= 90 + ~ M98 =
‘Top-Down SYSTEMS ANALYSIS AND MODELING CxU EE C8 HOUR ORES
by . = ‘
F. RECHENMANN re Yore
I. ‘THE “START SIMPLE" PRINCIPLE 49g
Ecole Nationale Supérieure d'Informatique
et de Mathématiques Appliquéea (ENS-INAG) . II. BOPIOH-UP VERSUS TOP-LOWN 500
BP 53 ~ 38041 GRENOBLE-Cedex FRANCE ~ ILI. EVALUATION OF THE TYO STRATEGIES 50%
CONCLUSION 508
REFERENCES: * 508
APPENDIX 509
According to an implicit “start simple" principle widely accepted by
system dynamics practione ively increased
model's complexity must be progr
during the wodeling.process. How this increase in complexity should come .
about has yet to be explained.
In this paper, two strategies are discussed and evaluated. Since a 1
top-down strategy starts with a high level of aggregation but includes. in
the model atl the main variables since the first formulation, it is to be
preferred to a bottom-up scheme. Moreover, the top-down strategy ensures
the global coherence of the model at any stage of its conception and appears
to be much more consistent with the system dynamics philosophy.
This paper emphasizes the need for an adequate computer modeling language
and bricfly describes a first attempt. The main property of such a language” 8
is to allow a hierarchical description of models, where any composing unit ' .
can be altered without the need for a complete recompiling of the whole.
= 499 - = $00 -
1 THe "START SIMPLE" PRINCIPLE : | 2 + MOFTON-UP VERSUS TOP-DOW
The systems analysis and modeling process is, in its very nature, progres~ While following bottom-up strategy, the modeler first concentrates on
sive and iterative. Once the goals of the study ~ the questions to be ansvered ie Welt Aiioa oF GaapseO-nodel Gubaystads. Ne balleW- aud teste the Corresponding
by the model - have been stated, the analyst defines a first simple model submodel by feeding its inpute ~ the variables not defined by the submodel
which will be expanded when necessary. Every (1) ystems dynamics practioner but which intervene in its dynamics ~ with exogenous time series or with in- *
will agree on this start simple principle, but no precision has ever, been fornation supplied by an over-simple environment model. In the same way, he
given to the method of expanding the model. Although it is certainly impos~ =~ builds the other sub-models and, by making them interact, obtains a global
sible to settle precise rules, some general guidelines can be provided to ==” model which constitutes the upper level of a beginning hierarchical structure.
assist the system analyst.
y 7 On Figure 2, which visualizes such a process, all the interconnections
‘Relationships and variables are added to a model either because a class evecdivect, Chet LaccancoulputFionvalbow Li a-dleeciliaple B8 another ibos
of system phenomena have been neglected in the past, or because the level of Such is rarely the case in reality. An input to a box is generally obtained
aggregation appears too broad to satisfy the objectives. On the other hand, as a functional combination of other box outputs. These linkage equations
relationships are removed when they link variables which appear to have no coastielite the/dynintes’ of the new level,
influence on the dynamics of the whole or when they embody an unnecessary
_ fineness in the level of aggregation. As a direct consequence, the question
of gradual model's expansion is directly related to the problems of choice
The model obtained can itself be considered a submodel whose inputa
are all the variables which have not been internally defined and whose out
puts are all the variables supposed to feed into the other submodels now to
of variables and of the level of aggregation.
be connected. Each time a new level is constituted, the limits of the system
5 The aim of the guidelines presented here is to reduce as far as possible are widened. The process stops when, regarding the questions of interest, all
the number of removals or replacement of relationships. These alterations are the phenomena have been included. Clearly, however, this convergence is not
indeed very costly, since they generaly force the modeler to recompute the generally ensured.
corresponding data (parameters and initial values) and always necessitate
structural modifications of the model. All these manipulations consume, com
puter and analyst time without bringing further understanding.
On the other hand, a top-down strategy tends to include in the model atl
the relevant relations and variables as early as the firet formulation. In
order to keep with the “start-simple" principle, a very high initial level of
‘The guidelines take the form of a building strategy which explains how degiigatton To tiaulvequteed., Wdesd)-laclelGe Bie plisnowmdod’ Will fol. BalGome
to increase the complexity of a model. Two main options are available, bers pletely described. They will appear as black boxes whose outputs are in fact
of which make great use of the notions of sub-systems and sub-models. "Sub' Inputs for the present model level and participate in ite dynamics.
is the name given to any part (= set of variables and relations) of the
aystem and of the model under study. We shall formally represent such a part HIRIGESeE Eoesseiene! model, such outputs have to be fed with time-series
as a base supplied with inputs and outputs, as indicated in Figure 1. or with siuple equations, which will be replaced by more complete and detailed
> submodels when the current level of aggregation will appear to be insufficient.
At their turn, these submodels will be composed of equations which link black
boxes. Each. time a lower level is developed, the level of aggregation is redu~
pe oo faa oourpue ced, and the process continues until a satisfactory level of aggregation ia
variables variables F reached,
—_——> ————> -
Figure 1. Symbolic representation of sub-model or sub-system
a -tisiasincnenbinenaner-sapbe ie nncieammnaNY ~onetommutntes s en ed
> 5uR
TOP-DOWN
LEVEL
on
wo
$2 >
BOTTOM-UP
Fig.2
Boltor-up vs top-down
= 502 -
‘The top-down conceptioy does not inevitably imply modular design as we
J assumed up to nov. In practice, due more specifically to the lack of an ade-
quate computer modeling language, a new model will be reformulated each time
a black box is opened. A hierarchy of models is then obtained, instead of a
hierarchically structured unique model. Anyhow, the basic principles are
identical in both cases, although a modular design presents self evident
advantages concerning the reduction of the apparent complexity of the model,
Figure 3 sums up the presentation of the two strategies by showing the
trajectories followed by an analyst in an hypothetical two dimensions space
in either case, It is a highly simplified diagram since, in fact, the level
of aggregation and the Limit of the system are not each other independant.
Limits
of the * Top-down
syatem O wk
Bottom-up
| Level of
aggregation
Figure 3.
“Top-down and bottom-up strategies as trajectories in an hypothetical concep-
tion space".
Because of its apparent facility, most model makers have decided for a
bottom-up strategy, although their procedures are certainly not so schematic
it would appear from our description. However, a top-down analysis is much
more consistant with the systems approach, since at any level the emphasis
is on the interconnections rather than the very details of the phenomena in-
volved. Moreover, the global point of view has a central role from the begin~
ning. On the other hand, the use of a bottom-up strategy supposes that a mo~
deler can study a part without knowledge of its environment. Such an accom~
plishnent is not possible however without the trials and errors which every
modeler wants to reduce,
~ 503 ~
ILI - EVALUATION OF THE TWO*STRATEGIES
This evaluation will be conducted while detailing the various stages of
each strategy displayed in Figures 4 and 5.
When using a bottom-up scheme, the initial: problem is to fix a-priori
level of aggregation for each subsystem of the lowest level. This choice
may have several motivations. The analyst could want to disaggregate at a
given level because, for him, complexity and size of model are synonymous
with validity and scriousness. In the case of a demographic submodel for
instance, he may decide to take into account eighty age levels and thereby
hopes to increase his chances for a realistic model. Another motivation in
the choice of level of aggregation may be the availability of corresponding
data, The modeler rarely has at his disposal the necessary data without
transformation and he could be tempted to fit the structure of his model
to the available statistics.
Many other reasons can be involved in aggregation decisions, such as
personal knowledge and the available literature. The only valid rationale
of course is really wether or not ‘the level selected will allow to answer
the questions raised at the beginning of the study. But it cannot be denied
that all the reasons listed above intervene in practice. This intervention
is quite unavoidable when the choice must be made without knowledge of the
other parts of the model.
Suppose that all the submodels associated to a part of the system under
study have been built. This part of the system may have been defined in
various way. It may have been delimited according to a well defined disci-
pline : ecology, financial economics, demography and so on. In the case of
8 big project involving several subgroups, it can be simply the product of
overall planning. Then, the following step consists in linking the sub~
models to get a model of the superior level. The linkage equations define
the necessary outputs of each submodel and the inputs to the present global
model. Problems 8£ linkage coherence may (and probably will) then appear.
The modeler may recognize that one or more submodel is unable to provide
the information some other submodel needs. These findings necessitate a
reconsideration of submodels involved and the transformations of structure
thus implicd can be very important : they can affect both the level of ag-
eregation and the limits of the subsystems. The level of aggregation at
= 508 -
Figue@e 4,
BOTTOM-UP STRATEGY Return on the
submodels
_ Submodel
1 ei |
Independent. Independent Independent
test test test
Combination of the submodels =
writing of linkage equations =
definition of input/output variables
Problem of linkage Yes
coherence ? >
+ No
Test of the whole
Satisfactory 7? No ,
Yes
> “¢ Return on submodels
of any inferior level
Combination with other
‘submodels
Problems of linkage Yes
coherence ?
No
= 505 -
s given level is indeed heayily dependent on the precedent choices, even
after several iterations, unless the sodeler decides upon a complete refor~
mulation, as happens quite frequently while ‘using the bottom-up strategy-
In the other hand, the complexity of one or more of submodel may appear
useless for the anount of information needed by the other submodels of this
level. Although useless complexity does not by itself necessarily requires
reformulations and alterations, it can lead to a.much bigger model than ne~
cessary, with all the well-known consequences for subsequent understandings
and applications.
Moreover, errors of formulation may appear much later in the study where
they will have much more severe consequences when, for instance, work of se~
veral groups has -to be joined. To avoid trouble requires a level of inter~
coumunication which in practice is very difficult, if not impossible, to
tisfy.
In short, the confrontation between the emerging model and the goals of
been
the project generally occurs too late : many irrevocable choices |
already made. The result will be often a partial failure even if the final
report tries to say otherwise.
With a top-down strategy, the initial problem is quite the same as with
a‘bottoni-up approach. The analyst has to define a level of aggregation, but
this time the choice is easier and less decisive. As previously explained,
some subsystems are enclosed in black-boxes for which the level of aggrega~
tion will be established later. The present choice implics only the intey-
connections. Since the vhole system is under consideration from the begin-
ning, it is much easier to conciliate the level of aggregation with the
objectives of the study,
The model can be tested by using time-series to feed the outputs of the
submodels, which then are inputs for the present level. However, it is much
more efficient to use simple over-aggregated submodels instead, since then
feedbacks exist between the inputs and outputs of the boxes, making the test
more useful and realistic. *
The black boxes are opened -that is, their associated models are disag-
gregated~ when the dynamics of the whole apparently cannot be correctly re~
presented or the present wodel docs not provide the variables which could
answer the questions. In avy case, this disaggregation is greatly assisted
Figures -
TOP-DOWN STRATEGY
= 506 ~
Elaboration of the model ¢
of the whole system
Yes
Satisfactory regarding No
questions to answer ? }
Yes v
Test
v
Satisfactory regarding
its global behaviour ?
Vv
Return on
the inter-
connections
on current
level
No
Disaggregation = opening
of black boxes = writing
of the associated models
“HR ei.
- 507 -
by the previous definition pf the interconnections, which include the inputs
* and outputs of each submodel. The analyst has two guidelines at his ‘disposal +
the variables which must be used by the submodel, and the variables vhich
must be generated. The minimum level of aggregation is determined in this
way, and coherence with already defined parts of the whole madel is ensured.
The same argument helds when the analyst wishes to take advantage of exi:
ting generic submodels or dynamic structures. Strictly speaking, such a
But we are interested in
a violation of top-down principle
practice
developing guidelines, not rules; so variations have to be accepted. The
obvious danger in using generic structures lies in the temptation to force
the analysie and the model to fit the features of the structure which, in
fact, may have been defined in a totally different context. Such a danger
is considerably reduced in a top-down analysis aince the context of use of
any submodel is defined before the submodel itself.
The process will go down until disaggregation woses further merit.
Returns on previous levels will of course take place from time to time when
the constraints imposed by a superior level cannot be satisfied. In any
cases, they will be very limited in extension and number, because, in opposi-
tion to the bottom-up scheme, the analyst does not have to make a priori
choices and coherence of the whole is insured at any stage of conception,
Moreover, the complexity thereby obtained is certainly minimal, If
the modeler has disaggregated one submodel too far, he goes back too an
earlier less disaggregated version.
Finally, top-down analysis and modeling present some more practical
advantages concerning documentation and reliability of the project. If a
modular approach is conjointly used,the resulting model displays a hierar~
chical structure as shown in Figure 2, The documentation report can then
also follow a top-down procedure while describing the model. The émphasie
is put on the overall structure and assumptions of the model. The reader
has not to bother with very details if he does not want to or has no tine
for. OWviously, this reduction of apparent complexity comes also into play
during the modeling phase. Unfortunately, no computer modeling language
allows for structural de:
cviption in a suitable way. The software described
in the Appendix is a tentative realization in that direction.
: = 508 -
“The increased reliability of a project is directly related to the way
the model “is developed. With a top-down strategy, a working model exists at
any stage of the study. Coumunication between modeler’ and client -if any-
is therefore improved, The same with the modeler’ morale since the progress
in the project is much more apparent. Finally, if accidentally the project
budget i cut back or the deadlines cannot be respected, an operational and
complete, although simplified, model is nevertheless available.
CONCLUSION
The dop-down strategy and its associated computer language have been
applied: during the actual development of a urban regional model (4), The
project focuses on the dynamics of interurban migrations in response to
local employment variations. Although the goals are far from being attained
at the present time, a simple model already exists which allows the study
‘of the interurban linkage equations. At that level, each city involved is
modeled through elementary equations.
These models will be expanded only when a satisfactory formulation of
the current level will be retained.
REFERENCES
1) KARPLUS W.J., NILSEN R.N., 1974 : "Continuous Simulation Languages : A
State-of-the-art Survey", Annales de L*AIcA, n° I.
2) RECHENMANN F., 1974 : "A Continuous Simulation Language for Dynamic Space
distributed Models", UNESCO Second International Seminar on Trenda in
Mathematical Modelling, Jablona, Poland.
3) RECHENMANN F, Sept. 1975 : "Equations Sorting in Multilevel Structurel
Models", AICA International Symposium on Simulation Languages for
Dynamic Systems, London, England.
4) UIETTA P., Sept. 1976
a Multi-level Model", Ville Congrés Internation
gration Dynamics in Urban-Kegional Systems +
1 de Cybernétique,
me
Namur, Bel
= 509 -
APPENDIX
‘The need for an adequate computer language in the. context of modular top-
down modeling approach has been emphasized in this paper. Such a Language™
has been defincd and implemented. As it has been thoroughly described else~
where (2,3) and as its functional’ properties are similar to those of other
“continuous simulation" languages, this Appendix will only present its
truc~
tural propertics.
The description of the two modeling strategies has made great use of
the term submodel with the meaning of
art", In fact, two main types of
submodels can be distinguished which differ duc to their interpretation re~
garding the system, .
The aim of geographical partitioning of a model into regions is to allow
for spatial disparities. Each composing region ie considered an open system
in the sense that its frontiers are crossed by material flows, partly con~
trolled by its internal dynamics. The dynamics are described by an associated
model. Each region can in turn be divided into subregions so that the re~
sulting structure is a hierarchy, the levels of which are called geographical
levels. In the language, the same generic modél can be assigned to several
distinct regions, with different respective sets of coefficients.
Each mode} associated with a region consists of sectors. This division
has the aim of reducing model complexity and permitting a progressive top-
down construction. To cach sector, a list of inputs/outputs indicating the
logical connections with the other sectors is attached. Within a region, the
inputs or outputs of a sector which are not connected to other sectors cor-
respond to interregional relationships.
For example, the following text :
Sector S(B; C, F);
S1(B, Es B, G);
$2(G; ¢, 15
$3(A, Ds F, E)5
End 8;
defines the structure displayed in tho lover part of Figure 2. The description
of such a sector as $1 may be provided anywhere: in the text and can be used
* LADESIE: Langage de 0
viption de Systiny
= 510 -
several times as needed, with different sets of paramcter and initial volucs.
Each sector. description bari include declarations and relationships to other
sectors. This inclusion facility defines a’hierarchical structure which
coexists with the geographical hierarchy.
-The majority of present day simulation languages offer possibilities
of definition and insertion of macros, generally in a recursive manner (1).
Nevertheless, macros are not apt to encompass the type of structure described
above. First, macro mechanisms are generally hard to handle because of their
universality, For instance, parameters, initial values and tabulated func-
tions are associated to different macro calls (expansions) in a particularly
inflexible fashion.
