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 
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