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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 ARCH+ 2 (1969) H.8