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Before going into these questions of verification and validity we will describe very briefly a typical urban simulation model. By reference to it some of the more abstruse aspects of abstraction, verification and vali- dation can be discussed in a specific context. The mode! is not presented in its entirety; only the essential rela- tionships and those pertinent to the discussion of this paper are included. THE TOMM URBAN MODEL TOMM is a simulation model designed to forecast land use, population and employment in Pittsburgh and Allegheny County, Pennsylvania. Its original formulation is due to Lowry (1), a revised version was developed by Crecine (2), and a second revision by Teplitz (3). Through this process of evolution the initial letters "T.O.M.M. Pe standing for "Time Oriented Metropolitan Model", have lost their descriptive meaning as a title. In its latest form it has finally reached the stage of practical usefulness. Nothing in the model’s structure is unique to Pittsburgh; with some adaptation it can be applied to other cities as well. We will describe the TOMM model in terms of a concep- tual framework and paradigm developed for this purpose in an earlier paper (4). According to this framework, the basic elements of a planning model are its subject, func- tion, theory and method. Roughly speaking, the subject of the model is the entity or activity that is projected, allocated or manipulated by the model. The model’s function is to project or allocate the subject, or to derive new subjects. The theory of the model is the set of relationships, stated or implied, that is assumed to prevail between the subject and the larger environment. The method is the mathematical form used to carry out the projection, allocation or derivation. Subject of the TOMM Model The subjects of the TOMM model are land use, popula- tion and employment. The model divides the Pittsburgh metropolitan area into 160 land tracts. For each tract TOMM considers the population, measured by number of households, in each of five categories: high status, older couples, lower-middle class, transitional, and low status These categories derive from a factor-analysis grouping of census variables. TOMM recognizes two types of employment, roughly de- fined as "basic" and "secondary". All employment in manufacturing, plus corporate staffs, universities, and other "export" industries is considered basic. The product of this employment is assumed to leave the model area. All other employment, mostly commerce and trade, is considered secondary and is assumed to serve only the model area. The model assumes that basic employment is the driving force of population growth. The user of the model! provides externally derived projections of basic employment for each land tract. The model then calcu- lates the corresponding number of households by the five categories and projects secondary employment levels to give a balance between population and the two classes of employment. As the model adds or removes households and secondary employment tract by tract, it continvally makes proportional adjustments in land use under the categories of industrial, commercial, residential and vacant. Functions of the TOMM Model TOMM is an equilibrium model. It does not forecast or project, since it has no mechanism for causing employ- ment or population to change from year to year. Its functions are to derive from externally prepared projec- tions of basic employment the corresponding levels of population and secondary employment and to allocate these to 160 land tracts. The value of the TOMM model Tes in its ability to show how a given amount of assumed growth will be distributed among the land tracts of the region. The function of the model is thus to determine the patterns of growth rather than the amount of growth. Theory of the TOMM Model To allocate households throughout the metropolitan area TOMM must contain a theory of why people locate where they do. The theory used is simply that people locate so as to be near, or have accessible to them, a center of employment. This accessibility concept is expressed as the gravitational law that the residential attractiveness of a tract of land varies inversely with its distance from an employment center. The over-all attractiveness, then, of any land tract is the weighted average of its distances from all centers of employment. In mathematical terms this becomes: 60 E. —— i=] D.. ! (1) A. is the attractiveness of tract j, E.! is the total employment in tract i, D'.. is the distance between tract i and tract {, a '!is an exponent fitted from empirical data. where Having established the number of households allocated to each tract, the model now divides them into the five household types. Each type of household is assumed to have a preference value for each of the other types, so that its total preference for a tract is the weighted sum of its preferences for the households already living there, as given in the following equation: N = ak Wıp HH 2 @ N; „ is the number of households of type 1 7 in tract I N’ 1 is the number NJ, j during the previous 7 kime period, is the preference of household type 1, for household type k, fitted from historical data, is the total number of households allocated to tract |. where After adding or removing households in a tract, TOMM updates the residential land use in that tract. If vacant land is available, it is converted to residential use at ;he same average density as the existing residential land. ARCH+ 2 (1969) H.8