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