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