unrealistic to expect public officials to devote as much 
time to understanding the model as the professional 
planners. But they certainly can be introduced to its 
assumptions, theories, and limitations and the uses to 
which it can be put. 
TECHNIQUE: SOME SUGGESTIONS 
Models of Systems and Subsystems 
As a practical matter in the development of applied ur- 
ban models it is generally wise to start with independent 
submodels for the smallest functional units and later to 
combine these into larger models. The development of 
submodels allows a division of labor among specialists in 
various aspects of urban growth and change. For instance, 
one group can work on a traffic submodel while another 
group attacks an employment or housing submodel. In- 
dependently constructed submodels must be designed and 
built with great care so that ultimately they will be 
comparable and additive. The variables that connect the 
submodels merit special attention. Those that do not fit 
directly into any submodel are sometimes in danger of 
slipping through the cracks, never to be seen again. 
An inherent problem in the development of submodels is 
the maintenance of comparable quality across the sub- 
models. Some subjects - traffic analysis, for example - 
are more analytically advanced than others. Efforts have 
to be allocated among the tasks so as to bring the greatest 
incremental gain to the total model. 
The concept of marginal analysis can provide a way of 
considering systematically the costs and contributions of 
submodels, As far as possible, relative accuracy of the 
submodels should reflect their relative importance to the 
predictive process of the full model. 
An important consideration, of course, is the selection of 
subsystems sufficiently critical to warrant development of 
a submodel. Most of the remarks we have made about 
selection of factors and variables for inclusion in the 
model apply here as well. 
We should note that the decision is frequently made to 
include more variables for analytic purposes than will be 
necessary for prediction. Quite simply, it is easier and 
better to delete variables than to add them at some later 
date. Some may not be projectable, but still can be use- 
ful for analysis. 
Extending the Use of Urban Models 
It is somewhat premature to speculate on the extension of 
urban models to new applications when the areas to which 
they have been applied thus far - land use, transportation, 
population, economic activity - have been scarcely in- 
fluenced by the process. These are still the prime areas 
for applied urban models, and it is hoped that the second 
generation of models, now being developed, will be more 
useful than were their predecessors. 
Nevertheless, speculation on possible new areas of appli- 
cation brings to mind planning for recreational facilities 
(11). Different people have different needs, but we do 
not yet have a systematic way of analyzing or comparing 
them. Another application would be planning for the 
location of schools, particularly high schools or commu- 
nity colleges. The placement of such facilities is 
governed by multiple objectives, including accessibility, 
area development plans, and contribution to racial inte- 
gration. Rational evaluation of objectives such as these 
could be facilitated by application of planning models. 
Similarly, planning for the location of other city functions 
such as hospitals, parking facilities, airports, water and 
sewage treatment plants, and so forth, could well profit 
From the use of a model. Further applications might be 
possible in air and water pollution control programs, and 
in the development of urban indicators which could tell, 
on a continuing basis, what critical changes were taking 
place in various zones or neighborhoods of a city. 
Another potential use of models is for the evaluation of 
other models. Computer simulation, while certainly far 
less costly than real-world experimentation, is neverthe- 
less expensive. Complex and comprehensive models con- 
tain far too many variable and parameters to permit test 
of all reasonable combinations. One solution to this 
dilemma is to run a model for a few key input combina- 
tions, and use a second model to interpolate between 
those key points; that is, to study the difference between 
established objective and forecast. The latter model would 
contain only those variables vital to the test area. 
Some new modeling techniques are yet to be applied to 
urban models. For instance, Bayesian decision theory can 
be used for sequential planning decisions made under 
uncertainty and with limited information. A planner can 
assess a prior probability distribution of events, and use 
such a model to choose from among alternatives. After 
implementation of the plan or project, new data are 
gathered from which a posterior distribution of events 
is developed. This updated distribution gives the planner 
an indication of how accurate his original estimates were 
and form the basis for the second round of decisions. As 
this cycle is repeafed, the probability distribution should 
approach the actual distribution of events. The planner’s 
ability at prediction improves correspondinglv 
This approach could be quite valuable in a planningsitua- 
ton involving a housing project, where the reaction of 
the residents is not known. A planner would make initial 
estimates of the location, design and size which will be 
acceptable to the public. With these assessments he 
decides whether or not to initiate action, make efforts to 
acquire land and so forth. As the public is heard from, 
their reactions serve to modify the original assessments if 
necessary. The Bayesian approach, as illustrated here, 
presents a formal method for accumulation of knowledge 
and experience. Actual experience can be compared with 
predicted experience and the deviation used to determine 
subsequent action. 
Future models must pay closer attention to the dynamics 
of response to public programs, and to the intricate inter- 
connection between segments of our society. Even now, 
highway planners are becoming interested in short-term, 
transient effects of new roads, as well as long-termin 
impact. Similarly, most of the recent air and water pol- 
lution programs have concerned themselves with the 
timing and phasing of action. 
A current research project (12) is attempting the devel- 
opment of mathematical models to describe the macro- 
economic growth and decay of cities. The city is viewed 
as a-dynamic process susceptible to analysis by the classi- 
cal solution methods for differential eauations. A set of 
ARCH+ 2 (1969) H.8