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 ®