
attracts people. But we are not treating the “attractiveness” as a theoretical concept,
treating it as a tool of real problems solving.
2. Can we get relative “attractiveness” in reality?
There are several theories on spatial distribution in intra-urban retail trade area, Central
Place Theory @) Circulatory System Theory ®) and Statistical Distribution Theory @.
They partially explain how retailers are distributed or located in cities. Some of them
teach us that the current spatial distribution is quite rational. But they cannot explain
how retailers in a city develop dynamically.
There have been developed another series of theories, how consumers select a retail
shop when they go shopping. Theories on consumers’ spatial activity are Retail
Gravitation Model ©, Intervening Opportunity Model ©, and Network Model ™.
Especially a Retail Drawing Power Model, a kind of Retail Gravitation Models
originally came from Huff’s, shows a suitable location of a new retail shop in a city. It is
useful in business. These theories can explain retailers’ development in a city in some
extent.
We have got some research results in order to explain how retailers agglomerate in a
city. We compare two simulation results, one condition in a uniform distribution of
population, the other radially populated so that we investigate how population
distribution affects the spatial structure of retailers’ accumulation in a city (Furihata,
Uchino, et al., 2003). These simulation models and other existing studies did not use the
attractiveness of shopping streets (areas) effectively in consumer choice because the
attractiveness of them includes many elements or factors. Of course although some
methods such as Drezner and Drezner(1998)® consider the attractiveness of shopping
areas, these models did not explain dynamically change under time series. So we focus
on the “attractiveness”, and develop an assessing method that infer retail facility
attractiveness from simple data which we can get easily without effort of getting
additional data, and simulate using real data on Niigata Prefecture in Japan (Furihata,
Uchino, et al., 2004). The paper is written in Japanese so we show a brief paper in
English written by one of joint researchers, as attached pdf file.
The paper attached show you that one of the latest researches on “attractiveness” related
spatial urban dynamics. In a certain situation we can make a mathematical model using
computer simulation and get relative “attractiveness” of agglomerated retail areas. We
use mathematical model and computer simulation because of we cannot solve the model
mathematically. It is true that we can get relative attractiveness in real spatial analysis.
But the condition to get it is very strict. We don’t believe we can apply the same method
in the urban dynamics.
Forrester (1969) develops urban dynamics model, which shows growth and stagnation
of a city, interacting industry, housing and people. The attractiveness of a city is
composed of job availability, housing availability, and land availability. Very simple but
it is easy enough explaining dynamics of a city. Of course his model is simple so that it
has no spatial point of view.
We believe we can treat relative attractiveness as a set of related factors in system
dynamics. But when we make an incursion into the spatial analysis, attractiveness
increases complexity.
3. “Spatial urban dynamics” by Sanders
The “Spatial urban dynamics” presented by Peter Sanders and Frank Sanders at ISDC
2004 in Oxford is very interesting. They expanded Forrester’s original urban dynamics
model in terms of spatial point of view.
1) They expand literally original Forrester’s urban dynamics model so that they can
compare the simulation results.
2) They build “The service industry” into the model. The basic industry is the same as
Forrester’s original model. The second type, service industry is location sensitive and
consists of one stock because of simplicity. Location sensitive means fluid or mobile
character suitable for spatial dynamics.
3) They introduce spatial analysis and use the equation in which the “trip distribution
function” is the distance between zone i and zone k to the power 2. They relate the
attractiveness of each zone in spatial distribution to the distance between zones.
4) They only show conceptual expanded model in urban dynamics in their presentation
but also they suggest there is a project to apply their spatial urban model to Rotterdam,
the second largest city in the Netherlands.
We evaluate their model very highly but place it ideal conceptual expanded model in
urban dynamics, only the first stage model in spatial dynamics. Because we believe
spatial concept in urban dynamics refer to real distance or real trip time between zones.
1) If there is not quite a far away between zones, a part of people living in a zone may
commute another zone.
2) If above 1) is true so that some of the zones have more attractiveness on housing
comparing to others. Each zone has characteristics and attractiveness, on housing,
schools, public facilities, shopping or business.
Environment
Environment
—
Figure 1. Original urban model and spatial urban model
The attractiveness of a retail facility is a composite index of many attributes. For
example, distance or trip time to the retail facility, selection of goods, prices, amenities,
parking spaces and so on. Even if we can treat retail areas, shopping center, shopping
malls, or huge retail facility, there are so many retailing shops. So we hesitate to treat
attractiveness of each small shop. But population as customers only goes shopping.
They don’t migrate. We cannot compare the complexity of customer behavior and
spatial choice modeling to the urban model. The point is that the spatial urban model is
enough complex that confuse the model builder.
Forrester’s urban dynamics model in 1969 was a fundamental archetype in urban
dynamics. Theoretically we discuss his model but in real situation we must make a new
model which depicts the real problem we face with.
We think Rotterdam is a big city and zone analysis is effective. If they will develop their
model in which each zone has own attractiveness and spatial differences, they will show
us a great example to develop spatial urban dynamics model. We are looking forward to
their success.
4. Spatial urban dynamics expands widely
Sectors in Sunders’ model are areas in a city. But if the sectors truly have spatial
character, sectors are like cities in wide area model. If we can treat spatial character
reasonably, we have got powerful tools to expand our model widely. Spatial urban
dynamics will leads wide area model, national model, and world nations’ model. The
relative attractiveness of one nation gathers immigrants from other nations. Even if we
cannot identify the relative attractiveness, we treat relative attractiveness in system
dynamics model and contribute toward improving social problems in the world.
5. Conclusion and Future Research (At the presentation)
In this paper we only discuss,
1) the importance of the concept of “attractiveness” in social sciences,
2) we can define relative attractiveness in a certain condition,
3) evaluate Sanders’ approach in spatial urban dynamics,
and
4) refer to a possibility of expanding spatial dynamics toward national wide models.
We must show our experience on spatial analysis concretely so that we are struggling to
make a small set of spatial urban dynamics model. The model has 6 sectors. Two has
attractiveness of industry area, one has high-class housing, and one has initially large
part of underemployed housing. They have locations, distance between sectors. This is
for a virtual city but we can show spatial characters through simulation.
As soon as we are ready for the model, we rewrite this paper and surely demonstrate the
model in the presentation.
Footnotes
(1) classical shopping streets, districts, intra-urban retail trade area
Retailer shops are commonly classified by the same technical terms. But the situation
is slightly different from country to country. There are a few facilities in Japan which
we call shopping mall in USA, or shopping center in UK. But classical shopping streets
or districts in this paper are slightly different, which sometimes are a mall or an arcade,
sometimes line with small shops, department stores, and super market. They expand
along the streets, or into a block or blocs in a city. We are discussing them in Japan. We
use shopping streets, shopping districts, and shopping or trade area replaceable in this
paper.
(2) Central Place Theory
Central place theory originated by Christaller(1966) has been developed in economic
geography. This theory was based on classical economic assumptions such as the
uniformity of consumers and travel without considering the attractiveness of shopping
areas in consumer choice. Nevertheless, it has been widely used to explain the retail
hierarchy: a town centre core radiating progressively further out with greater number of
district centers, neighborhood centers and finally local centers.
(3) Circulatory System Theory
Circulatory system theory is based on the relationship between transport system and
retail centers in urban areas. This theory shows that retail centers configure at the
intersection of main arteries, and along the main arteries.
(4) Statistical Distribution Theory
Rogers(1974) presented that spatial distribution of retail facilities(stores) in urban
areas conforms the statistical distribution such as a negative binomial distribution.
(5) Gravity Model
The origin of gravity models dates back to well-known “The law of gravitation’
proposed by Reilly(1929). A general equation of the models is follows:
where P, is the probability that a consumer i purchases at a shopping destination j,
A, is the attractiveness of a shopping destination (store) j, R, is the resistance
measure perceived from the consumer i’s shopping trip to the destination j such as
the distance and time. According to an above gravity model the probability that a
consumer i patronizes a shopping destination (store) j is proportional to its
attractiveness and inversely proportional to the resistance measure. By the definition
of the attractiveness and resistance measure on the above equation, many gravity
models are formulated. In the representative model proposed by Huff(1962), for
instance, the attractiveness and resistance measure substitute for the retail sales floor
area of shopping destination (store) and distance between the origin i and the
destination 7.
(6) Intervening Opportunity Model
Stouffer(1940) who is a sociologist proposed an intervening opportunity model.
The fundamental idea of this model is follows: the probability that a consumer chooses
a store proportional to the purchase opportunity served by its store and inversely
proportional to the total opportunity from the consumer’s origin to its store. This
model comes to the conclusion that the distance and time between the consumers’ origin
and the destination are not fundamental to explain for consumers’ behavior but the
spatial order of stores is a most important factor.
(7) Network Model
Network model developed by White and Ellis(1971) captures consumers’ behavior as
flows in network configured by arteries and public transportation. The network
consists of nodes such as consumers’ origin and the destination(stores) and arcs
connected the nodes. This model defines some assumptions to flows in the network,
and estimates the outflow(the number of consumers or total sales volume in each stores)
based on the inflow(the number of consumers or total expenditure in its consumers’
origin).
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