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If vacant land is unavailable, the residential density in that tract will be increased, up to the limit allowed by the zoning regulations. Beyond that no further households will be added. TOMM applies several stability constraints, or rate-of- change limitations, when shifting households and land use. The model assumes that it would be unreasonable to have more than a certain fraction of the population move, or a certain percentage of the land converted from one use to another in a single time period. If the popu- lation or land use changes exceed these stability limits, they will be stopped. With all the households now in place, TOMM next adds the secondary employment needed to serve them. Agravi- tational rule, somewhat similar to that used in placing households, allocates secondary employment to each tract based on its distance from centers of population and employment. Each type of household has a different need for retail and other services, so the requirements of a tract will vary with its population size and type. The relationship is given as: 160 160 dB. + ie) 17 Ni P+P.-D +P. +0. 1 a On a 5 = i=1 (3) is the secondary employment required by tract ], is the employment (secondary + basic) in tract i, is the secondary employment required of household type 1, MG is the number of households of type 1 in ”” tract i, D.. is the distance between tract i and tract j, Pr P, are constants fitted from empirical data, P_’d where C, Method of the TOMM Model The method of the model is the iterative solution of the above set of nonlinear equations with their constraints. The model cycles through the program distributing and re- distributing secondary employment and households until equilibrium is reached. Using the paradigm developed in the paper previously referred to (4), the operation of the model is shown in Figure 2 Figure 2 TOMM Model Diagram External Projections Basic employment for each of 160 tracts Equation 5 5 Total households a Equations 1,2 and 3 Recycle Internally Househelds for each Output of 160 tracts Equations 4 and 6 Secondary employment for each of 160 tracts International Information -low Land use equations I Land use by type for each of 1l60o t+racts Output A clustering requirement is imposed on the number of secondary employees allocated to a tract. If the tract’s secondary employment falls below the number needed for a cluster, those employees are moved elsewhere, preven- ting the model from generating too diffuse adistribution of employment. Finally, TOMM seeks to maintain a balance between employment and population. The retail employment must be large enough to serve the population adequately, and the total population must be large enough to supply the specified number of basic and secondary workers. For this balance two conditions must be satisfied: HH = E + FC E=EB+HH BB (4) 5) Equation (4) is the requirement that the total number of households (HH) equal the total employment (E) times the number of households needed to supply one member of the labor force (FC). Equation (5) says simply that the total employment (E) equals basic employment (EB) plus the number of households (HH) times the number of secondary employees (B) needed to serve one household. LEVELS OF ABSTRACTION: ILLUSTRATIONS FROM THE TOMM MODEL We may now look back at our earlier discussion of the levels of abstraction and examine the process once more in the specific context of the TOMM model. The first step of abstraction is from the real world to a general concep- tual scheme. ARCH+ 2 (1969) H ®