econometrically derived equations, whose parameters 
are fitted by statistical measurements, will be developed 
to describe the manner in which cities change over time. 
Since the fundamental concern is effective public policy, 
the project will emphasize analysis of those parameters 
which can be linked to available policy options. 
The concepts of systems theory have crept into our every- 
day thinking. Planners, and indeed the general public, 
no longer view slums simply as areas with dirty run-down 
buildings, but recognize them as complex interrelated 
systems of people, schools, housing, business and govern- 
ment, all with critical problems. To cope with this kind 
of system urban models undoubtedly will draw more upon 
the notion of feedback control theory, recognizing 
situations of positive feedback (vicious cycles) as well as 
negative-feedback (stabilizing influences). Already 
several projects are underway to build urban models more 
cognizant of the dynamic interactions between urban 
systems. 
In the next decade, the field of urban planning must 
assume the staggering simultaneous burden of developing 
its theoretical base while providing leadership and guid- 
ance as if that base were already full grown. We believe 
that analytic methods, and especially symbolic models, 
will prove invaluable both in the development of the 
theory on which increasingly effective action can be 
based, and as an aid to the decision-making which must 
oroceed concurrently if our cities are to flourish. 
(1) The Annotated Bibliography following this paper 
presents descriptions of the major urban models 
developed to date 
( 2) Items 2, 7, 12, 15, 16 und 21 of the Annotated 
Bibliography give reference to several types of 
gravity models 
(3) Items 9, 16 and 20 of the Annotated Bibliography 
refer to models employing this technique 
( 4) The most comprehensive simulation models devel- 
oped for urban planning are referred to in items 9, 
10, 13, 19 and 21 of the Annotated Bibliography 
(5) M. Kilbridge, R. O’Block, P. Teplitz, "A Con- 
ceptual Framework for Urban Planning Models", 
Management Science (Application Series), February 
1969 
( 6) See models referenced as items 3, 6, 7, 9, 10, 13, 
14, 15, 20 and 21 in the Annotated Bibliography 
( 7) See models referenced as items 2 and 3 in the 
Annotated Bibliography 
( 8) See models referenced as items 1, 3, 8, 9 and 17 
in the Annotated Bibliography 
( 9) See models referenced as items 1, 3, 8, 9, 12, 16 
and 17 in the Annotated Bibliography 
(10) U.S. Bureau of Census. Measuring the Quality of 
Housing: An Appraisal of Census Statistics and 
Methods. Working Paper 25, 1967 
(11) See e.g., Jack B. Ellis, Herman E. Koenig, & 
David N. Milstein, Physical Systems Analysis of 
Socio-Economic Situations, Michigan State Uni- 
versity, October 1964 
{12) By Professor Jay Forrester of the Sloan School of 
Management of the. Massachusetts Institute of 
Technology 
ANNOTATED BIBLIOGRAPHY OF URBAN MODELS 
Berman, Barbara R., Chinitz, Benjamin, and Hoover, 
Edgar M., Projection of a Metropolis, Cambridge, 
Harvard University Press, 1960 
New York City 
Input-output used to forecast for 1965, 1975, 1985 
employment, output, and value added by 43 industry 
classes. Demographic, employment and population 
Forecast made sequentially. Inputs, coefficients, 
Functional relations, industry classifications and output 
tables presented. 22 counties in New York Metropo- 
litan Region. 
Bevis, Howard W., "A Model for Predicting Urban 
Travel Patterns", Journal of the American Institute 
of Planners, Volume XXV, Number 2 (May 1959), 
pp. 87-89 
Gravity model and linear programming used experi- 
mentally to predict residential and nonresidential 
traffic volumes. "Travel functions" minimized subject 
to trips generated (using gravity concept) which must 
equal interchange volumes, which must be greater 
than or equal to zero. More powerful than simple 
gravity model trip projections. 
Brand, Daniel, Barber, Brian, and Jacobs, Michael, 
"A Systematic technique for Relating Transportation 
Improvements and Urban Development Patterns', 46th 
Annual Meeting of Highway Research Board, January 
1967 
Empiric Land Use Model 
Simultaneous equations (derived using regressing 
techniques) forecast activities (population and em- 
ployment characteristics, number of automobiles and 
school enrollments) for 626 traffic zones in Eastern 
Massachusetts. Fifty variables, data required, and 
model sequence presented. Accessibility theory im- 
plied 
Donnelly, Thomas G., Chapin, F. Stuart, Jr., and 
Weiss, Shirley F., A Probabilistic Model for Re- 
sidential Growth, Chapel Hill, North Carolina, 
Institute for Research in Social Science, May 1964 
This experimental model’ s regression equation deter- 
mines land "attractiveness", which is used to assign 
new residential locations (using random numbers) to 
land. Simplifying assumptions, inputs, specifications, 
orogram components and test results presented. 
Doxiadis, C.A., Emergence and Growth of an Urban 
Region, The Developing Urban Detroit Area, Vol. Il: 
Future Alternatives, Detroit, Detroit Edison Company, 
1967 
Distributes population on the basis of accessibility to 
employment. Projects and allocates transportation 
needs on the basis of population distribution. Methods 
are regression equations and other analytic forms. 
Graybeal, Ronald S., A Simulation Model of Resi- 
dential Development, Berkeley, California, Univer- 
sity of California, 1966 
New residential land development formulated, em- 
ploying user and space interaction, growth and re- 
sponse to policy (land use controls, transportation, 
etc.). Parameter definition, 18 equations, algorithm 
ARCH+ 2 (1969) H.8