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 ®