The General Conceptual Scheme
At the heart of the TOMM model is a theory of human
interaction, a general conceptual scheme used to explain
why households locate where they do. This theory is
based on the concept of social and economic gravity, the
notion that an employment and population center has
some sort of attractive force that pulls people to it de-
pending on its mass, or size, and distance away. The
analogy is with Newtonian physics, in which the force
of gravitational attraction between two bodies isdirectly
proportional to the product of their masses and inversely
proportional to the square of the distance between them.
One can conceive of many different forms this relation-
ship can take in explaining forces of social attraction.
The force itself, as measured by human interactions, can
take both physical and non-physical forms. Travel between
the places, shipment of goods and services, reciprocal
commercial transactions, and exchange of newspapers
and letters, are all forms of physical interaction, while
telephone calls and television and radio are forms of
non-physical interaction. The concept of urban concen-
tration, or mass, is also multi-factored, consisting of all
those economic, social and cultural activities that make
a city attractive. The concept of distance, in its full
meaning, must include the notion of accessibility, or the
time and cost involved in overcoming distance for the
purpose of human interaction.
The general conceptual scheme underlying the TOMM
model, then, postulates an attractive force influencing,
and thus measured by, all forms of interaction, and it
explains this force by urban concentration, or mass, and
the time-cost distance separating the centers of mass.
This is obviously too complex a scheme to serve directly
as the basis of a modeling effort. It must be reduced first
to a manageable set of relationships.
centroids, as though the total population and employment
of a tract were concentrated at a single point.
The Computer Program
When programming for a large and fast computer, espe-
cially given the specifically designed simulation languages
now available, this step of abstraction involves far less
violence to reality than the previous ones. TOMM is
programmed in FORTRAN IV, the language considered
most suitable to its form. Minor concessions to programming
can be mentioned. The distance function 1/r2, in the
model is approximated by a 150-segment piecewise linear
curve instead of a continuous curve. Time, although con-
tinuous, is grouped into discrete intervals of one or five
years. An error of 1/2 % is allowed in the convergence
of iterative solutions.
An overview of the abstraction process in TOMM can be
given with reference to the concept of accessibility, or
the time and cost of overcoming distance in human inter-
action, as shown in Figure 3.
We return now to our general discussion of verification
and validation of simulation models.
Airline Distance
Between Tract
Centers Rounded to
Nearest 1/2 Mile
Airline 2 Mile
Distance (Computer
Program)
Distance Model
Accessibility (Manageable
Relationship)
General
Scheme)
Real World
A Manageable Set of Relationships
In the TOMM model physical travel is taken as the sur-
rogate for all forms of human interaction and its means is
limited to the automobile. Since accessibility cannot be
measured directly, air-line distance is used as a poor but
measurable substitute. Basic employment and population
together are made to serve as the proxy for all economic,
social and cultural activity.
Population is aggregated into five classes, and employ-
ment into basic or secondary. All usable land isassumed
to be classifiable into four categories. The quality of the
assumptions underlying these aggregations will determine
their relevance. Without tests it is not really possible to
tell whether the process renders the study of these impor-
tant characteristics invalid. With these feats of abstrac-
tion the system to be modeled, although becoming rather
remote from reality, approaches manageability .
The Model
To achieve the model represented by the five equations
of the previous section it was found practically necessary
to restrict the measure of automobile travel to trips from
home to work and back and from home to shopping and
back. Air-line distance was defined as that between tract
Figure 3: Levels of Abstraction in Applying the
Concept of Accessibility in the TOMM Model
VERIFICATION AND VALIDATION OF URBAN
SIMULATION
Verification means the process of checking the abstract
system we have created for internal consistency to be sure
that no logical errors have been made in its structure and
that no essential relationships have been omitted or dis-
torted. This can be done by first examining each concept
or proposition and following it through the levels of ab-
straction, as we have done for accessibility in the pre-
ceding example of Figure 3, to see that the initial sense
has not been garbled or twisted. Next one can assemble
various combinations of related concepts and repeat the
ARCH8 2 (1969) H.8