Maurice Kilbridge, Jon Didrichsen 
ABSTRACTION, VERIFICATION AND VALIDATION IN 
URBAN SIMULATION 
The term "simulation", when used with reference to ab- 
stract models, has come to have two meanings. One has 
to do with the way in which the model is used as a sub- 
stitute or imitation of reality, while the other has to do 
with the structure of the model itself. When the latter 
meaning is taken, as it is in this paper, it serves to 
distinguish analytic models from simulation models on the 
basis of mathematical structure and tractability. Analytic 
models contain precise mathematical statements that can 
be solved - at least theoretically - by standard mathe- 
matical operations, while simulation models usually in- 
clude statements about relationships between elements 
which, though sufficiently clear and well structured for 
conversion to a computer program, may have no mathe- 
matical solution. 
A simulation model is a formalized abstract system with 
approximate rules that enables one to predict or describe 
reality within certain limits. The power of simulation 
rests in its ability to accept weak and inelegant theory - 
a class into which most urban theory now falls. Descrip- 
tive statements that can be reduced to the logic of a 
computer program can constitute the model. A realistic 
simulation model is one that comes as near to the system 
of reality as we can get; that is, the theories built into 
the model are valid assertions about the way in which 
reality behaves. 
Unlike the laboratory scientist, the urban planner can 
seldom manipulate the objects of his study to find their 
best arrangement or discover their natural properties or 
laws. The scales of cost and time are usually too large 
to allow experimentation with the physical elements of 
planning, and controlled experimentation with the social 
elements is rarely possible. By making a simulation model 
to represent urban functions, the planner can create an 
artificial envirönment for experimentation in which he 
can test hypotheses or try out alternative public policies 
and programs. 
LEVELS OF ABSTRACTION IN SIMULATION 
The development of a simulation model is an exercise in 
abstraction, the removal from the real world of those 
elements and relationships that are considered non-essen- 
tial to the.theory of the model and the retention of the 
essential. In urban simulation abstraction is achieved 
mostly through aggregation and by assumptions that narrow 
the range of situations. Aggregation is the grouping of 
particular phenomena which share an essential common 
characteristic into a single uniform set which is thereafter 
considered and used as an entity. In the illustrative simu- 
lation model presented later in this paper, the population 
of an urban area is aggregated into five classes, employ- 
ment into two, and land-use into six, thus reducing an 
uncountable number of possible combinations to a manage- 
able set. Abstraction by assumptions is achieved by 
constraining the real world system in order to eliminate 
uninteresting, irrelevant, or non-essential states of the 
system. 
With increasing abstraction the model becomes a more 
and more structured and manipulable way of thinking 
about real world phenomena, but it also becomes less 
applicable, in that it can no longer pertain to all cases 
at all times and under all circumstances. At some point 
the gain in managability will no longer outweigh the loss 
in applicability. 
The process of abstraction in the development of a simu- 
lation model forms a continuum with the real world at one 
&nd and a computer program at the other. To provide a 
systematic way of thinking about the process we will 
divide this continuum into four sections. Each is a de- 
finable and clearly conceived level of abstraction. Figure 
] depicts these levels as a staircase starting from the real 
world at the ground level, abstracting to a general con- 
ceptual scheme, a manageable set of relationships, a 
model and finally a computer program. We will now 
examine each of these levels in detail. 
From the Real World to a General Conceptual Scheme 
The general conceptual scheme is the total theory about 
how that sector of reality being modeled seems to behave, 
It contains both systematic and intuitional knowledge 
about relationships among elements of the city and tends 
to be somewhat vague, qualitative and comprehensive. In 
the illustrative simulation model to be described in the 
next section, the general conceptual scheme is based on 
the concept of gravity, the notion, deriving from an anal - 
ogy with Newtonian physics that people and economic 
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