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Making Complex Network Analysis in System Dynamics
Hans Hennekam
Delft University of Technology
Faculty of Civil Engineering
PO Box 5048
2600 GA Delft (The Netherlands)
Phone/fax: +3 1641312733/+3 1765985523
E-mail: 251090@student.fbk.eur.nl
Frank Sanders
Delft University of Technology
Faculty of Civil Engineering
PO Box 5048
2600 GA Delft (The Netherlands)
Phone/fax: +3 1152781780/+3 1152785263
E-mail: F.M.Sanders@citg.tudelft.nl
Abstract
As urban models in system dynamics are extremely complex if an area is subdivided in
many dynamic and interacting areas, managing complexity of the urban network
interactions is essential. A recently developed interregional model of The Netherlands
illustrates the implementation of the spatial dimension in urban dynamics. The model
describes 40 self-organizing urban areas and distribution of migrants, firms and
commuting between 40 regions simultaneously. Developments in regional labor
markets, housing markets and land-use can be explained by internal as well as by
external regional conditions.
The applied approach gives many opportunities to make large disaggregated models in
system dynamics. Spatial or sectional interactions (network models) can be modeled
while model structures remain manageable. In general, as vector-based and matrix-
based calculations can be implemented in system dynamics easily, many (existing)
static models can be applied dynamically. Hence, the usefulness of system dynamics in
modeling complex systems broadly is enlarged.
Key words: Network Analysis, Urban Dynamics, Spatial Interaction, Managing
Complexity
History of urban dynamics
Jay W. Forrester’s publication Urban Dynamics in 1969 introduced a new
perspective on analyzing urban problems, forming a bridge between engineering and the
social sciences. Urban dynamics research programs started in order to integrate the
urban dynamics perspective into the decision-making processes of urban areas (Alfeld
and Graham, 1976). Several applications of urban dynamics are made since, giving
more understanding of urban behavior and how the urban system can be managed.
Although system dynamics and its application to the dynamic modeling of social
systems might be one of the most insightful system dynamics applications ever
developed, urban dynamics generated intense controversy (Alfeld, 1995) and practically
died out in the seventies. Only a few remarkable academic publications are left and the
hope that urban dynamics will revive one day.
This paper describes fundamental criticism of urban dynamics and how these critics
can be reduced. A case study of The Netherlands describes regional socioeconomic
changes of 40 regions, all interacting with each other. The approach used may not only
inspire and therefore contribute to the field of urban dynamics, but gives —more in
general- many opportunities to make large disaggregated models of different fields of
study in system dynamics while model structures remain manageable. The usefulness of
system dynamics in modeling complex systems is thereby enlarged.
Understanding traditional urban dynamics
As many systems the urban system is complex, which behavior is dominated by
many nonlinear feedback processes. Traditional urban dynamics models show an urban
area as a complex multi-loop structure of industry, housing and people. Two important
driving forces that control urban behavior and give opportunities for an effective
decision-making process are (1) resource constraints, and (2) relative attractiveness
(Alfeld, 1995). These forces define the principal interactions of the urban area. Figure 1
summarizes overall interactions between population, business, houses and business
structures, which are all regulated by an area’s resources.
a job
availability
_ NK +
firms “" population
() 1).
siness situ housing
|, availability
\\ (J
business .
structures sg fo houses
2 land
availability
Figure | Traditional interactions between population, business, houses and
business structures in urban dynamics
Figure | illustrates that if the population increases, the availability of housing will
decline, for people will have to live somewhere in the area. As the population increases,
the availability of jobs also declines because people will have to work in order to obtain
money to buy food, clothing and shelter. Because people depend upon jobs to support
themselves and because people need to shelter, the availability of jobs and the housing
availability are important motivations for moving. The linkages back to population
inhibit migration according to employment conditions and housing availability.
In this text the term housing availability very broadly denotes not only the vacancy
rate in the housing stock but also other concomitants of the housing supply as rent
levels, diversity of choice in size and location, and quality (Alfeld and Graham, 1976).
Job availability corresponds to several job-market conditions as unemployment, job-
openings, promotions and overtime. People tend to move away from areas where
aggregate attractiveness is relatively unfavorable to areas where market opportunities
are greater. When job-market and/or housing market conditions are relatively favorable,
market conditions tend to stimulate in-migration and tend to discourage out-migration
of people.
As business activity increases, the business structures availability for firms declines
and the job availability increases in the urban area. For firms need accommodation, and
business activity provides jobs. Because labor and accommodation are necessary inputs
for most firms, the availability of labor and accommodation also influence firms’
locational behavior and expansion decisions. When jobs are scarce, labor is readily
available allowing business greater flexibility in choosing employees and shorting time
necessary to find qualified persons to fill specific positions. Moreover, high labor
availability tends to decrease wage competition for labor among firms (Alfeld and
Graham, 1976). Just like an increased business structures availability for firms, an
increased labor availability is an important pull factor and therefore tend to stimulate the
attraction of new firms and will encourage present firms to expand.
In general, a decreased housing or business structures availability corresponds to a
situation when houses or business structures are scarce. High rents, low vacancy rates,
and a lack of quality housing/business structures in desirable locations all indicate that
new construction is likely to be profitable. Stimulated by high demands, new housing/
business structures will be developed, which in turn increases the number of structures,
as shown in Figure 1.
The bottom loops in Figure | show how land use by firms and by population defines
the availability of land, while land acts on population and firms through housing
availability and business structures availability. As an area begins to approach full land
occupancy, land prices will grow and traffic congestion increases. The increasing
density tends to inhibit further construction. Land supply ultimately limits urban
growth. On the other hand, low land occupancy will inhibit construction also. Lack of
infrastructure and lack of other kinds of facilities and utilities give the area an
unattractive potential for further urban land development.
Fundamental criticism of urban dynamics
One of the most difficult parts of problem formulation is the definition of the system
to be studied. Defining the system is problematically because all systems are themselves
subsystems of larger systems. Where is the boundary between the system of interest and
its environment best to be chosen? Traditionally, in urban dynamics it is roughly the
jurisdictional boundary of an urban area that separates the system of study and the
environment. Figure 2 illustrates the traditional relationship between an urban system
and its environment in urban dynamics.
x
limitless environment \
Te
H
\ area
Figure 2 The urban boundary concept
urban boundary
Figure 2 draws on two important fundamental points of criticism, which will be
discussed in this paper:
1. The problem of the ‘limitless environment’
2. The ‘boundary problem’
The problem of the ‘limitless environment’
A first fundamental point of criticism concerns the problem of the ‘limitless
environment’. The traditional model boundary assumes no system-environment
feedback relationships of critical importance, but cross-boundary flows such as
migration or commuting are possible. The environment of an urban area is actually the
rest of the universe, being the source and recipient of all cross-boundary flows. The
environment is therefore limitless, in the sense that there are more potential in-migrants
than the urban area can possibly contain and that potential out-migrants always succeed
in moving to the system environment. The limitless environment plays also an
important role in the ‘boundary problem’.
The ‘boundary problem’
Internally created flows as well as flows that cross the urban boundary create
changes in urban conditions. Examples of internally created flows are the number of
births and deaths, defined as a percentage of the population within the area. Other flows
determined by internal conditions are for instance housing construction, business
construction and demolition of structures.
There are also flows that cross the urban boundary, such as migration of people,
migration of business (jobs) and commuting (labor force). Figure 3 illustrates how the
amount of population is influenced by net migration.
population net migration
NY internal ea ae external
attractiveness attractiveness
Figure 3 The concept of relative attractiveness
The attractiveness of an urban area is an important driving force regarding flows
that cross the urban boundary. For modeling purposes, absolute measures of the
attractiveness of the urban area are unimportant. Traditional urban dynamic models
recognize only factors that differentiate the urban area from its environment (Graham,
1974). Cross-boundary flows change when the differences between the attractiveness of
the urban area (internal attractiveness) and the attractiveness of the environment
(external attractiveness) change. If there are no differences in attractiveness, then the
normal cross-boundary flows (migration in Figure 3) take place. Any change in internal
or external conditions can change the relative attractiveness of an urban area and its
environment, triggering flows such as migration across the system boundary. If relative
attractiveness to accommodate or/and to work in an area increases with respect to the
urban environment, in-migration will increase and out-migration will decrease.
The principle of relative attractiveness is often misinterpreted and one of the most
criticized fundamental principles of urban dynamics. From this point of view, it is
essential to understand the idea that the urban area’s environment functions as a moving
reference point, with which to compare conditions within the area to govern cross-
boundary flows. For this reason, a traditional urban dynamics model need not and does
not consider such effects as technological change, nor does it portray explicitly the
dynamics of the national economy (Graham, 1974).
Fundamental criticism exists whether the internal system interactions or external
forces primarily cause socioeconomic development of an urban area. In defining the
urban area and in specifying the system boundary, urban dynamics implicitly assumes
that the significant behavior of an urban area is generated within the urban boundary.
Traditional urban dynamics applications portray the urban area as a self-organizing
system. But, doesn’t feedback between the urban system and its environment help to
explain urban behavior? Experts have questioned the self-organizing assumption of
traditional urban dynamics. As the impacts of a system has on its surroundings may not
be immediate and may possibly rather complex, perhaps following chains of interrelated
responses in its environment may then feed back to the system itself.
The problem of drawing a system boundary so that internal elements cannot
influence variables outside the system that in turn exert a significant influence on the
system, is called the ‘boundary problem’. Although the boundary problem depends on
the goals and objectives to be studied, it is impossible to define the perfect system
boundary. It is in a certain way impossible to define within the boundary all the
dynamic structure necessary to explain and possibly cure the problem of study.
However, further research into the urban boundary problem would be very useful in
order to reduce the boundary critics. How can this be done? The answer seems to be as
simple as it seems to be impossible: model the environment.
Spatial distribution in urban dynamics
When suburban areas or more distant rural and urban areas also define the urban
system dynamically, an adequate model should represent spatial interactions between
spatial subsystems explicitly. For instance, interactions between a city and its suburbs
are stronger and more extensive than interactions between a city and its larger
environment. An explicit subsystem representation is needed to account for migration
and commuting between the central city and its suburbs, because the city and its suburbs
together represent the metropolitan system.
Spatial disaggregated models can not only generate more accuracy but certainly also
extend the ranges of policy issues addressed by the model. Several attempts have been
made to tackle the boundary problem by simply extend existing urban models.
Traditional city-suburb models contain two parallel but separate geographical sectors,
each based upon structures of traditional urban dynamics models (Schroeder III, 1975).
Figure 4 shows the city-suburb concept in a two-sector model.
Figure 4 The city-suburb concept
Flows between the city and suburb sectors represent the ‘interface’, which
interconnects separate sectors (city model and suburban model as shown in Figure 4).
The interface takes care of the spatial distribution of migrants and commuters within
the total system modeled.
Traditional interconnecting interfaces are quite complicated already. What if a
system consists of many interacting subsystems? Under these circumstances, the city-
suburb concept will not be adequate. Defining a subsystem in a web of interacting and
dynamical subsystems in system dynamics is as difficult as interesting. Modeling spatial
interaction is the ultimate challenge. In general, spatial distribution or sectional
distribution of activities is important and of common interest among modelers. In
transportation planning as well as in economic shift-share analyses and economic input-
output analyses, modeling distribution of activities over time is of common interest.
How can this easily be implemented in system dynamics? How can many urban areas
be implemented in urban dynamics? Controlling the complexity of spatial distributions
will be of vital importance.
Managing complexity: an example in system dynamics
Figure 5 shows a simple network system of eight entities (nodes). Each entity is
explicitly interconnected with every other entity in the network system. Every
connection between entities refers to a feedback loop. If each entity is interpreted as an
urban area in a network of interacting and dynamical communities, each area defines
and will be defined by conditions in every other area in the network system.
Figure 5 The network concept
Between n interconnected entities will be (n’-n) flows. Figure 5 shows 56
interactions (8-8), represented by 28 connections. Although this system seems to be
quite simple, managing all spatial flows in system dynamics with traditional interfaces
is unfeasible. This is why a new approach of modeling distribution in system dynamics
is necessary, which —more in general- would make it possible to implement different
kinds of interaction in system dynamics. This method will be demonstrated with an
example within the field of urban dynamics. Therefore the network concept as shown in
Figure 5 is considered to be a network of eight interconnected urban areas. How can
these urban areas best be modeled in system dynamics?
When modeling eight urban areas, copy and paste is the most straightforward way to
represent the multiple parallel urban model structures involved. Unfortunately, the
associated visual complexity of the resulting model diagram can become hard to
manage, both for the builder of the model and the user of the model. Arrays provide a
simple yet powerful mechanism for managing this visual complexity. By
"encapsulating" parallel model structures, arrays can help you to present the essence of
a situation in a simple diagram (HPS, 2001).
Separate urban model structures can best be implemented in system dynamics with
one-dimensional arrays. And how can spatial interaction between all areas be
implemented in system dynamics? This is possible with two-dimensional arrays, as will
be explained.
Modeling eight urban subsystems
In the example of Figure 5, each non-arrayed variable of a initially made visual
model structure of one urban sector is transformed into an one-dimensional arrayed
variable. The one-dimensional array’s dimension is named “area”. Within the dimension
area a set of eight elements is made, named: /,2,3,4,5,6,7, and 8. The equation logic for
each element within the array is to be defined in generic either uniquely. In this
approach, eight separate self-organizing systems are implemented in system dynamics,
visualized in one simple model diagram.
Modeling spatial interactions
Between eight urban areas, as mentioned before, 56 interacting flows must be taken
into account. For instance, people tend to migrate from one area to another if
opportunities are expected to be better in another area. In this example, all possible
households’ movements can be summed in a matrix, as shown in Figure 7. Diagonal
elements excepted, all elements in this matrix correspond to aggregated spatial
interaction or distribution (in this case migration). Two important questions are how to
define the equation logic of migration and how to implement this logic in system
dynamics.
The separate urban sectors (/,2,...8) describe migration in response to relative
attractiveness of the urban area compared with its external environment. Migration, in
turn, influences the composite attractiveness of the urban area for further migration. In
the example illustrated, the external environment of each urban area exists of seven
other urban areas, all dynamically related. How can these complex relationships be
managed?
Spatial distribution of migrants can be managed by implementing classical gravity
models into system dynamics. Gravity models are frequently employed in demography
and economics. Gravity models of migration assume that the flow of migrants between
two locations is proportional to the product of opportunities in both locations and is
inversely proportional to the distance between these locations raised to a decay power.
Mathematically, a simple relation of migration is analogous to the law of gravity:
_PO,
i DD
F,= 1\P,O,D,B} for example: FF (1)
Where:
Fj = flow of migration between area i and area j
P; = population of area i
O; = opportunities of area j
Dj, = distance between area i and area j
B =decay of distance
If O; in equation | represents a variable of production (such as total population) of
area i, and if O; represents the attractiveness of an area j (such as available houses or
available jobs), the gravity model depicts all households’ movements. The gravity
model assumes that most movements have destinations within the area of origin. Real
migration depends of destination area’s attractiveness and its accessibility. An attractive
area i nearby other areas j with less favorable conditions will attract many people, which
in turn influences the attractiveness of area i.
Urban changes can occur as a result of changes in both endogenous and exogenous
regional levels. As the gravity model functions as the interface between self-organizing
urban subsystems, urban interaction may affect the behavior and response of the whole
system. The network feedback idea is visualized in Figure 6. Figure 6 illustrates that all
elements are affecting each other simultaneously in time and space.
self-organizing
urban subsystems
gravity model
spatial
interaction:
distribution
NG t of migrants
Figure 6 Simultaneous interurban feedback process
© Population
© Jobs
© Houses
Equation | shows just a simple gravity model with a lot of drawbacks and
limitations. However, the correctness of the gravity model is not the major issue in this
chapter. The main goal of this chapter is to show how to implement a gravity model into
system dynamics.
As every variable with two indices correspond to a matrix, calculating with a gravity
model is nothing more then calculating with matrices. The gravity model of equation |
contains two matrices: matrix D (with all distances) and matrix F (with all migration
flows). Matrix F, with all origin-destination flows F;;, is visualized in Figure 7.
> > = arraysum (i, *)
i
v
>= arraysum(*, j)
Figure 7 Distribution matrix
As two-dimensional arrays have to be interpreted as matrices when written on paper,
all calculations with two-indices-variables can be implemented in system dynamics by
two-dimensional arrays. Therefore, the general argument discussed in this paper is that
every matrix-based calculation (either spatial or sectional) can be implemented in
system dynamics simply by two-dimensional arrays.
The gravity model as shown in equation | exists of exactly 5 variables: Fi, Pi, Oj,
Dj, and parameter f. All variables have to be implemented in system dynamics software,
for instance STELLA®. Where f is an universal parameter, Dj is a matrix containing
unique internally distances and unique interurban distances. Variables P; and O;
correspond to variables as defined in each urban sector. For instance, variable O; refers
to available jobs or available houses in area j. Finally, matrix Fy gives the migration
flows, which in turn influence the self-organizing urban areas. Figure 8 shows a system
dynamics diagram of the gravity model. Numbers in Figure 8 correspond to generic
logic, which will be explained.
calculated outmigration
Available Jobs or Houses
Figure 8 Spatial interaction diagrammed in system dynamics
Although the network system is quite complex, its diagram remains visually
remarkable simple and manageable. However, the complexity of the overall system
remains unchanged. Visually can’t be seen how many subsystems are defined, but there
may be over a hundred! By examining variables’ dimension and set of elements, the
system’s complexity can be estimated. It is clear though that both the builder and the
user of the model are supposed to have good understanding of the system as a whole
and need to have a good interpretation of arrays. If so, many possibilities will arise.
While defining variables into system dynamics, the big challenge is to avoid
invertible arrays. Moreover, creative avoiding and ‘fooling’ of arrays is absolutely
necessary to succeed in implementing spatial or sectional complexity in easy-to-use
system dynamics software.
Figure 8 shows how variables of urban model structures are input for the gravity
model. The urban model structures represent different rates of flows that cause system
levels to change. In the example visualized, the urban model structures are made by
transforming variables of one initially made urban model structure into one-arrayed
variables with dimension name 7. Eight elements are made within dimension name i.
Population, available jobs and houses are calculated uniquely for eight urban sectors.
Both population and available houses or jobs are levels that are inputs for the
gravity model, but they have a different dimension. As equation 1 shows the calculation
of Fy, the population P is dimensioned i while the opportunities O are dimensioned /. In
other words: people in urban area i look at opportunities in every area j. However, all
levels of the urban model structure are dimensioned i. The level of population is
dimensioned i already. The levels of opportunities, however, which are dimensioned i,
will have to be transformed in variables dimensioned j. Therefore, Figure 8 shows a
new variable ‘opportunities j’, which is dimensioned j, with all elements defined
manually. The matching transformation process in order to avoid invertible arrays is
visualized in Figure 9.
Available Jobs
output urban subsystems: or Houses [i]
array dimension i element | value
Available Jobs or Houses
input gravity model:
array dimension j
Orbe:
‘opportunities j
fo= |
|
=(
Wiley 1 [2 [3 [4 [sho [7] 8
cs EE Cy) t [eye
Figure 9 Manually transformation process of arrays
Imagine dimension 7 as rows and think of dimension j as columns, as shown in
Figure 7. Note that the transformation process of arrays is a manual task. Every row-
element in the variable of origin (dimensioned 7) has to be linked manually into the
referring column-element in the variable of destination (dimensioned /), as Figure 9
shows.
Matrices F;; and Dj; are implemented as double-arrayed variables with dimension i
(rows) and dimension j (columns), as to be matrices interpreted as in Figure 7. After Dy
is defined with real data-characteristics and parameter f is estimated, the generic logic
of the gravity model (equation 1) can be defined in variable Fj:
(Population[i]*opportunities_j[j])/Dij[ij/°B ))
As shown in Figure 7, column summation over eight rows (minus internal
migration) defines the amount of in-migrants of destination area 7, who move out of
other areas of origin 7 present in the network system (7 other areas). Row summation
over eight columns (minus internal migration) defines the total number out-migrants of
area of origin i, descended from other seven areas of destination j. These summations
can be made by the “‘arraysum-command”, which are made in the auxiliaries ‘calculated
inmigration’ and ‘calculated outmigration’ (Figure 8). The amount of in-migrants and
out-migrants have to be manually corrected for each area by diminishing the array
summations with the amount of internal movements. For example, the calculated
amount of in-migrants and out-migrants of area 5 are defined respectively:
ARRAYSUM(Fij[*,5])-Fij[5,5] (2)
ARRAYSUM(Fij[5,*])-Fij[5,5] (3)
In making it possible defining these calculations, invertible arrays must be avoided.
That is why the variable in which the arraysum-calculation is made must have the same
dimension as the dimension that is not summed within the calculation. Therefore, the
variable ‘calculated inmigration’ is dimensioned j. However, the feedback loop as
shown in Figure 6 is just complete when the calculated amounts of migrants define the
migration flows in the urban model structures. As these urban model structures are
dimensioned i, calculated in-migration has to be transformed into a_ variable
dimensioned i. Therefore i-dimensioned variable ‘inmigration i’ is made, which is
defined manually in a similar procedure as visualized in Figure 9, transforming in-
migration in an appropriate dimension.
Finally, in-migration flows and out-migration flows are defined with generic logic,
respectively:
inmigration_ifi] (4)
calculated_outmigration[i] (5)
A case study of Dutch spatial development
The network-concept illustrated is applicable to different kinds of systems in social
and economic science. In urban planning, complexity theory can be applied to a city and
its suburbs as well as to regional subsystems. The principle of multiple interacting self-
organizing systems has recently been applied in a large case study of The Netherlands.
The Dutch case study made is an attempt to understand spatial developments of
Dutch regions. For this, driving forces of regional developments are studied. This study,
initiated at Delft University of Technology at the department of Civil Engineering, has
an underlying goal in surveying the regional impacts of large infrastructure measures.
As it is widely accepted that transportation defines spatial development, planners of
infrastructure are very interested in the indirect spatial effects of infrastructure
measures. Moreover, large infrastructure investments aim at indirect spatial effects. At
this time Dutch politics investigate a very large investment in infrastructure. This
appealing project concerns realization of extremely fast and expensive railway
infrastructure (‘Transrapid’) in the West of The Netherlands, as will be explained. In
order to understand this project’s regional impacts, driving forces of regional changes
are captured in system dynamics (STELLA®).
40 Dutch regions
In order to understand spatial development of regions, the most important
interrelationships between economic and demographic aspects are of interest. Several
major internal forces control the balances of population, housing and firms within an
urban area. These forces go with several markets that can be distinguished, such as the
housing market, labor market and market for business structures. On the national level,
each market is segmented spatially as each market consists of a large number of
submarkets that are more or less independent of each other and, therefore, between
which interaction is limited. Neglect of this spatial segmentation leads to an
inappropriate understanding of markets phenomena (Rietveld, 1984). Therefore, the
regional dimension can best study market changes. The question rises, which is the best
spatial scale to describe regional economics and demographics.
As a department of the Ministry of Economic Affairs, Statistics Netherlands collects
statistics of different regional classifications. Statistics Netherlands distinguishes four
important regional classifications, which are: land parts (4), provinces (12), Corop-
regions (40), and municipalities (537). The statistical Corop-regions, designed in the
early seventies, originally account for self-organizing functional relationships within the
urban area as interregional flows such as migration and commuting are minimal. The 40
Corop-regions (Figure 10), therefore, integrate statistics used in urban planning and
socioeconomic planning. From a traditional point of view, the Corop-boundary would
be the best Dutch urban boundary in regional analysis. Therefore, the Corop-regions
have been applied in the Dutch case.
Figure 10 The Netherlands divided into 40 counties
(source: Statistics Netherlands)
Although the Corop-classification and its regional socioeconomic processes are
more or less independent of each other originally, interactions between Corop-regions
have intensified during history. Changes in regional attractiveness, due by changes in
regional accessibility amongst other developments, have intensified interregional flows
such as migration and commuting. Hence, in understanding regional change and indirect
spatial effects of infrastructure, interregional flows must be taken into account.
Case model overview
In capturing mechanisms underlying long-term evolution of urban areas, different
markets can be distinguished, as shown in Figure 11. Labor force and firms are
confronted with each other at the /abor market; people seek for housing at the housing
market and firms seek for accommodation at the market for business structures.
Demography of people as well as demography of firms are distinguished, which are
described by demographic concepts of birth, death and relocation. Principles of
relocation modeled are (1) internal migration of people due to labor market conditions,
(2) internal migration of people due to housing market conditions, (3) internal migration
of firms, and (4) internal commuting, as illustrated in Figure 12. Urban stakeholders’
behavior defines urban attractiveness and finally defines changes in urban Jand use.
job
Pf oa
os NN
firms ~ population
f ) \\
+
business structures housing
ilability availability
business h
structures 7 a jouses
- land .
availability
Figure 11 Renewed overall urban interactions
In this case, for a national centralized region (region ‘Utrecht’ for instance, as
defined by Corop 17 in Figure 10) the ‘problem of the urban boundary’ as well as the
‘problem of the limitless environment’ are strongly reduced. Hence, the approach
applied improves traditional urban dynamics approaches fundamentally.
Therefore, urban network analysis needs adjustment of fundamental principles of
urban dynamics. Especially the principle of relative attractiveness has to be renewed
compared with traditional approaches. Because on the Corop-level the Dutch
environment is modeled also, interaction with the limitless environment concerns only
cross-country flows such as immigration of foreigners and emigration to other
countries. Although cross-country flows of migration of people, cross-country migration
of firms, and cross-country commuting are modeled as in traditional urban dynamics,
cross-country flows are not significant with respect to nationally internal flows and
therefore do not detract the model from its renewed theoretical fundament.
Dutch internal flows are not only initiated within a closed system, flows within this
system are triggered by literal comparison of market conditions. An attractive region’s
power of attraction of migrants depends of other regions’ attractiveness. If other regions
are far more attractive, another —but less- attractive region’s net migration could even
decline. While the traditional concept of relative attractiveness is abstract, the renewed
principle of relative attractiveness is far more real. The renewed principle of relative
attractiveness is the exponent of the increased complexity of the urban dynamics model.
The renewed overall causal-loop diagram in Figure 11 illustrates the increased
complexity of urban dynamics, as it has been applied in the Dutch case.
The renewed principle of relative attractiveness concerns cross-boundary flows at
regional level. As can be derived from Figure 11, interregional migrations of people as
well as migration of firms and commuting are being calculated uniquely for every DT,
simultaneously with other self-organizing urban processes. In other words, 1600 flows
of migration of people, 1600 flows of migration of firms and 1600 flows of commuting
are taken into account as the system moves from one state to another, influencing many
self-organizing systems, which in turn influence spatial distributions again. As
illustrated in Figure 12, gravity models apply all spatial interactions.
40 self-organizing
urban subsystems
gravity models
© Population
¢ Labor force spatial interaction:
° Firms ¢ Residential migration of people
© Jobs ¢ Labor migration of people
© Houses ¢ Migration of firms
¢ Business structures ¢ Commuting
¢ Land use
Figure 12 Overview developed model structure
Interconnecting 40 urban models requires many entities in the software. As every
double-arrayed variable consists of 40 rows and 40 columns, every double-arrayed
variable consists of 1600 entities. As the amount of entities in the software is limited,
the model structure is made only as complicated as necessary. Moreover, a large
network model, by definition, has a broader focus than a traditional urban dynamics
model. Accordingly, neither sector of the network model need be as detailed as
traditional urban dynamics models. Hence, each urban sector is based upon an
aggregated urban dynamics model structure containing only a few levels, as shown in
Figure 12. Every urban sector of the network model should be fully consistent in
behavior with the traditional urban dynamics model though, but they operate at a higher
level of aggregation. The final causal-loop diagram of each urban sector is illustrated in
Figure 13. In fact, the total model developed exists of 40 causal-loop diagrams as shown
in Figure 13, all applied in one STELLA® model.
The case-model shows non-linear microscopic interactions that give rise to
macroscopic states of behavior. To understand this behavior, the interregional
processes’ theory must be clear. Because internal migration as well as internal
commuting is modeled, people (and therefore houses) and firms (and therefore jobs and
business structures) will relocate over regions in time. In extreme cases, functions can
drive out others, influencing distribution of socioeconomic functions eventually.
cross-country firm
business structures in ‘immigration
tht tiben acter + fiom
. in-migration usiness + business
gravity model inutioe tlre potential cx onsinction ~~ demolition
firm migration analy i otha a ania yt business ‘
f structures* ~~ |
| Ke —
firms in other relative business“ 7
WWomsccior: —satruchis avail land fraction occupied
" eucaares ayallebility by business structures
gravity model | ‘7
siscsersens ficonalaecommiling availability of
labor migration iy other urban sector -cciBil im ia
and commuting i ‘out-migration 4
labor force availability e + land fraction
outgoing commuting | 7 _ rf + ++ |
in other urban sector | abot force waiisiig allay
hemes aemalition
construction
resistance betweei i
\ availabilty 7,
urban sectors cross-country cross-country
incoming outgoing
| ‘ : \ Ve f
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| i ~~ \ || we + immigration
| elaunstien | job in
| urban sector aay \ \ NN
| — .
{ i potential residential heals in other
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| |
: |,
| | residential
\ If |
a al in-migration
| soasteas 7 Ss
\ other urban sector relative job outgoing Se
\ 4 {] availability ‘commuting \ | households housing relative housing housing availability in
\ i| NW t availability availability other urban sector
\ f° Hi 5 / _L_, “incoming births | __population deaths . a
} commuting z — — individualization f
labor force in other] (i A TAN\N Js
ubansector fl P ( [fh 7 \ {\ |
willingness to time distance “ residential tential residential
\ potential labor NTE between urban | out-migration ee oa Population in other
LZ
a
labor
* out-migration ,
gravity model
residential migration
|
\
distance between
someon potential labor
— in-migration /
commuting
emigration
Figure 13 Urban dynamics case
Interurban migration of people and commuting
Migration of population and commuting are closely related in reality as well as in
the model developed. As commuting is an alternative for migrating, an adequate
approach will have to take this interdependency into account. Therefore, migration is
segmented according to motivation. The model explicitly distinguishes migration due to
housing market conditions (residential migration) and migration due to labor market
conditions (labor migration). Only the latter is coherent with commuting in an aggregate
approach. This chapter only discusses migration due to labor market conditions and its
relation with commuting, because this defines -and makes it possible to study- spatial
distribution of population (houses) and jobs (business) in essence.
Model’s gravity formulation involving labor migration and commuting show how
many people from every area occupy jobs in their own area and in other areas.
Mathematically, the gravity model applied depicts how many people of area 7 occupy
jobs in areas j. Therefore, distribution of labor force of region i over jobs in regions j
depends of:
e Labor market attractiveness of region i
e Labor market attractiveness of other regions j
e Accessibility of region j in terms of time, money and trouble
Whether people commute or migrate due to labor market conditions, is defined by
travel time distance between areas in an aggregate approach. These relationships are
visualized in Figure 14 and Figure 15. The causal-loop diagram of Figure 14 shows how
labor in-migration and incoming commuting of every region is defined. Figure 15
shows the way labor out-migration and outgoing commuting is defined. Actually, these
Figures are visual illustrations of the gravity model used.
Te
labor force
-_
job
jobs in other availability \"
urban sector yesistance between + 4
\ urban sectors . 4 < aie?
\ _— jobs participation
job availability in relativejob + > Sincoming population
other urban sector - bility comuting.
+ " a \
4 distance between {
urban sectors + time distance
wilingness to
| 1 evel between urban
labor force in other ___ potential labor : sectors
ibaa coctor in-migration / incoming \
commuting e
+
labor _
in-migration
Figure 14 Urban labor-in-migration and incoming commuting
As Figure 14 and 15 show, the gravity model applied is quite complex in its causal
relationships. The mathematical definition of the gravity model, however, still is
manageable and gives perhaps a more comprehendible insight of the processes defined.
job labor force
\
jobs in other availability
urban sector resistance between ie
urban sectors 5 + labor
+ _f jobs participation
a {
job availability in relative job ___-» outgoing Spuaba:
other urban sector = availability ‘commuting, Pop'
wr | + ra
- distance between
turban sectors ce wilingness to time distance
. between urban
al f travel
labor force in other Hal labor sectors
urban sector out-migration / outgoing \
commuting +
labor
+ out-migration
Figure 15 Urban labor-out-migration and outgoing commuting
Social sciences distinguish within the decision-making process of migration two
important phases: (1) the desire to migrate and (2) the destination of migration.
Theoretically, people’s desire to migrate and their possible destination are closely
related as the presence of alternatives of destination plays an important role in the desire
to migrate. When people want to migrate, but other areas do not seem to inhibit more
opportunities, potential migrants do not migrate after all. To apply this process in urban
dynamics, the phenomenon of ‘potential migration’ has been taken into account.
First, a regions’ amount of people occupying jobs in other Dutch regions (pot-
OUTLF) is estimated (referring to ‘potential-phenomenon’) with a push factor of
internal employment conditions, as shown in equation 6. If these people really occupy
jobs in other regions still isn’t defined, as will be explained.
pot _OUTLF = Laborforce,* pct_OUTLF ;* AJM _OUTLF, (6)
Where:
pot_OUTLF; = potential amount of labor force of region i that occupy jobs in
other Dutch regions, based on internal employment conditions
in region i
Laborforce; = living labor force in region i
pet_OUTLF; = percentage of living labor force in region i that occupy jobs in
other Dutch regions, based on normal employment conditions
in region 7
AJM_OUTLF; = attractiveness-of-jobs multiplier, which is a push factor
regarding interregional job occupancy based on employment
conditions in region i
The coefficient pct-OUTLF defines a proportional relationship between the amount
of living labor force in an area and the amount of people in this labor force that occupy
jobs in other Dutch areas. Hence, a large labor force is assumed to generate possibly
large migration and/or commuting. Moreover, the percentage pct-OUTLF is
differentiated regionally, which takes account of different kinds of discrepancies in
regional labor markets (for instance, an area’s character of business).
The attractiveness-of-jobs multiplier 4JM_OUTLF modulates the rate of potential
out-migration and outgoing commuting in response to internal employment conditions.
This multiplier is defined in a multiplier table, as shown in Figure 16. When the labor-
force-to-job-ratio LFJR equals 1.0, employment conditions are supposed to be ‘normal’,
and the ‘normal’ out-migration and outgoing commuting takes place as defined by
equation 6 and the value of AJM_OUTLF.
The used ratio LFJR in Figure 16 represents a surrogate measure of many aspects of
internal employment conditions (Alfeld and Graham, 1976). Dividing the number of
persons in the labor force by the number of jobs gives the labor-force-to-job-ratio. An
LFJR value greater than 1.0 gives unfavorable employment conditions (a surplus of
labor over jobs) relative to normal conditions. Inversely, a value less than 1.0 indicates
favorable employment conditions relative to a normal period. When employment
conditions are not normal, the labor force may not correspond precisely to the actual
number of people seeking work, and jobs may not correspond precisely to the actual
number of employment positions in the urban sector. Consequently, the LFJR bears no
simple quantitative relationship to actual employment rates, as unemployment is only
one possible symptom of unfavorable employment conditions; other possible
manifestations of unfavorable employment conditions include low wages, reduced
overtime, a lack of promotions, slow hiring rates, and layoffs.
AJM OUTLF
0,5
LFJR
Figure 16 Attractiveness-of-jobs multiplier table AJM_OUTLF
As shown in Figure 16, unfavorable labor market conditions (indicated by a value of
LFJR greater than 1.0) stimulate potential labor out-migration (indicated by a value of
AJM_OUTLF greater than 1.0). the left side of the attractiveness-to-jobs multiplier table
depicts favorable employment conditions, representing the hypothesis that job
conditions are good and less people potentially tend to migrate or commute to an other
area.
The question rises how many people really occupy jobs outside the area, how many
people will commute, and how many people finally migrate due to labor market
conditions. Therefore, a gravity-model depicts all possible flows of labor between 40
Corop-regions. The distribution of labor-migrants and commuters of an area i over areas
J is defined by ‘indices of accessibility’ and ‘potentials of accessibility’.
A first estimation of potential labor-in-migrants and incoming commuting (pot-
INLF) of an area j, is derived from a pull factor of urban employment conditions in
urban sector j (equation 7). An attractiveness-of-jobs multiplier AJM_INLF represents
this pull factor, which is actually the inverse of Figure 16. Hence, under favorable
employment conditions the attractiveness-of-jobs multiplier AJM_INLF rises above 1.0
and stimulates the rate of potential in-migration and potential incoming commuting.
When the labor-force-to-job ratio LFJR rises above 1.0, job conditions worsen and
potential in-migration and potential incoming commuting will decline. As equation 7
defines, potential labor-in-migration and incoming commuting depend of the amount of
jobs in urban sector j, as every job is a potential opportunity for migrating or
commuting. The percentage pct-INLF, regionally differentiated due to different kinds of
discrepancies in regional labor markets, defines potential labor in-migration and
potential incoming commuting under normal employment conditions in urban area /.
pot _INLF j7Jobs ;* pct _INLF j AIM _INLF j (7)
Where:
pot_INLF; = potential amount of in-migrants or incoming commuters of
region j based on internal employment conditions in region j
Jobs; = amount of jobs in region j
pet_INLF; = measure of pull of potential labor in-migrants or incoming
commuting of region j, based on normal employment
conditions in region j
AJM_INLF; = attractiveness-of-jobs multiplier, which is a pull factor
regarding labor in-migrants and incoming commuting, based on
employment conditions in region j
The amount of people in area i who actually occupy jobs in regions j depends of
acquaintance with region j and employment conditions of region j relative to other
potential regions of destination. Distance is an sophisticated factor in the process of
migration and commuting. People are most familiar with local job market conditions
and people are likely to have friends and relatives in the neighborhood that can pass
along information about job opportunities within areas nearby. As people don’t give up
their social life easily, keep motives result in relatively much commuting over short
distances and labor migration over long distances. This phenomenon is described by
distance decay, as illustrated in Figure 17.
Figure 17 also illustrates that discontent about present living standards, possibly
resulting in migration or commuting, can be triggered by changing labor market
attractiveness between urban sectors as employment conditions in people’s present area
change or/and employment conditions in alternative areas change.
destination j
Figure 17 Derivation gravity model of labor migration and commuting
In mathematically defining the phenomenon illustrated in Figure 17, attractiveness’s
of regions of destination j -for labor out-migrants or outgoing commuters of region i-
are defined by indices of accessibility (BI_LFMC). Variable BI_LFMC; describes the
accessibility of inmigration’s/incommuting’s attractiveness of potential regions of
destination j for people of origin i, as defined in equation 8. Further, the value of
P_LFMC; defines the accessibility of a region’s environment for potential out-migrants
and outgoing commuters of region 7 (equation 9).
pot_INLF ,
BI_LFMC,-—~,, 4 efactor_LFMC,, (8)
P_LFMC,=¥.BI_LFMC,=> p
afi
Where:
BI_LFMC;
pot_INLF;
Dj
b,
ij
cfactor_LFMC;
P_LFMC;
ij
ot _INLF ,
——“ta (9)
Fi Di’
= index of accessibility for labor migration and commuting from
region / to region j
= potential amount of in-migrants or incoming commuters of
region j, based on internal employment conditions in region j
= average time traveling distance between region i and region j
(measure of acquaintance with region j for people in region i
= decay power of Dj (time, money and trouble of distance)
= factor that corrects correction labor flows from region i to
region j, which takes account of attractiveness of employment
conditions in region i relative to employment conditions in
region j
= potential of accessibility for labor out-migration or outgoing
commuting of region 7
Multiplier table cfactor_LFMC; modulates the complex relationship between the
desire to migrate or commute and rea/ migration or commuting. Multiplier table
cfactor_LFMC; shows the difference between labor market attractiveness between two
regions, as shown in Figure 18. Therefore, a region’s Dutch environment truly exists of
moving reference points.
cfactor_LFMC;
1 a ABM_INLF;— ABM_INLF;
Figure 18 Multiplier table cfactor_LFMC;
If employment conditions are unfavorable in region i, more people (relative to
normal employment conditions) want to occupy jobs in other regions based on internal
labor market conditions. But if employment conditions in other Dutch areas are
unfavorable also, perhaps not so many people want to occupy jobs in other regions after
all. Multiplier table cfactor_LFMC; modulates this phenomenon by affecting the values
of indices of accessibility BJ_LFMC; (equation 8). If employment conditions in other
areas are even far more unfavorable, employment conditions in region i will be
relatively favorable and an increasing labor migration and/or incoming commuting is to
be expected. The value of P_LFMC of this relatively favorable region will then be
relatively large with respect to other values of P_LFMC, as all indices of accessibility
BI_LFMC from i to j are stimulated. Finally, this will increase labor migration and/or
more incoming commuting, as migration and commuting are distributed by the relative
value of P_LFMC; in the sum of all values of P_LLFMC; (equation 10). This illustrates
how multiplier table cfactor_LFMC, regulates pull and push forces underlying labor-
migration and commuting.
If employment conditions seem to be favorable based on internal labor market
conditions, but other urban areas are even more favorable, people will be relatively
unsatisfied. The pull forces of other regions will attract migration and commuting
through by which many people want to occupy jobs in the area’s environment after all.
In this case, multiplier table cfactor_LFMC; will decline the particular value of
P_LFMC; (because all indices of accessibility BJ_LFMC from i to j are declined), and
will stimulate labor out-migration and outgoing commuting eventually (equation 10).
Equation 10 defines the actual distribution for which the gravity model is designed
originally. Equation 10 regulates the distribution of interregional job occupancy by the
relative value of P_LFMC; in the sum of all values of P_LFMC;,. As can be derived
from equation 10, a network’s central urban sector with relatively favorable
employment conditions will attract many labor migrants and commuters. This, in turn,
will influence employment conditions in this urban sector and will eventually decrease
in-migration and incoming commuting, modulated by a decreased relative value of
P_LFMC. By this, the gravity model functions as interface between 40 regions.
BI_LFMC,,
LFMC y* pot_OUTLF "5 Teac, (10)
Where:
LFMC; = direction of job occupation of labor force, based on relative
employment conditions
pot_OUTLF; = potential amount of labor force of region i that occupy jobs in
other Dutch regions, based on internal employment conditions
in region i
BI_LFMC,; = index of accessibility for labor migration and commuting from
region i to region j
P_LFMC; = potential of accessibility for labor out-migration or outgoing
commuting of region 7
People who occupy jobs outside their area of living have two options. They either
commute (then travel from their area of origin/living to their area of destination/work),
or they will migrate due to employment conditions. Therefore, the value of LFMC;
exists of two components: commuters (Commuters,) and migrants (LFM,). People of
region i who are not willing to commute to their work in an other urban sector, migrate
due to employment conditions in the model developed. When travel time distance is
little, many people will commute. However, even when travel time distance is little,
some people will migrate due to employment conditions, as job occupancy is coupled
with upward socioeconomic positions sometimes. As people get a better job, they
sometimes may allow a house more expensive. Therefore, migration due to employment
conditions over short distances always exists. However, if travel time distance between
two regions is very large, not only few people will occupy jobs in that other region, but
also few will travel between these regions as they will migrate.
The amount of interurban commuters in every direction between region i and region
/ is estimated with multiplier table pet_Commuting,, as defined in equation 11.
Commuting ;=LFMC .* pet_Commuting , (e8D)
Where:
Commuting = amount of commuters of region i to region j
LFMC,; = direction of job occupation of labor force, based on relative
employment conditions
pet_Commuting, = percentage of labor force in region 7, who work in region j and
still live in region i
Multiplier table pct_Commuting; modulates people’s behavior regarding travel time
distance in an aggregate way. Living far from work and working far from home are
phenomena modulated by the principle of Figure 19.
pet_Commuting;
A
1
| > travel time; — willingness to travel
0 I
critical value
Figure 19 Aggregate estimation of commuting in interurban labor flows
As Figure 19 shows, the x-axis contains two elements: (1) travel time distance, and
(2) willingness to travel (with respect to commuting). Together they define the value of
pct_Commuting;. For instance, when (average) travel time between two urban sectors is
approximately 15 minutes, while people have a willingness to travel of about 30
minutes, many people who occupy jobs in that particular other region are assumed to
commute. Because people do not have a problem with this traveling time, many people
will commute as pct_Commuting; is nearly one. As mentioned before, however, some
labor migration will exist, defined by the function not fully be | if (travel time;—
willingness to travel) equals 0. As (exaggerated) illustrated in Figure 19, a critical value
of (travel time;—willingness to travel) will result in a fast decrease of commuting, as less
people are willing to commute between regions.
Furthermore, the model posses universal trends in both travel time; and willingness
to travel, which in reality are variables that change in time. Technological developments
in the supply of transportation systems, among which faster conveyances and
infrastructure improvements, have lead to declining travel times. Willingness to travel
has changed due to changing willingness to pay for transportation costs, in terms of
budget, time and comfort.
After all commuting flows between regions are defined by equation 11, total
incoming commuting (JNC;) and outgoing commuting (OUTC)) can be derived from
variable Commuting; Equation 12 and equation 13 show how total incoming
commuting /NC; and outgoing commuting OUTC; are calculated. The principle of these
calculations has already been shown in Figure 7. Column summations and row
summations, reduced by internal flows of labor force, give final outgoing commuting
and final incoming commuting of each urban sector. Equation 12 shows outgoing
commuters of every urban sector of origin 7 who work in other urban sectors j. Equation
13 shows that in every urban sector of destination j, commuters can possibly be
expected from all other Dutch urban sectors.
OUTC =X Commuting ,- Commuting ,_, (12)
d
INC ;= XU Commuting ,- Commuting ,_, (13)
Where:
OUTC; = outgoing commuters of region i, based on relative employment
conditions
INC; = incoming commuters of region /, based on relative employment
conditions
Commutingiy = amount of commuters of region i to region j
Commuting;-; = amount of potential commuters who do not work in an other
region
People who occupy jobs in other regions, but who do not commute, will migrate due
to employment conditions. The direction and amount of labor migrants is defined by
equation 14.
LFM i -(LFMC; -Commuting , )* persons _ household , (14)
Where:
LFM; = amount of labor migrants from region i to regions j,
based on relative employment conditions
LFMC; = direction of job occupation of labor force, based on
relative employment conditions
Commuting = amount of commuters of region i to region j
persons_household; = average amount of people per household in region i
As equation 14 assumes, only whole households migrate. The approach is therefore
abstract, as in reality labor migrants do not have an average profile. Labor migration is,
for instance, very dependent of household size as parents with many children will not
migrate easily. Further, the average number of persons per household is assumed to
have declined due to individualization during history. Eventually, the total number of
labor out-migrants (LFOUTM)) and labor in-migrants (LFINM)) of each Dutch urban
sector is defined in equation 15 respectively equation 16.
LFOUTM ;= XLFM j- LFM j=; (15)
J
LFINM j= XLFM 4- LFM j=; (16)
Where:
LFOUTM, = amount of labor out-migrants of region i, based on relative
employment conditions;
LFINM; = amount of labor in-migrants of region j, based on relative
employment conditions;
LFMy = amount of labor migrants from region i to regions j, based on relative
employment conditions
LFM;-; = amount of potential labor migrants who do not leave their region of
origin 7
Case results and strategy
The model’s regional results are validated by regional statistics from 1972 until
1999. This relatively long period gives good opportunities for calibrating the model as
good as possible. Especially central regions in The Netherlands are interesting in this
respect, because the theoretical backgrounds of the approach applied are most strong
here. The ‘boundary-problem’ as well as the ‘problem of the limitless environment’ are
strongly reduced for central Dutch regions, as a central region’s Dutch environment is
modeled also, within a national closed system of internal flows.
For nationally central regions, for example Utrecht (Corop 17), good results were
made. Results of different levels, such as population and houses, show an average
estimation error of less than 3 percent. Underlying flows sometimes show results more
diffused. This is mainly caused by the model structure of the gravity models used.
Gravity models seem to have a rather robust character, as internal distances show to be
quite dominant. Therefore, differences in size of Corop-regions result in unbalanced
estimation errors. Overall results, however, are very acceptable.
Finally, the model developed is used in the field of transportation planning. The
model’s structure should be adequate to explore possible indirect spatial effects of large
infrastructure measurements. In this respect, an interesting topical project is the
realization of fast railway infrastructure (Transrapid) in the West of The Netherlands, as
shown in Figure 20. The West of The Netherlands, also called ‘Randstad’, is defined by
Corop-regions 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, and Corop 29 (Figure 10).
Figure 20 Planning of “Transrapid Randstad” in The Netherlands
(source: Consortium Transrapid Nederland)
The underlying idea of the “Transrapid Randstad” project is to accelerate
socioeconomic developments in the Randstad, so that the Randstad will improve
functioning as a metropolitan system. If so, the Randstad (about 6 million residents)
could become more competitive with international areas as for instance London (about 7
million residents) and Paris (about 9 million residents). How does the model developed
react on such a strategy?
The impact of the Transrapid project is simulated in the model by declining mutual
decay powers bj in the gravity models used between Corop-regions involved. This
simulates an increased internal accessibility of the Randstad regions, as supposed to be
realized. Further, a simulation gives insight of Transrapid’s effects of migration and
commuting, eventually resulting in indirect spatial effects. As Figure 21 shows,
Transrapid investments lead to increasing internal flows of labor in the Randstad,
illustrated by values of a performing index, which are greater than values of a reference
performance index.
14 Fe
112 A ——
——————
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
i Reference index of performance commuting Randstad
—® Transrapid index of performance commuting Randstad
Figure 21 Effect of internal commuting in experiment Transrapid Randstad
Figure 21 illustrates a Randstad’s labor market widened by infrastructure
measurements. Firms can recruit more easily by an increased labor force availability.
This is an important pull factor of firms, which will be attracted by the Randstad.
Further, economies of scale will result in more business activity, indicating an increased
job availability. Increased employment conditions will attract migrants from outside the
Randstad, by which not only more firms, but also more people will be concentrated in
the Randstad. Eventually, the experiment confirms the realization of a large Dutch
metropolis.
In the long term, however, diseconomies of scale limit urban growth. A particular
threat, as indicated by the model results, is threatening decline of labor force in the long
term. Declination of labor force threatens labor markets, partly caused by decreased
commuting flows. Further, spread-effects of people and firms to outside the Randstad
can possibly threaten the concentration of Randstad’s activities.
However, real indirect spatial effects of Transrapid Randstad are difficult to
estimate. A more sophisticated approach would be to implement changed travel time
distances in the gravity models more accurate. More accurate results would also demand
more socioeconomic detail of processes. The model developed is, consequently,
particularly of strategic value. More detail would enlarge tactical value, but would
demand stronger software capacities.
Conclusions
The model developed illustrates a large urban network of 40 interconnected urban
sectors. Hence, ‘boundary-problems’ in space and time, and the ‘problem of the
limitless environment’ are strongly reduced, as region’s Dutch environment is modeled
also within a national closed system of internal flows. Regional model structures remain
aggregated, however, as interregional flows are emphasized and software capacity limits
the amount of entities applied. In this case, the model structure is mainly of strategic
value in network analysis.
Setting up and designing the Dutch multiregional urban dynamics model was and is
to a large extent a pedagogic methodological exercise. Implementing large
disaggregated models in systems dynamics have proven to be an interesting challenge.
This paper discussed an innovative approach of managing complexity in system
dynamics, illustrated in the field of urban dynamics. The approach used, however, gives
many opportunities for modeling disaggregated systems in general.
Discussion
The making of the case-project gave some insightful relationships of managing
complexity in modeling large models in system dynamics, as portrayed in Figure 22.
- +
—f -
visual capability and model
complexity usefulness of model functionality
structure
+
+ +
Figure 22 Aspects of managing complexity
Disaggregating processes enlarges a model’s detail and (probably) its usefulness. In
urban dynamics, for instance, multiple urban sectors can be showed (capability), not
only approximating reality more accurate, but also generating more urban information
and enlarging the model’s usefulness with respect to policy analysis and decision-
making. However, functionality refers also to the phenomenon that models can become
too large in terms of entities allowed by software capacity and RAM (Random Access
Memory) needed, as models will not operate at all. As STELLA® can possibly contain
up to 32767 entities, kernel problems loom up if the modeler wants to exceed this
maximum amount of entities allowed. On the other hand, an increased model
functionality enables more opportunities in extending a model’s capabilities and
usefulness.
The left loop, as defined in Figure 22, illustrates relationships between visual
complexity and model capabilities. This loop shows an increased model structure
(increase of entities and relationships) will enlarge model’s visual complexity. Declined
surveyability makes it harder to comprehend model structure, so that model structures
will have to remain simpler than possibly desired. Processes will have to be aggregated
or eventually ignored, finally limiting the usefulness of system dynamics models.
As model structure limitation is defined by software and hardware capabilities, this
is not a modeler’s interest really. Enlarging model capabilities and its usefulness,
however, definitely are. Hence, this paper suggests opportunities of enlarging model
capabilities and its usefulness in system dynamics, as shown with the dotted graphic in
Figure 23.
usefulness
>
detail
Figure 23 Idea of enlarged usefulness of system dynamics modeling
Although model structures simulate efficiently by arrayed structures, software limits
model capabilities finally. However, limited detail can be overcome by new software
technology. Moreover, just as in old DYNAMO-series, three-dimensioned arrays will
increase model opportunities, as —if applied within the field of urban dynamics-
migration or commuting can be segmented.
Although the double-array approach is applied to urban dynamics and transportation
planning, the double-array approach’s usefulness may spread many academic fields and
its applications. The array-method applied enables matrix-based models (variables with
two indices) and vector-based models (variables with one index) —often calculations that
are made in software applications like Excel- to be implemented in system dynamics
easily, while model structures remain manageable and visually understandable.
Urban planning, transportation planning, as well as economic and financial
modeling for instance, can benefit from this approach in which all kinds of phenomena
can be studied dynamically. All kinds of network models, either spatial or sectional
interactions, can be studied with two-dimensional arrays. As traditional gravity models
can be implemented in system dynamics, also (double) constrained gravity models,
neural networks, logit-formulations, entropy maximizing models, input-output
formulations, and shift-share models for instance, easily can be studied dynamically in
system dynamics software environments.
As three-dimensional arrays would allow segmented spatial or sectional
relationships to be studied, four-dimensional arrays would account for spatial as well as
sectional analysis in system dynamics. Hence, new software technology will strengthen
system dynamics’ weaknesses. Together with its past strengths (easy-to-learn and easy-
to-use approach to modeling), this will stimulate system dynamics in general as hard
programming will become inconvenient more and more.
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