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\THE DEVELOPMENT AND APPLICATION
OF A STATE ACTIVITY ALLOCATION MODEL/
by
Cathy Digges,Schlappi
Thesis Submitted to the Graduate Faculty of the
Virginia Polytechnic Institute and State University
in partial fulfillment of the requirements for the degree of
Master of Urban Affairs
APPROVED:
L. J. Simutis R. C. Stuart
Blacksburg, Virginia
November, 1974
ACKNOWLEDGMENTS
The design, programming and testing of the Statewide
Activity Allocation Model (SAAM) were funded by the Federal
Highway Administration (FHWA) Contract #DOT-FH-11-8131 with
Alan M. Voorhees & Associates, Inc. (AMV). I am indebted
to many persons who assisted me in this effort.
and of FHWA provided useful insights throughout
the design, implementation and report review stages.
and are AMV per-
sonnel who were especially supportive during this study. My
thanks also to of AMV who programmed and debugged
the SAAM under stringent time constraints.
I am especially grateful to at V .P .I.S.U.
who has provided helpful guidance in his review of this
thesis and all of my graduate work. My thanks to
and who are also serving as
V.P.I.S.U. advisors on my thesis committee.
In this project, as in all of my work, I am grateful to
my husband who has endured my late hours and travel
with commendable patience.
ii
TABLE OF CONTENTS
List of Figures
List of Tables
v
vi
Chapter
I
Page
INTRODUCTION . . • • . • . . • • . • . • • • • • • • . • • • • • . 1
A Framework for Classification of
Activity Allocation Procedures
Trend Analyses ...................... .
Econometric Models •••...•.•••••••••..
4
7
9
Probability-Based Models ...•••••.•••. 13
II THEORETICAL FOUNDATIONS OF THE
STATEWIDE ACTIVITY ALLOCATION MODEL 26
The Lowry Model ••••••••.••••.•.•••••• 26
British Contributions ••.•••.••••••••• 31
Other Contributions •.•.••••••••••.••• 34
Theoretical Problems ••••.•.•••••••••. 36
III THE STRUCTURE OF THE STATEWIDE
ACTIVITY ALLOCATION MODEL .••••.•••••••. 40
Definition of Non-Movers and Movers .• 40
Submode! I . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Submode! I I . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3
Submode! III . . . . . . . . . . . . . . . . . . . . . . . . . 44
Submode! IV • • • • • • • • • • • • • • • • • • • • • • • • • • 52
iii
TABLE OF CONTENTS (cont.)
IV CALIBRATION OF THE STATEWIDE ACTIVITY
ALLOCATION MODEL - CONNECTICUT ..••••.•• 54
Description of the Calibration Area •• 54
A Summary of Data Sources ••••••••.••• 56
The Definition of Primary and
Service Employment •••••••.••••••••••• 57
Input Data Requirements of Submodels
I-IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Calibration Results .•.•••.••••••••••• 71
Treatment of Externals •••••••••••.••• 84
V A SENSITIVITY TEST OF THE SAAM ...•••••• 89
VI
Test Case Transportation Inputs •••••. 89
Test Case Holding Capacity Inputs .••• 89
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
FORECASTING WITH THE SAAM 101
Input Data Requirements for Internal
Zones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Input Data Requirements for External
Zones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
VII CONCLUSIONS AND RECOMMENDATIONS •••••••• 112
REFERENCES . • • • • • • • • • • • • • • • • • • • • • • • • • • • • 121
APPENDIX A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VITA •..•••••••••••••••••••••••.••••••••
iv
123
127
Figure
1
2
3
4
5
LIST OF FIGURES
Page
The SAAM Heritage . . . • • . • • . . • • • • • . . • . . • . • • 27
The Lowry Model Allocation Process •••.••• 28
Structure of the Statewide Activity
Allocation Model •.•......••..••.•.•.••..• 41
Connecticut 141 Zonal System............. 55
The SAAM Submode ls . • . • • . • . . • . . . . . • • • • • . • . 5 9
6 A Graphical Representation of the
7
8
Percent Non-Movers Relationships .•.•••..• 74
Estimated Trip Length Distribution for
78 Non-Mover primary Labor Force •.......•.•.
Estimated Trip Length Distribution for
Non-Mover Retail Employment ....•.•.•.•... 79
9 Estimated Trip Length Distribution for
Non-Mover Services Employment............ 80
10
11
Connecticut External Zone System ....•....
Urban Development Opportunities and
86
Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2
12 Change in Population Density Versus Speed for
the Most Urbanized Connecticut Zones .•.•. 98
13 Change in Employment Density Versus Speed for
the Most Urbanized Connecticut Zones ..... 99
V·
Table
1
LIST OF TABLES
A Comparison of the Lowry Model and Its
Operational descendants •••••••••••••••• 30
2 The Non-Mover Primary Labor Force
Distribution Function . . . . . . . . . . . . . . . . . . 45
3 The Non-Mover Service Employment Demand
Distribution Function . . . . . . . . . . . . . . . . . . 46
4 The Mover Work-to-Home Distribution
Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5 The Mover Service Employment Demand
Distribution Function •••••••••••••••••• 49
6 Connecticut Primary and Service Employment
Definiti'ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
7 Suggested Independent Variables for
Submode! I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2
8 Submodel II Calibration Data .•••••••••• 63
9 Submodel III Calibration Data . . . . . . . . . . 67
10 Submodel IV Calibration and
Verification Data •••••••••••••••••••••• 70
11 1970 Percent Non-Mover Regression •••••• 73
l2 1970 Actual Versus Estimated Constrained
Population by County ••••••••.••...•..•• 81
13 1970 Actual Versus Estimated Employment
by County . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
vi
LIST OF TABLES (cont.)
14 Calibration Data Requirements -Connecticut Externals . . . . . . . . . . . . . . . . . . 88
15 Experimental Design for Sensitivity
Test of SAAM . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
16 A Comparison of Scenarios I-VI for
Selected Zones . . . . . . . . . . . . . . . . . . . . . . . . . 95
17 Input Requirements for a 1980 Forecast . 102
18 Input Requirements for a 1980 Forecast . 109
vii
CHAPTER I
INTRODUCTION
The impacts of a transportation system on activity
patterns and land use have traditionally been simulated by
urban activity allocation models. Since the early sixties,
these models have been useful as heuristic devices; and
more recently they have also been useful as policy-testing
tools.
The enthusiasm generated by comprehensive studies in-
volving the most complex urban activity allocation models!/
was dampened by the excessive cost and time required in
implementation. As a result, many of the most elaborate
activity allocation procedures never graduated beyond con-
ceptual or experimental stages.
On the other hand, developers of those urban activity
allocation models which have become operational have
adopted less ambitious goals. They have strived for a
balance between over-simplification of the activity sys-
terns to be modeled and overly-demanding data requirements.
1/ The Pittsburgh Urban Renewal Simulation Model, the San Francisco Community Renewal Model, and the South-eastern Wisconsin Regional Planning Commission Model. (JAIP, May 1965).
1
2
Models such as EMPIRIC, the Projective Land Use Model (PLUM),
and the Urban Systems Model (USM) have achieved this balance
and are currently being used to measure the impact of
alternative transportation and land use plans on the future 1/
location of urban activities.-
A recently completed survey sponsored by the National
Science Foundation revealed that 27 percent of the planning
agencies responding were either developing or using urban
models (35 percent of these had activity allocation models).
Furthermore, 68 percent of the urban models in use were
considered to be "very useful" by the agencies responding
(Pack, 1973). The results of this survey suggest that
urban models in general and activity allocation models in
particular are being applied increasingly in a policy
making context.
While most activity allocation modeling efforts have
focused on metropolitan regions, which are distinct economic
entities, a metropolitan region does not generally have a
governmental structure which is capable of effective policy
action. In contrast, a state has a well-defined political
u EMPIRIC, PLUM, and the USM are described in the next section.
3
structure for transportation and land use policy formulation
and implementation. A policy-sensitive activity allocation
model could perform a useful role in assisting decision-
makers at the state level by providing insights as to the
effects of transportation and land use policy changes.
The successful application of activity allocation models
as urban policy testing tools suggests that similar models
be considered for use at the state level. This approach has
been adopted in developing a state activity allocation model
for the Federal Highway Administration (FHWA) . The State-
wide Activity Allocation Model (SAAM), which is the product
of this study, is based upon an operational, policy-sensi-
tive urban model, which was selected by a formal evaluation
and screening process. A description of the models which
were evaluated is presented in the next section. The model
selection process is described elsewhere (Voorhees, 1973C).
The next chapter discusses the theory upon which the
Statewide Activity Allocation Model is based including a
description of the Lowry Model, British contributions,
mobility concepts and central place theory. Chapter III
contains an overview of the structure of the SAAM. Chapters
IV and v present the methodology and results of the cali-
bration and application of the SAAM for Connecticut.
4
Chapter VI addresses the data requirements for forecasting
with the SAAM. The final chapter describes study conclu-
sions and recommendations for use of the SAAM in other
states.
A FRA...l'.1EWORK FOR CLASSIFICATION OF ACTIVITY ALLOCATION
PROCEDURES
The proper framework for the organization of urban plan-
ning models has been discussed widely in recent literature
(See, for example, Kilbridge, O'Block, and Teplitz, 1969;
King, 1969; Lowry, 1968; Wilson, 1968). For the purposes
of selecting a statewide activity allocation model, the
simple classific~tion scheme suggested by Kilbridge, et.al.,
seems most appropriate. They maintain that models are most
conveniently classified by their subject, function, theory
and method. Because of the specialized requirements of
this study, the subject and function of the activity alloca-
tion model are predefined. However, the theory and method
of the Statewide Procedure have not yet been determined and
therefore provide a basis for organizing the models to be
considered.
Subject The subject of a model refers to the types of
output data it produces. In this case, the state activity
5
allocation model will produce, at a minimum, the activity,!!
socioeconomic, and land use input requirements for the FHWA
state transportation planning models. Specifically, these
data include population, non-agricultural employment, retail
employment, net residential density, auto ownership, and
median family income at the 141 zone level. The model may
also provide other residential profile characteristics,
including age of residents and household size.
Function The function of a model refers to the role
which it assumes in order to produce the desired data. Since
many states already utilize population and employment projec-
tion techniques such as Cohort-Survival and Input-Output,
this study is concerned only with the development of an
activity allocation procedure of activities within a state.
Therefore, the function of the selected model will be to
distribute regional activity levels to small areas and sub-
sequently to derive other land use and socioeconomic data
related to the activity distribution. In the terms of the
chosen organization framework, these are allocation and
derivation functions.
l/ Activity is defined as population and employment
6
Theory and Method Theory represents the body of principles
which have been established to explain urban phenomena.
Method refers to the type of mathematical technique used to
obtain the desired data. Theory and method are distinct cate-
gories in the Kilbridge, et. al., framework. However, theories
are often linked with the methodology of existing activity
allocation procedures. For example, operational Lowry models
are all characterized by similar non-linear mathematical al-
gorithms. Therefore, for the purposes of this evaluation,
theory and method will be considered simultaneously, and
methodology will provide the primary basis for grouping of
operational activity allocation models.
Three groups of activity allocation procedures have been
identified in the literature on the basis of methodology.
These are trend analyses, econometric models, and probability-
based models. The methodology of the first two groups is
directly related to the theoretical structure selected for the
model. That is, trend models assume that future activity is
based upon past levels of activity alone, while econometric
models assume that the relationship among urban development
factors may be determined empirically during the calibration
procedure. Most of the probability-based models are based
upon more rigid theories about the urban development process
and these theoretical considerations are addressed in the
discussion of each probability-based model.
7
The operational procedures which have been chosen as
possible candidates for statewide application are grouped
in the discussion which follows according to methodology.
TREND ANALYSES
Trend analyses incorporate methods for distributing
activity totals to small areas on the basis of extrapolated
or base year levels of activity. This type of methodology,
as currently used in the States of Illinois and Missouri,
assumes that future activity levels by small areas are
based solely on the base year distribution or recent trends.
A discussion of the Illinois and Missouri applications of
trend analysis techniques follows.
Illinois
H. L. Dwyer at Argonne National Laboratory has developed
a package of programs in conjunction with the Illinois River
Basin Pilot Project to forecast and allocate activities to
counties and municipalities in Illinois (Argonne National
Laboratory, 1973}. The program package description suggests
that the state should be divided into subregions consistent
with past growth trends, i.e., fast, stagnant, or indepen-
dent. Projections based on historical data for each activity
8
(stratified to the extent to which data are available) are
then made for each municipality, county, and subregion. The
procedure assumes that subregion projections are more
accurate than county and county are more accurate than
municipality. Therefore, normalization of county to sub-
region totals and municipality to county totals is performed
in pyramid fashion.
Missouri
The Missouri State Highway Department, in cooperation
with the University of Missouri at Columbia and the Bureau
of Public Roads, has applied a projection and allocation
methodology which utilizes a trend analysis technique
(Pinkerton, Campbell, and Harmston, 1968). As in Illinois,
counties are divided into distinct groups: metropolitan,
urban-rural, rural, and mining. Population projections are
made for counties by group and urban places with more than
10,000 population via a component method. This involves
the application of birth, death, and migration rates to
base year levels of population. These county and urban
place population projections are allocated to traffic zones
on the basis of the base year level of activity.
9
However, all projections and allocations are examined
for logic and consistency, and modifications are made
accordingly. Other activity data, such as employment by
type, are projected on a trend line basis by county or other
large area and allocated to zones on the basis of the fore-
cast year zonal population.
ECONOMETRIC MODELS
The econometric models examined in this report require
the solution of a simultaneous equation system to determine
future activity distributions. Such models are "theory-
laden" rather than "theory-based" in that they represent
loosely-structured, empirical statements about the phenomena
to be modeled (Kilbridge, et.al., 1969). The two econo-
metric models to be presented here are quite similar,
although EMPIRIC has been applied in many urban areas and
is more flexible than the model developed for Connecticut.
Connecticut
A differential shift model has been developed by Alan M.
Voorhees for application in Connecticut (Alan M. Voorhees,
1966). The simultaneous equation system which characterizes
the model may be expressed generally as:
D ij(t+l)
where:
Dij(t+l)
i
10
= bl I: Dij(t+l) + b2 Eij(t) + i
b3 '!: Eij(t) + b4 Aij(t) + i
b J 5 ij (t) Equation
= Differential shift of activity in town or zone j between base (t) and forecast (t+l) year
(1)
= Level of activity type i in town or zone j in base year
= Base year accessibility of town or zone j to activity of type i
= Base year holding capacity of town or zone j for activity of type i
= Population by income tertial or employ-ment by type
= Coefficients by type (may equal 0) deter-mined by two-stage least squares regres-sion technique
The differential shift obtained by solution of the
simultaneous equation system represents the change in fore-
cast year activity level relative to competition with other
11
towns (zones). This quantity is added to the proportional
share which the town (zone) receives of statewide growth,
where the proportional share in the forecast year may be
expressed as:
PS = ij (t+l)
where:
PS = ij(t+l)
E ij (t)
E j
E ij(t+l)
E E j ij (t)
E E j ij (t)
Equation (2)
proportional share of activity i held by town or zone j in the forecast year (t+l)
with all other definitions as above. Thus, the net change
in activity by type for a town or zone in the forecast year
is obtained by adding the proportional share to the dif-
ferential shift for each zone.
The model to allocate activity to 169 Connecticut towns
is composed of nine equations, corresponding to three income
groups and six employment types. A second model of a simi-
lar form with slightly different independent variables was
formulated to allocate activity from 169 towns to 804
traffic zones •. This zonal allocation model is composed of
three sets of five equations, representing population and
four employment types, where each equation set corresponds
to a town type: central city, suburban or other.
12
EMPIRIC
The EMPIRIC model developed by Traffic Research Corpora-
tion for the Boston Metropolitan Region has since been
applied in several American Cities (Peat, Marwick and Mitchell,
1972). It has undergone considerable revision since its ini-
tial application in Boston. However, the basic econometric
framework has remained intact. The EMPIRIC simultaneous
equation structure may be represented as follows:
AE .. l.J
where:
AE .• l.J
E .. l.J
AZlj
= Equation (3)
= Change in share of activity type i in zone j over forecast interval
= Change in share of activity type k in zone j (~ i) over forecast interval
= Base year share of activity i in zone j
= Change in share of policy variable 1 in zone j over forecast interval
Coefficients determined by two-stage least squares regression technique
The policy variables in Equation (3) include accessi-
bilities and holding capacities. Activities may be strati-
fied by 3-15 income groups and employment types. It follows
that the EMPIRIC simultaneous equation set forecasts the net
change in activity rather than the differential shift. This
marks the primary difference between the Connecticut and
EMPIRIC equation modules.
13
However, the EMPIRIC model is much broader than the
single simultaneous equation module. In fact, the EMPIRIC
program encompasses a land consumption submode! as well as
routines for projection of other socioeconomic variables.
EMPIRIC output may be stratified in a variety of ways, and
the program has extensive data manipulation capabilities.
These qualities of the EMPIRIC program package render it
more attractive in terms of general state utility than the
Connecticut model.
PROBABILITY-BASED MODELS
The term "probability-based" is a methodological umbrella
for a group of techniques which allocate activity to small
areas on the basis of zonal attractiveness probabilities.
These probabilities are composite indices representing land
use, travel, and socioeconomic characteristics. Only one of
the models to be discussed is actually stochastic; the other
models incorporate deterministic algorithms which assign
activities to small areas in direct proportion to the small
area attractiveness probabilities. The main modules of all
of the probability-based models may be formulated as follows:
A j
= A P(i,j) i
Equation (4)
where:
A j
A i
14
= level or increment of zone j activity
= level or increment of zone i activity
P(i,j) = an element of a vector of attraction proba-bilities based on travel times between zones i and j and/or the intrinsic attrac-tiveness of zone j; ~ P(i,j) = 1
i
The variables in the above equation are defined more
specifically in the discussion of each of the probability-
based models.
As noted in the foregoing discussion, the probability-
based models are grouped on the basis of methodology. How-
ever, these models diverge significantly on the basis of
theory. Three of the probability-based models have strong
theoretical structures: The Chapin-Weiss Residential Model,
the Projective Land Use Model, and the Urban Systems Model.
The first simulates the residential land conversion process,
while the latter models attempt to address location theory
in terms of market processes. The remaining two probability
based models, AVPALM and the Opportunity Accessibility Model,
have somewhat looser theoretical structures, governed pri-
marily by the non-linear formulation of Equation (4) and
the variable selection process.
15
AVPALM
• Method AVPALM is an incremental procedure available
in the TRIPS (Transportation Improvements Programming
System) package which allocates urban zonal activity,
land use, and travel characteristics (Alan M. Voorhees
1973B). The procedure also offers a holding capacity
constraints procedure so that policies related_ to
sewer system and some density restrictions may be in-
corporated into the allocation process. The procedure is
quite general and, therefore, may be used to allocate
activities other than population. From Equation (4), the
AVPALM algorithm may be defined as follows:
liA. J
where:
t.A. J
Et.A. . J J
O· .J
T .. l.J
= E flA. J
j I: j
0. T .. J l.J
O. T· · J l.J Equation (5)
= Change in population of zone j between base year and forecast year
= Regional population growth between base year and forecast year
= Attraction index (i.e., holding capacity x em-ployment) for zone j in base year
= Travel time factors between i and j in the forecast year
•
16
Theory AVPALM's theoretical structure is dictated by
the activity, attractiveness and policy factors which
are chosen as independent variables. Since these
variables may change for each application, the algorithm
serves as a non-linear framework in which variables in-
fluencing the distribution of urban activity may be
tested.
The Chapin-Weiss Residential Model
• Method The Chapin-Weiss Residential Model differs from
the other probability-based models in several respects.
First, it is a true probabilistic model in that discrete
units.of residential development are allocated to cells
via a randomizing procedure which is biased by cell
attractiveness indices (Chapin and Weiss, 1968). Secondly,
unlike the other models examined here, the Chapin-Weiss
model does not incorporate explicit measures of access-
ibility in the attractiveness indices. The initial value
of the attraction index is based on the assessed value
of a cell which only indirectly incorporates increased
attractiveness due to the accessibility of developable
land.
•
17
Although the Chapin-Weiss model is stochastic in nature,
it may be conveniently represented in terms of Equa-
tion (4) as follows:
6A· J
where:
6A. J
E 6A. j J
Q. J
j
= E Equation (6) j
= Number of residential units of 2.5 acres allo-.cated to eel+ j in a forecast time period
= Total number of residential units of 2.5 acres to be allocated in a forecast time period
= Cell j attraction index; defined as assessed land value in the time period and modified by priming actions, density and housing constraints in successive time periods
= An element of a vector which determines the number of residential units to be allocated to each cell j
= Cells of 23 acres
If n = the number of residential units to be allocated
in time period (t+l), then components of this (lxn)
vector may be represented as:
a . .::.J. n where: a. = O, 1, 2, ••. n and
J = 1.
Theory The Chapin-Weiss Model has been developed as a
simulation of the residential land conversion process
and is characterized by a tight theoretical structure.
18
The site and timing of new residential development
is determined by a random process which is biased by
attractiveness indices. These indices are based on
assessed value of developable land and the occurrence
of priming actions, such as the building of roads,
schools, etc. This approach presumes that units of
residential development will be more likely to locate in
the most attractive cells. However, since the residen-
tial land market forces are quite complex, the model
allows for the development of less attractive sites via
the random selection process. The model addresses the
differing economic circumstances and density prefer-
ences of households by stratifying developable land into
subdivided and open categories and by considering ten
density-value classes of residential development.
The Opportunity-Accessibility Model
• Method The Opportunity-Accessibility Model is a static
equilibrium model which distributes increments of
activity originating in zone i to all other zones on
the basis of an opportunity formula (Peat, Marwick and
Mitchell, 1973). The model has generally been used as a
transportation planning tool to distribute population
and employment among selected zones. Its formulation
•
19
is quite similar to that of PLUM and the USM, which are
discussed below, although its theoretical framework is
not as rigidly defined. From general Equation (4):
A .. l.J
where:
A .. l.J
o. J
0
e
Theory
= I: j
A .. l.J
-LO -L (O + OJ·) e -e Equation (7)
= Amount of activity i allocated to zone j in the forecast year
= Total amount of activity i to be allocated in the forecast year
= Probability of a unit of activity i locating at a given opportunity (expressed in terms
=
=
=
of land use variables such as vacant develop-able land or densities)
Number of opportunities in zone j in the forecast year
-Number of opportunities up to but not in-eluding j
Base of natural logarithm and is equal to 2.7123 •.•
The Opportunity-Accessibility Model presents an
opportunity formula framework for the allocation of ac-
tivities. The opportunity formula explicitly considers
the attractiveness of competing zones in the activity
allocation process. The opportunities themselves are
usually defined in terms of land use variables, such as
holding capacities, and the probabilities are derived via
an evaluation of the base year distribution of activities,
PLUM
20
the base year transportation network, and other base year
travel considerations.
• ,Method PLUM, or the Projective Land Use Model, a static
equilibrium model of the Lowry type, distributes popula-
tion and service employment to small areas on the basis
of the location of basic employment, small area attrac-
tion indices, and travel time probabilities (Goldner,
et. al., 1972). The service employment output of the
model may be disaggregated by as many as nine types, and
holding capacity constraints may be invoked to incorpor-
ate land use policies into the allocation process. In
addition, the model may be used in an incremental mode.
The PLUM program package has been subject to considerable·
modifications with each application and in its most recent
version, contains an implicit land use accounting proce-
dure and numerous subroutines for the derivation of socio-
economic data. The travel time probabilities in PLUM
are obtained by integrating a probability density function
over small time intervals. The form of the probability
density function has varied with its application.
21
The PLUM calibration process involves the selection of
travel parameters for the probability density function
using base year data.
The algorithm which represents the home-to-work and
home-to-service distribution processes in PLUM may be
expressed in terms of Equation (4) as:
1: i
A·. l.J
where:
1: A •. i l.J
A. l.
o. J
T{i,j)
= A· l. 1: j
o·. T (i, j) J 0. T (i, j)
J
Equation ( 8)
= Level of increment of activity (i.e., popu-lation or service employment) in zone j in forecast year
= ~evel or increment of activity (i.e., basic employment) in zone i in forecast year
= Attraction index (i.e., residential density time vacant developable land) specific to zone j in the base year
= Travel time probabilities of zone j deter-mined by a reciprocal transformation or log normal relationship representing travel between zones i and j in the forecast years
• Theory PLUM is characteristic of other Lowry-type models
in that it requires an exogenous allocation of basic
employment from which the model generates the location
of population and service employment. The location of
basic employment is considered to be an independent and
22
highly complex process which should be analyzed via an
economic base study of the urban area to be modeled.
However, once the allocation of basic industries has
been made, the model distributes basic employees to
homes with a work-to-home allocation function. The basic
employees and their families generate service demand
which is distributed using a home-to-service allocation
function. Service employees are distributed to homes
via the work-to-home function and the service demand
procedure is iterated until the population and service
employment control totals are reached.
Thus, the model hypothesizes that the primary influences
on residential location are basic and service employment
locations, work travel characteristics, and the intrinsic
attractiveness of the residential zone. Similarly, the
location of service employment is dependent upon the
location of basic employment, service center travel
characteristics, and the attractiveness of a zone as a
service center site.
The USM
• Method The USM, or Urban Systems Model, is a Lowry-
type static equilibrium model which produces the most
23
probable distribution of population and service employ-
ment under given travel and activity system constraints
(Alan M. Voorhees, Inc., 1972). A holding capacity con-
straints procedure is an integral part of the model
formulation.
The USM program package presently includes activity
evaluation measures such as market potential, accessi-
bility, and density indices. It also provides activity
measures such as air pollution exposure indices and
airport noise intensity levels, given the environmental
characteristics of the urban area.
The USM calibration process is a well-defined and rela-
tively simple procedure compared with those of other
Lowry-type models. It involves the comparison of the
trip length distribution curves produced by the model
with real world trip length distributions. The calibra-
tion parameters of the functions are modified until the
shape and mean value of the distribution approximate
the real world curves.
The algorithms which represent the work-to-home and
home and work-to-service center allocation functions
in the USM resemble Equation (4} :
•
where:
E A·. . 1J 1
A. 1
o. J
Theory
= A. 1.. E 0.
J j
24
-at .. 1J e Equation (9)
= Level of activity (i.e., population or ser-vice employment) in zone j in forecast year
= Level of activity (i.e., primary employment) in zone i in forecast year
= Attraction index (e.g., lagged residential f1oorspace) in zone j
= Measure of spatial separation between zones i and j
The USM is a typical Lowry model in the sense
that it allocates population and service employment to
small areas on the basis of an exogenously-supplied
distribution of primary (growth-generating) employment,
system travei characteristics, and small area attraction
indices. However, the USM is also a product of the
theoretical contributions of A. G. Wilson at the Centre
for Environmental Studies in London. Wilson has
approached the Lowry formulation from the viewpoint of
statistical mechanics and information theory and has
proven that the USM algorithm produces the most probable
distribution of trips subject to the conditions that all
origins locate destination zones and that the total
travel in the system is a known constant. Wilson has
further shown how the USM formulation relates to
25
transport, interregional commodity flow, and location
models, among others and how the model may be used
generally to disaggregate activity (by type) by mode
of travel (Wilson, 1970) .
As a result of an evaluation of the models summarized
above, the Urban Systems Model was chosen as the basis of
the Statewide Activity Allocation Model (Voorhees, 1973C).
The next chapter describes the theoretical foundations upon
which the statewide model was developed.
CHAPTER II
THEORETICAL FOUNDATIONS
OF THE STATEWIDE ACTIVITY ALLOCATION MODEL
As Figure 1 illustrates, the Statewide Activity Allo-
cation Model is a descendant of the model developed by Lowry
for the Pittsburgh Comprehensive Renewal Program (CRP) during
the period 1962-1964. However, the development of the SAAM
has also been strongly influenced by the work of Wilson at
the Centre for Environmental Studies in London. The most
important theoretical contributions to the State Activity
Allocation Model are discussed in the sections which follow.
THE LOWRY MODEL
The original Lowry model is based on a stratification
of employment into basic (export-oriented) and service
(population-serving) sectors and utilizes the allocation
process diagrammed in Figure 2. Given the exogenous speci-
fication of population and service employment control totals,
and a basic employment distribution, the Lowry model distri-
butes basic employees to their homes based on a work-to-
home allocation function. The basic employees and their
families generate a demand for services which is distributed
to their homes via the work-to-home function, and this
26
l TOMM (1964r
Crecine for Pittsburgh
TOMM II (19681 CrKlne for Metro Project
Univ. of Michigen
27
Figure 1 The SAAM 1-Jeritage
Lowry Model (19621 w/Rand for Pittsburgh
l BASS I '1965)
Goldner Ill Graybeal at Berkeley
! Gerin·Rogen
Contributions (19661
CLUG '19661 Feldt
Cornell
i~---1 PLUM (1968) Goldner for
S.n Francisco
A. G.Wilson Contributions (19691
at Center for Environmental Studi•, London
! Urben Systems Model 11972)
Alan M. Voorhees Ill Assoc.
! Statewide Activity
Allocation Model (1974) Alan M. Voorhees & Assoc.
BASIC EMPLOYMENT --
28
Figure 2. The Lowry Model Allocation Process
BASIC ---+ HOUSEHOLDS -·-·-·_..
SERVICE ----+ HOUSEHOLDS -·-·-· ... INCREMENT
SERVICE --· HOUSEHOLDS -·-·-·-+ INCREMENT
SERVICE -· HOUSEHOLDS -·---·--+ INCREMENT
~ - MINIMUM , - SIZE ~
THRESHOLDS ,~
~ -
KEY
- - - -+Work-to-Home Allocation Function
-· -· - ·+Home-To-Service Allocation Function
SERVICE EMPLOYMENT INCREMENT
SERVICE EMPLOYMENT INCREMENT
-
SERVICE EMPLOYMENT INCREMENT
SERVICE · EMPLOYMENT INCREMENT .
Total Households= Basic Households+ All Service Households Increments
Total Service Employment= Sum of Service Employment Increments
•
-
- -
29
procedure is iterated until the population and service
employment control totals are reached.
Subsequent theoretical and operational modifications to
the Lowry Model have not altered the operational sequence
nor the need to partition employment. However, many other
improvements have been added to the Lowry framework during
the last decade, and these changes may be classified in the
following manner:
• Treatment of the time dimension
• Degree of disaggregation
• Handling of development constraints
• Definition of areal units
• Type of allocation function
• Calibration and evaluation techniques
Table 1 presents a comparison of the original Lowry Model
and several of its operational successors including the
SAAM in terms of the above criteria.
Goldner has documented the pre-1970 theoretical and
operational revisions to the Lowry Model and the reader is
referred to his excellent discussion for a detailed descrip-
tion of these changes (Goldner, 1971).
Tre
abne
nt o
f th
e T
ime
Dim
ensi
on
Deg
ree
of A
ctiv
ity
Dis
aggr
egat
ion
Han
dlin
g of
Dev
elop
men
t C
onst
rain
ts
Def
init
ion
of A
real
Uni
te
(num
ber
of z
ones
by
appl
icat
ion)
Typ
e of
All
ocat
ion
Func
tion
W
ork-
to-h
ome:
Hom
e-to
-ser
vice
:
Tra
vel
Impe
danc
e V
alue
s
Cal
ibra
tion
Tec
hniq
ues
Sup
plem
enta
ry S
ubm
odel
e
1 So
urce
: L
owry
. 19
64
2 Sou
rce:
G
oldn
er.
et a
l..
1972
' Sou
rce:
V
oorh
ees.
197
2
TAB
LE 1
A C
OM
PARI
SON
OF
THE
LOW
RY M
OD
EL A
ND
IT
S O
PER
ATI
ON
AL
DES
CEN
DA
NTS
The
Low
ry M
odel
1
Stat
ic e
quil
ibri
um
"ins
tant
met
ropo
lie11
Ser
vice
em
ploy
men
t st
rati
fied
by
neig
hbor
hood
. lo
cal.
and
met
ropo
lita
n sh
oppi
ng
Ma.
xim
um p
opul
atio
n d
en
siJ
of 6
5 du
/acr
e. m
inim
um s
erp
ce
empl
oym
ent t
hres
hold
s by
typ
e of
sho
ppin
g co
mpl
ex
One
mil
e sq
uare
gri
ds
(456
-P
itts
burg
h)
Neg
ativ
e po
wer
fun
ctio
n
Fitt
ed q
uadr
atic
Air
line
dis
tanc
e
Em
piri
cal
eval
uati
on o
f ba
se y
ear
wor
k an
d sh
oppi
ng
trip
dis
trib
utio
ns
Non
e
PLU
M2
Com
para
tive
sta
tics
Ser
vice
em
ploy
men
t st
rati
fied
by
as m
any
as
9 SI
C t
ypes
Popu
lati
on a
nd s
ervi
ce
empl
oym
ent h
oldi
ng
capa
city
cei
ling
s
Cen
sus
trac
ts
(291
-Sa
n F
ranc
isco
) (6
63 -
San
Die
go)
Rec
ipro
cal
tran
sfor
mat
ion
in l
ogar
ithm
ic f
orm
Rec
ipro
cal
tran
sfor
mat
ion
in l
ogar
ithm
ic f
orm
Peak
and
off
-pea
k sk
im t
rees
in
clud
ing
term
inal
tim
es.
if a
vail
able
Coe
ffic
ient
s of
the
impe
danc
e fu
ncti
ons
equa
l th
e m
ode
of
wor
k or
sho
p tr
ip l
engt
h fr
eque
ncy
dist
ribu
tion
s
Lan
d us
e ac
coun
ting
pro
-ce
dure
. ho
useh
old
inco
me,
dw
elli
ng u
nit
valu
e. h
ousi
ng
stru
ctur
e ty
pe,
tax
reve
nue,
re
side
ntia
l de
nsit
y, s
tree
ts-
high
way
acr
eage
USM
'
Stat
ic e
quil
ibri
um
Non
e
Popu
lati
on a
nd s
ervi
ce
empl
oym
ent h
oldi
ng
capa
city
cei
ling
s
Tra
nspo
rtat
ion
zone
s/di
stri
cts
(504
-D
alla
s/F
ort W
orth
) (1
08 -
Bal
tim
ore)
(3
15 -
Kal
amaz
oo)
Neg
ativ
e ex
pone
ntia
l
Neg
ativ
e ex
pone
ntia
l
Pea
k an
d of
f-pe
ak s
kim
tre
es
(tim
e or
cos
t) ,
if a
vail
able
Coe
ffic
ient
s in
the
im
peda
nce
func
tion
s ar
e ca
libr
ated
on
regi
onal
tri
p le
ngth
cha
ract
eris
tics
Acc
essi
bili
ty,
mar
ket
pote
ntia
l an
d de
nsit
y in
dica
tors
. a
ir
poll
utio
n, n
oise
pol
luti
on,
inlr
a-st
ruct
ure
serv
ice
subm
odel
e.
SAA
M
Sem
i-dy
nam
ic;m
over
s an
d n
on-
mov
er t
reat
ed i
ndep
ende
ntly
ove
r ti
me
Ser
vice
em
ploy
men
t st
rati
fied
by
as m
any
as
5 SI
C t
ypes
Popu
lati
on h
oldi
ng c
apac
ity
ceil
ings
; ce
ntra
l pl
ace
fact
ors
form
min
imum
ser
vice
em
ploy
men
t le
vels
Min
or c
ivil
div
isio
ns w
ith
sepa
rate
zo
nes
for
urba
n ar
eas
(rec
omm
ende
d)
(159
-C
onne
ctic
ut)
Neg
ativ
e E
xpon
enti
al
Neg
ativ
elE
xpon
enti
al
Peak
and
off
-pea
k sk
im t
rees
(t
ime
or c
ost)
if
avai
labl
e
Coe
ffic
ient
s in
the
im
peda
nce
func
tion
s ar
e ca
libr
ated
on
stat
e tr
ip l
engt
h ch
arac
teri
stic
s
Net
res
iden
tial
den
sity
, m
edia
n fa
mil
y in
com
e. a
uto
owne
rshi
p.
and
labo
r fo
rce
' w
0
31
The effect which the development and documentation of
the Lowry framework has had on subsequent land use modeling
efforts may not be understated. The model spawned a line of
successors with meaningful improvements, because:
"firstly, the model is probably the most general of all the models proposed to date, linking to-gether the major subsystems of the city system; and secondly, the model explicitly deals with the interactions between these subsystems " (Batty, 19 7 2).
The first major change to the basic Lowry Model frame-
work occurred in 1966 when Garin developed a matrix solution
method to replace the iterative process of Figure 2. This
change assured an immediate, deterministic solution of the
work-to-home and home-to-service allocation functions
(Garin, 1966).
BRITISH CONTRIBUTIONS
Since 1967, British researchers have been developing
and testing Lowry-type mod~ls for towns and subregions in
England. (Batty, 1972) Due to the large number of Lowry-
type models which are actually operational in Englana11, these
1/ At the subregional scale, models are in operation for: Bedforshire, Central Lancashire, Merseyside, Nottingham-shire-Derbyshire, and Severnside; at the town scale for: Cambridge, Stevenage, Hook, Milton Keynes, and Reading.
32
researchers have been able to test many refinements to the
basic model, including those proposed by Wilson at the Centre
for Environmental Studies in London.
He has approached the Lowry foundation from the viewpoint
of entropy-maximization and has developed a conceptual frame-
work which provides the most probable distribution of activity
under given locational and cost constraints 21 (Wilson, 1970).
Both the Urban Systems Model (USM) and the SAAM have adopted
Wilson's entropy-maximizing approach to activity allocation.
In addition, Wilson has proposed other refinements to
the activity allocation process, including the partitioning
of population into movers and non-movers prior to activity
distribution. This concept has been operationalized in the
SAAM and is discussed more fully below.
Concepts of Residential Mobility
The Lowry Model and its descendants are static equi-
librium models which allocate state population and employment
2/ Wilson has shown that the SAAM allocation functions (Tables 2-5) will produce the most probable distribution of trips if the destinations equal the origins and the mean trip length of the trip distribution is known.
33
levels to small areas at one point in time. A static
equilibrium approach is less realistic than a dynamic one
in which changes over time are considered explicitly.
However, dynamic models require time series data which is
often difficult to obtain, while static models require more
easily accessed cross-sectional data and are generally easier
to calibrate and apply.
The primary criticism of the static equilibrium or
"instant metropolis" approach has been that residents and
industries do not make locational decisions as a collective
body on the basis of a single set of base year conditions.
Rather, discrete locational decisions are made continuously
over the ten year interval on the basis of socioeconomic
and accessibility considerations.
In order to retain the advantages of the static Lowry
model, while increasing its theoretical validity, small
area population has been stratified into two groups in the
SAAM; movers and non-movers. Non-movers are those persons
in a small area who have not changed residence during the
preceding ten year interval, while movers represent all
those persons in the state who have moved into or within
the state during the ten year interval. The movers are
allocated to small areas by the SAAM in the traditional
34
static equilibrium manner and the non-movers are estimated
in a separate process. The advantage of this approach is
that it separates the non-movers (stock) from the movers
(flow) and allocates only the mobile segment of the state
population on the basis of activity, accessibility and
income levels in the base year.
OTHER CONTRIBUTIONS
In addition to the Lowry framework and the modifications
suggested by Wilson, the structure of the SAAM has been in-
fluenced by the tenets of Central Place Theory (See for
example, Smith, et. al., 1968; Berry, 1967). Central Place
Theory maintains that there is a continuum or hierarchy of
service activity centers within an economic region, and this
hierarchy is dependent upon the size of the center, the income
of the consumer, and perceived distance to the service center.
Central place concepts are integrated into the SAAM
service employment demand allocation functions (Tables
3 and 5). These functions distribute service employees to
service centers on the basis of the distance between the
consumer (population and basic employment) and the potential
service center and on the basis of the size of the service
35
center (base year service employment) • The income of the
consumer is also explicitly considered in the SAAM alloca-
tion of service employment if a cost skim tree (area to area
travel cost matrix) is input to the model.
In addition, Central Place Theory has influenced the
definition of minimum service employment levels in the SAAM.
When the zonal system in a state is designed as suggested in
Chapter VII, with important activity centers defined as
separate zones, the hierarchy of central places in a state
may be maintained by applying central place factors to the
service employment allocation process. The SAAM provides
the capability to input central place factors (expressed
in terms of service employment per person by small area)
which is multiplied by the small area population forecasts
to produce minimum service employment levels for designated
small areas. The central place factors for forecast years
may be derived from a statistical relationship between the
central place factor and activity center ranking indices
by small area. If ranking indices such as population, em-
ployment, and median family income are used in the rela-
tionship, then the forecasting of central place factors
may be based on previous output of the SAA.~.
36
THEORETICAL PROBLEMS
Despite the many improvements which have been added to
the SAAM, the model has two problems which must be resolved
in the calibration process. These are common to all Lowry-
type models:
• The definition of basic (primary) versus service employment
• The distribution of basic (primary) employment for the forecast years.
The Partitioning of Employment
Basic and service employment are defined somewhat
differently in the USM and SAAM than in the original Lowry
Model. Basic employment which, in an input-output sense,
refers to export-oriented industries is called primary
employment in the SAAM. Primary employment in the USM and
SAAM contains "growth-generating" employment sectors including
"export-oriented activities, unique-locating activities,
import-saving activities and other local market activities
which influence the overall study area rate of economic
growth " (Voorhees, 1972). The service sector is defined
as the remaining economic activities.
37
These definitions for primary and service employment are
not easily represented in terms of the Standard Industrial
Classification (SIC) system upon which most employment data
are based. For example, large hotels and hospitals may
actually perform "growth-generating" economic functions,
although they are "services" by SIC definition. Such prob-
lems are most evident when the activity allocation procedure
is conducted on a highly disaggregated spatial scale. There-
fore, users of the SAAM must be especially careful in par-
titioning primary and service employment for smaller zones
which define important activity centers.
The Forecasting of Primary Employment
A second difficult problem in all Lowry-type models is
the forecasting of primary employment by small area. This
forecast is accomplished outside of the main allocation
submodels, and it is generally assumed that an economic base
study will provide the necessary background for such a fore-
cast. However, several problems are evident with this
approach. First, despite the theory to the contrary, pri-
mary employment location is influenced by the location of
population and services. That is, primary employment is not
solely site-oriented with respect to the location of popula-
tion and service employment, but receives feedback from the
38
location of these activities. Second, an economic base
analysis will not provide information as to the effect of
alternative transportation and land use policies on the
location of growth-generating employment. Since policy-
testing is an important consideration in a state's use of
the SAAM, policy-sensitive variables should be considered
in the primary employment allocation process.
Although the problem of forecasting primary employment
loc·ation is a difficult one, Chapter VI presents a policy-
sensi tive technique which is responsive to the level of
population and service employment in a small area for a
previous point in time (lagged level) . This technique has
not been tested, however, and it is hoped that users of the
SAAM will apply such an approach in developing primary
employment input for the forecast years.
In summary, the SAAM is a Lowry-type model which has
incorporated the entropy-maximizing framework and a mover/
non-mover stratification scheme proposed by Wilson. The
major drawbacks to the SAAM involve the difficulty in
partitioning primary and service employment and the lack
of a tested, policy-sensitive procedure for forecasting the
location of primary employment. At the same time the most
important assets of the SAAM are its strong theoretical
39
heritage, the proven operationality of similar urban develop-
ment models, and the meaningful improvements which have been
added to its structure.
The next chapter provides an overview of the structure
of the Statewide Activity Allocation Model, including a flow-
chart of the four component submodels and the mathematical
form of the four SAAM allocation functions.
CHAPTER III
THE STRUCTURE OF THE STATEWIDE ACTIVITY ALLOCATION MODEL
The essential objective of the first three submodels of
the Statewide Activity Allocation Model (SAAM) illustrated
in Figure 3 is to project small area!/ levels of population
and service employment associated with alternative state
land use and environmental/transportation policies. On the
basis of the projected levels of population and employment,
the last submodel derives small area estimates of net resi-
dential density, median family income, auto ownership and
labor force. The general structure of the SAAM and the
function of each of the four SAAM submodels is summarized
in Figure 3. The terms "movers" and 'hon-movers" used
throughout the description of the SAAM are defined in the
section which follows.
DEFINITION OF NON-MOVERS AND MOVERS
The term "non-movers" is synonymous with "non-mover
population" and refers to the number of persons in a small
area who have remained at the same residence during the
1/ Small areas may be defined as traffic zones, minor civil divisions or groups of traffic zones or minor civil divisions. The SAAM is capable of handling up to 1000 small areas.
40
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42
preceding ten year interval. Non-movers in a small area are
treated as a population cohort; the size of the cohort at
the end of the ten year interval is determined by a regres-
sion relationship involving base year population character-
istics of the small area.
On the other hand, "movers" or "mover population" refers
to the total number of persons moving into or within the state
during a ten year interval. The total number of movers in a
state at the end of the ten year period is determined by
subtracting the non-movers from the total projected population
of the state. This total number of movers or mover pool is
used as a control total for the SAAM mover primary employment
allocation process in Submode! III of Figure 3.
Other terms related to the mover/non-mover concept used
in the SAAM require definition. It has been established
above that movers and non-movers are defined in terms of the
mobility of small area residents during a ten year period.
A subset of these small area residents are also members of
the labor force. In the discussion of the SAA.~ which follows
these residents are referred to as mover and non-mover labor
force. Those members of a small area's labor force working
in primary jobs (see definition of primary, Chapter II) are
called mover and non-mover primary employees at their place
43
of work. Mover and non-mover service demand represents the
number of service employees demanded by mover and non-mover
population at home and at work (employment) •
The function and processing of each of the SAAM sub-
models is summarized below. A more detailed description of
the SAAM submodels and their calibration procedures is
contained in Chapter IV.
SUBMODEL I - PURPOSE: To estimate the percent of non-movers
by small area in the forecast year.
The first submodel in the SAAM estimates the future
number of non-movers in a small area as a percent of the
base year population. This submodel is calibrated inde-
pendently of the other submodels, using regression tech-
niques which are available in standard statistical packages.
The independent variables, which are regressed against the
percent of non-movers in Submodel I, represent the intensity
of development, age of residents, and income characteristics
of a small area.
SUBMODEL II - PURPOSE: To estimate small area non-mover
population, labor force, mover and non-mover primary employ-
ment, and non-mover service employment by type.
44
Once the percent of non-mover population has been derived
for each small area, the actual number of non-movers in each
small area is calculated in Submode! II. Non-mover labor
force is calculated using labor force participation rates by
small area. Military labor force estimates, unemployment
rates, and primary labor force percentages are then applied
to produce the level of non-mover civilian labor force employed
in primary industries. These persons are distributed from
home-to-work by the distribution function defined in Table 2.
The output of the distribution function by small area is
subtracted from the total primary employment to produce mover
primary employment by small area. 1/
The demand for services of different types, which is
generated by non-mover population and primary employment, is
estimated by applying state population and employment-
serving ratios. The service demand by type of employment
is then distributed to service centers using the function in
Table 3.
SUBMODEL III - PURPOSE: To estimate small area mover popu-
lation and service employment by type.
1/ Forecast year total primary employment by small area is an exogenous input determined by an economic base study or other similar analysis. See Chapter VI for a discussion of primary employment allocation techniques.
45
TABLE 2
THE NON-MOVER PRIMARY LABOR FORCE DISTRIBUTION FUNCTION
General Equation: T·. 1] = A.O.D. e 1 1 J
-St .. 1]
where:
1/
T.. = Number of home to work trips made between small 1 J areas i and j by non-mover primary employees
o. 1
D. J
e
t·. 1]
-1
= Non-mover primary labor force (civilian employed) living in small area i
= Total primary employment working in small area j
= Base of natural logarithm (2.7123 ... )
= Calibration parameter based on the mean state home-based work trip length
= Peak travel time between small areas i and j
All definitions represent calibration or forecast year values unless "base year" specified.
46
TABLE 3
THE NON-MOVER SERVICE EMPLOYMENT DEMAND
DISTRIBUTION FUNCTION
General Equation: =
where: 11
1/
Tijk = Number of work trips made between small areas i and j by non-mover service employees of type k
A •. 1)
e
t .. 1J
= [
E D.k . J 1
-Bkt .. e 1J J
-1
= Non-mover population and primary employee demand for service employees of type k in small area i
= Base year level of service employees of type k working in small area j
= Base of natural logarithm (2.7123 . .. )
= Calibration parameters based on the mean length of type k trips in the state
= Off-peak travel time between small areas i and j
All definitions represent calibration or forecast year values unless "base year" is specified.
47
The small area location of mover primary employment,
determined in Submodel II is an important factor in deter-
mining the residential location of mover population and the
work location of types of mover service employment. The
mover primary employees are first distributed from work-to-
home small areas by the function in Table 4. A state
activity rate is then applied to the mover primary employees
at their residences to determine the amount of mover popula-
tion dependent upon these primary employees.
The mover primary employees and dependent population
generate a demand for services of different types, the levels
of which are determined by applying state population and
employment-serving ratios. The generated mover service
demand by type is then distributed to service centers via
the function in Table 5.
Once the mover population and service employment by
type have been distributed, they are added to the non-mover
population and service employment by small area. The esti-
mated population for each small area is then compared with
the population holding capacities input by the user. If
the estimated population exceeds the holding capacity, then
the attraction index, Dj, in Table 4 will be reduced
as follows:
48
TABLE 4
THE MOVER WORK-TO-HOME DISTRIBUTION FUNCTION
General Equation: T .. l.J
= A. 0. D. l. l. J
-at .. l.J e
1/ where:-
1/
T·. l.J
A. l.
o. l.
o. J
e
a
t .. l.J
= Number of work to home trips made between small
0 -Bt·] -1
o. l.J = e J
= Mover primary employees working in small area i for the first iteration; the mover service employment increment thereafter
= A residential attraction index for small area j; based on developed and developable acreage or base year population and income levels
= Base of natural logarithm (2.7123 •.• )
= Calibration parameter based on the mean state home-based work trip length
= Peak travel time between small areas i and j
All definitions represent calibration of forecast year values unless "base year" is specified.
49
TABLE 5
THE MOVER SERVICE EMPLOYMENT DEMAND DISTRIBUTION FUNCTION
General Equation: =
where: 1/
!/
Tijk = Number of work trips made between small areas i·and j by mover service employees of type k
e
t .. 1)
[
-Skt. ·] -l I: D. e 1 ) . Jk J
= Mover population and primary employee demand for service employees of type k in small area i
= Base year level of service employees of type k working in small area j
= Base of national logarithm (2.7123 ... )
= Calibration parameters based on the mean length of type k trips in the state
= Off-peak travel time between small areas i and j
All definitions represent calibration or forecast year values unless "base year" is specified.
=
where:
o. = J
HC. = J
,.. POP. =
J
n, n+l =
50
HC. J
Equation ( 10)
The mover residential attraction index for small area j in Table 4.
The population-holding capacity for small area j.
The SAAM population estimate for the prior iteration for small area j.
Successive iterations of the allocation function in Table 4.
The allocation function in Table 4 is solved again with
reduced values for the residential attraction indices as
defined above. This constraint process is repeated until
all holding capacities exceed population estimates or a user-
'f' d 't t' l' 't11 . h d speci ie i era ion imi - is reac e . Mover service em-
ployment is then redistributed on the basis of the last
constrained population distribution.
Similarly, the total service employment by type by small
area is compared with service employment minima which may be
input by the user as central place factors.~/ The central
l/ Usually specified as one through ten. 21 Alternatively, the user may specify the service employ-
ment minima directly.
51
place factors are expressed as a ratio of service employment
by type to population which is multiplied by the constrained
population level of a small area by Submode! III to produce
the minimum service employment expected for that small area.
If any small area service employment minimum is not met by
a service employment estimate, then the mover service em-
ployment attraction index in Table 5 is increased as follows:
o.k J n+l
where:
D •. Jk
n, n+l
=
=
=
=
=
Equation (11)
The mover service employment attraction in-dex by type k for small area j in Table 5.
The service employment minimum by type k for small area j
The SAAM service employment estimate by type k for small area j
Successive iterations of the allocation function in Table 5.
The allocation function in Table 5 is solved again
with increased attraction indices until all service employ-
. . . f. d . t . 1 . . t 1/ ment minima are met or a user-speci ie i eration imi -
is reached.
l/ Usually specified as one through ten.
52
Both population holding capacities and central place
factors may be applied to all, a few, or no small areas, as
determined by the user. Submode! III prints out total un-
constrained and constrained population and service employ-
ment by small area as well as population and service em-
ployment summaries.
SUBMODEL IV - PURPOSE: To produce small area estimates of
net residential density, median family income, auto owner-
ship, and labor force.
The final submode! in the SAAM derives several data
items from the small area activity levels produced by
Submodels II and III. Net residential density in the fore-
cast year is derived from small area population estimates
and exogenously input new development densities.
Forecast year median family income and auto ownership
are estimated via regression equations which are calibrated,
and input to the Submode! by the user. The projected
median family income and the base year variance of income
for a small area may then be applied to an exponentially
lognorrnal distribution to produce a complete forecast year
income profile of a small area.
53
Mover labor force (civilian, employed) by small area
is produced by summing the columns of the mover work-home
trip table produced by the distribution function in
Table 4. Unemployment rates and mover military forces are
then applied to the mover labor force by small area, and
the non-mover labor force, calculated in Submode! II, is
added to produce total labor force by small area.
The calibration and application of each of the four
submodels which compose the Statewide Activity Allocation
Model are described in Chapters IV and V. A more detailed
description of each SAAM Submodel is also contained in the
next chapter.
CHAPTER IV
CALIBRATION OF THE STATEWIDE ACTIVITY ALLOCATION MODEL--
CONNECTICUT
The State of Connecticut was chosen as the test case
for the calibration of the SAAM. Agencies such as the Con-
necticut Department of Transportation and Off ice of State
Planning have developed a broad statewide data base which
has greatly facilitated the SAAM calibration and sensitivity
testing process.
DESCRIPTION OF THE CALIBRATION AREA
The ·calibration of the SAAM focuses on the area illus-
trated in Figure 4. The State of Connecticut has been
divided into 141 transportation zones, which are the basis
for the SAAM allocation of activities.
· Connecticut contains eleven Standard Metropolitan
Statistical Areas (SMSA's) and a 1970 population of 3,031,671
in an area of only 4,862 square miles which lends an overall
urbanized image to the State. However, the most highly
urbanized areas of Connecticut are focused along Interstates
91 and 95; northwestern and eastern portions of the State
are markedly rural in character.
54
55
e • -... > ..... G c 0
N
.... -::> -~ -... ..
~
.. t:: c: 0 v
.... ~ . • ..
:::. cw
.....
56
The transportation zone system has been devised to take
into account both the urban and rural aspects of Connecticut.
Small zones have been created for the central portions of
large cities such as Hartford and New Raven, so that the static
or declining population levels in these cities may be moni-
tored independently of the burgeoning suburbs around them.
At the same time, many of the rural transportation zones
were created quite large since these areas have consistent
activity growth patterns.
A SUMMARY OF DATA SOURCES
The SAAM calibration process requires 1960 and 1970
data bases. All of the 1960 or 1964 population, employment,
and land use data compiled at the Connecticut town level
(169 minor civil divisions) by the U.S. Census, the State
Employment Commission, and the Office of State Planning were
converted to 804 transportation zones by the Connecticut De-
partment of Transportation. In addition, the Connecticut
Department of Transportation provided the transportation
characteristics of the 1960 statewide highway system used in
the calibration process. The 1970 population and employment
data provided by the U.S. Census and the Connecticut Depart-
ment of Transportation at the town level were allocated to
141 transportation zones and this allocaticn procedure is
documented in the Appendix.
57
The following section establishes the definition
of primary and service employment used in the Connect-
icut calibration of the SAAM.
THE DEFINITION OF PRIMARY AND SERVICE EMPLOYMENT
As Chapter II has suggested, the definition of
primary and service employment in terms of aggregate
SIC codes is critical to the operation of all Lowry-
type models including the SAAM. This partitioning
may be difficult to effect for many zones, such as those
which represent urban areas in a state. However, for
the purposes of the Connecticut calibration, the SIC
codes presented in Table 6 have been used to define
primary, retail, and services employment in each zone.
These definitions are consistent with those used in
Phase I of the Statewide Study (Voorhees, 1973A).
INPUT DATA REQUIREMENTS OF SUBMODELS I-IV
The Tables contained in this section present the
Connecticut input data used for each SAAM submode!
illustrated in Figure 5. Those data items from Tables
7-9 which require further explanation are discussed
in the paragraphs which follow.
58
TABLE 6
CONNECTICUT PRIMARY AND SERVICE
EMPLOYMENT DEFINITIONS
(By 1967 two-digit SIC)
Primary Employment
• Agriculture • Mining • Construction • Manufacturing • Transportation, Communications, Utilities • Government • Nonclassified Establishments
Service Employment
Retail
• Wholesale and Retail Trade
Services
• Finance, Insurance and Real Estate • Services • Government
SIC 1-9 SIC 10-14 SIC 15-17 SIC 19-39 SIC 40-49 SIC 91-92 SIC 99
SIC 50-59
SIC 60-67 SIC 70-89 SIC 93-94
59
Figure 5· The SAAM Submodels
SUBMODEL I r - - - - - - - - - - - - ---, I PURPOSE: ~ I '*TO ESTIMATE PERCENT NON-MOVERS I I BY SMALL AREA I L _____________ _J
SUBMODEL II I
PURPOSE: TO'ESTIMATE SMALL AREA NON-MOVER POPULATION, LABOR FORCE, PRIMARY EMPLOYMENT, SERVICE
EMPLOYMENT, AND MOVER PRIMAR'( EMPLOYMENT
~I
SUBMODEL Ill '
PURPOSE: TO ESTIMATE SMALL AREA MOVER POPULATION AND
SERVICE EMPLOYMENT
SUBMODEL IV r:: - --:- - - -~ - - - - - -, I PURPOSE. TO ESTIMATE SMALL AREA I
NET RESIDENTIAL DENSITY, I LABOR FORCE f ,- - - *MEDIAN FAM~ Y~COM;,- I I AUTO OWNERSHIP I t--- - - - - - - - - - - --I
*calibrated independently via regression techniques
SAAM ALLOCATION FUNCTIONS
ALLOCATES NON-MOVER PRIMARY EMPLOYEES
TO WORK SMALL AREAS. SEE TABLE 2
ALLOCATES NON-MOVER SERVICE EMPLOYEES TO WORK SMALL AREAS.
SEE 'fABLE 3
ALLOCATES MOVER PRIMARY EMPLOYEES
TO HOME SMALL AREAS SEE TABLE 4
ALLOCATES MOVER SERVICE EMPLOYEES TO.
WORK SMALL AREAS SEE TABLE 5
60
Submodel I
Submodel I is a regression relationship in which the
dependent variable is the number of non-movers in the
calibration year (1970) expressed as a percentage of base
year (1960) population. For example, if four hundred (400)
persons moved into a small area between 1960 and 1970 and the
1970 population is one thousand (1,000) persons, then the
number of non-movers in 1970 is six hundred (600). If the
population of the small area were 900 in 1960, then the
"percent non-movers" used as the observed dependent variable
is 600 divided by 900,or 67 percent.
The percent non-movers was calculated for Connecticut
minor civil divisions (MCD's) on the basis of the 1970
Fourth Count Census of Households. The percentages of non-
mover households derived from the Census were applied
directly to the 1970 MCD population to produce 1970 non-
mover population. That is, it was assumed that there was no
consistent bias in household size among non-movers in each
minor civil division. 1970 MCD non-mover population was
divided by the 1960 MCD population for each zone and the
resultant percent non-movers was converted to the 141
transportation zone level by the procedure described in the
Appendix.
61
The independent variables which were considered for
inclusion in the final percent non-movers zonal regression
relationship are presented in Table 7. These same variables
were tested on the 169 minor civil division level as well as
the 141 zonal level. Because the Connecticut MCD data is
more reliable than the zonal data, the regression relationships
were generally more statistically significant for MCD's than
zones. The final form of the percent non-movers zonal regres-
sion is presented in the section entitled "Calibration Results."
Submodel II
Submode! II determines 1970 non-mover population and
labor force, non-mover and mover primary employment, and non-
mover retail and services employment by zone. Table 8
presents the Connecticut input data required to calibrate
Submode! II.
Service civilian-employed labor force was calculated
by adding the following categories for each county and city
in Connecticut from the County and City Data Book, 1972:
Wholesale and Retail Trade, Services, Educational Services,
and Government. This sum was then divided by the total state
civilian-employed labor force to produce service labor force
percentages. (Primary civilian employed labor force is equal
62
TABLE 7
INDEPENDENT VARIABLES CONSIDERED FOR SUBMODEL I
Data Item Year Source
Percent Population Under 25 1970 u. s. Census
Percent Population 25-34 1970 II
Percent Population 35-44 1970 " Percent Population 45-54 1970 "
Percent Population 55-64 1970 " Percent Population Over 65 1970 II
Unemployment Rates 1970 " Median Family Income 1960 Connecticut DOT
Labor Force Participation Rates 1960 II
Population 1960 II
Population Density 1960 II
Net Residential Density 1960 II
63
'mBI.E 8 SUEM>DEL II CALIBRATION DATA
Analysis Data Itan Year Ievel Source Caments
Population 1960 ZOne Conn oor Used in calcula-ting 1970 non-nover population
labor force parti- 1970 7.one U.S. Census Used in calcula-cipation rates ting 1970 non-
nover labor force
Unenploynent rates 1970 Zone U.S. Census Used in detennin-ing 1970 primary
Military labor force 1970 Zone U.S. Census non-:rrover Civilian enployed labor
Primary and service force labor force percentages 1970 Zone U.S. Census
Ibne-work skim tree 1960 Zone Conn oor Used in calibra-airl ting the ilrq;:>edance
Trip length distribution 1960 State Conn oor function of Table 2
Pr:iirary enployrcent 1970 zone Conn r:or!/ Used in calibra-ting 1970 :rrover primacy enployrrent
Ietail enployrcent 1960 7.one Conn oor!/ Attraction indices
Conn oor!/ for the Table 3 Service enploynent 1960 Zone allocation equation
Ibne-woi:k skim tree 1960 Zone Conn r:or!/ Used in calibra-ting the inpedance
lk:lte-shop trip length 1960 State Conn oor function of Table 3 distribution
Ietail enploynent 1970 State Conn oor1_f Used in detennining
Conn r:or!/ 1970 :rrover retail Services employrrent 1970 State employrrent, service
errployrrent and popu-Population 1970 State U.S. Census lation control totals
respectively
1 1960 and 1970 enployrcent data.by 169 r-KD's was received frcm Conn oor and this data was allocated to 141 zones by A.W staff as described in the Apperrlix
64
to one minus the service percentages.) The county percentages
were applied to all zones within the same county except zones
representing parts of cities, which were assigned the primary
and service labor force percentages calculated for that city
from the County and City Data Book. However, if a state
uses minor civil divisions as the spatial scale for applica-
tion of the SAAM, as recommended in Chapter VII, then the pri-
mary and service labor force percentages will be available
for every MCD from the U. s. Census. This of course is a
more desirable approach than the simplistic one applied for
Connecticut.
The only other data besides Census and employment data
required to calibrate the SAAM is that provided by a statewide
transportation study. Travel time matrices representing the
1960 highway system were used for Connecticut. This implies
a 10-year lag between the completion of new highway
facilities and the full impact of these facilities on residen-
tial and employment locations. However, a 1965 highway system
might be more appropriate since the lag time between the com-
pletion of a highway facility and its impact on residential,
commercial and industrial relocation is probably closer to
five years than ten.
65
Travel cost matrices might also be used instead of
travel time in the SAAM allocation functions. Travel cost
matrices were used in the activity allocation process applied
in the Dallas Fort Worth regional study and these are defined
in Volume II of the final report for that study (Voorhees,
1972).
The SAAM calibration process also requires the trip
length frequency distribution (TLD) and mean trip length for
k t . d . t . l/ . th t t wor rips an service rips- in e s a e. The state mean
trip length is used in estimating the initial calibration
parameter B (beta} for the SAAM allocation functions (Tables
2-5). Based on this B (beta) parameter, the travel times
between small areas,· and the attraction indices, the SAAM
produces a state trip length distribution and mean trip
length for each mover and non-mover activity. During calibra-
tion the actual TLD and mean trip lengths for each activity
are compared with the SAAM estimated TLD's and mean trip
lengths and the B is adjusted if necessary, to improve the
SAAM estimates. (See Chapter V for a description of the B (beta} adjustment procedure.}
1/ For Connecticut, service trips were divided into retail and services types and the trip purposes assigned to each are listed in this chapter.
66
It is important to note that the state mean trip
length is used only to calibrate the macro-level trip charac-
teriati~s e~timated by the SAAM. Variations in mean trip
lengths among zones is maintained via the travel time matrices
which are also input to the SAAM allocation functions. That
is, although the SAAM calibration process is conducted on a
state level at which the differences in zonal travel character-
istics may be hidden, these differences become apparent in the
zonal travel time matrices used by the SAAM allocation
functions.
Submode! III
Submode! III determines the 1970 mover population,
retail employment, and services employment by zone. Table 9
presents the Connecticut input data required to calibrate
Submode! III.
The same 24-hour skim tree is applied in work-home
and home-work allocation equations.
The population holding capacities used in calibrating
the SAAM were derived from the 1964 Land Use Study conducted
by the Connecticut Office of State Planning. A file developed
by this study contained estimates of "Net People," the
67
TABLE 9
sum.!::JDEL III CALr:tm.:.TION DATA
Analysis Data Item Year Level Source Comments
Popuiauon 1960 Zone ::::onn DOT Used in calculating the mover residen-tial attraction index
Median family income 1960 Zone .Conn DOT (Table 4)
24-hour skim tree 2 1960 Zone Conn DOT lJsed in calibrating the impedance func-
Work-home trip 19f:l0 State Conn DOT tion in Table 4 leng"Ji distributic;n
Population 1970 Zone U.S. Census Used to compare actual with estir.1ated population output of Submodei !II
Population Office of Used as an upper holding ~apacities 1964 Zone State Planning constraint for
population in the allocation equation of Table 4
.ttetai1 employment .u160 l.one Conn .UU1 Used as la1;rged
Services employment 1960 Zone l service employ-Conn DOT ment attraction
indices in Table 5
24-hour skim tree 1960 Zone Conn DOT Used in calibrating the impedance func-
Home-shop trip tion in the allocatio!1 length distributio!1 1960 State Conn DOT eq11ation of Table 5
Retail employment 1970 Zone Conn DOT 1
Used to compare
Services employment 1970 Zone Conn DOTt actual with estimated retail and serviceg output of Submodel III
Retail and services Used by Submode! m employment to population in calculating retail ratios (central place and services employ-factorii) 1960 Zone Conn DOT ment miniina for the
allocation equation \v. Table 5
1 196fJ and 1970 employment :iata by 169 MCDs was received from the Conn DOT and this data was allocated to 141 zones by Ar.iv sta.ff as described in Appendix
2 Peal..-hour skim tree can be used, if available
.. . .
68
maximum growth potential of a zone in terms of 1964 zoning
classifications. These estimates were available at the 1725
zone level and were aggregated to the 141 zone system by
AMV staff. "Net people" were then added to the 1960 population
of each zone to form the maximum population ceilings (holding
capacities) which were input to Submodel III. Chapter III
describes the role which the population holding capacities
play in the allocation process.
The last data item which requires clarification in
Table 9 is the central place factors of 1960 retail and ser-
vices employment-to-population ratios,which are discussed
in Chapter III. These ratios were specified for the twelve
zones in Connecticut containing parts of the largest cities
(zone numbers are in parentheses): Bridgeport (84),
Bristol (116), Danbury (124), Hartford (62), Meriden (46),
Milford (82), New Britain (58), New Haven (95), Norwalk (131),
Stamford (136), Waterbury (107), and West Haven (80). In
Submodel III the central place factors are multiplied by the
future population estimates for each zone to produce minimum
retail and services employment. Submode! III then checks
the estimated retail and services employment against these
minima to ensure that they are met for each fo the twelve
zones. If they are not, then Submodel III will increase the
attractiveness of the zone to service employment in the
,
69
manner described in Equation (11) of Chapter III and the mover
service employment distribution function (Table S} will be
solved again. This process will continue until all service
employment minima are satisfied or an iteration limit is
reached.
Submode! IV
Submode! IV derives 1970 net residential density,
median family income, auto ownership, and labor force from
the activity estimates of Submode! ·II and III. Table 10
presents the Connecticut input data required to calibrate
and verify the operationality of Submode! IV.
Net residential density is calculated in Submode! IV
by subtracting 1960 population from the estimated 1970 popu-
lation and dividing by expected new development densities to
produce consumed net residential acreage during the 1960-
1970 interval. For lack of more accurate estimates, 1960
Connecticut net residential densities might be substituted
for the new development densities (of course, this implies
that the 1970 net residential densities output by the Submode!
IV will equal 1960 net residential densities}. The consumed
acreage estimate by zone is added to the 1960 developed net
residential acreage, and this sum is divided into the 1970
70
TABLE 10
SUEM>DEL 'IV CALIBRATIOO AND VERIFICATIOO' DATA
Analysis Data Item Year level Source carmen.ts
Net residential density 1960 Zone Conn 001' Used in calculating 1970 net residential
Population 1960 ZOne Conn 001' density
Net residential density 1970 Zone Conn 001' Used in calibrating a 1970 median family
Population 1970 zone Conn oor i.ncate regression equation
Median family in~ 1960 zone Conn 001'
Median family incane 1970 zone U.S.Census
Population 1960 zone Conn 001' Used in calibrating a 1960 autos/person
Median family in~ 1960 Zone Conn oor regression
Net residential density 1960 Zone Conn 001'
Autos owned 1960 Zone Conn 001'
Military labor force 1970 Zone U.S.Census Used in calculating nover labor force
71
estimated zonal population to produce 1970 net residential
density.
The median family income regression equation is actually
calibrated outside of Submodel IV, using the data suggested
in Table 10 and standard regression techniques available on
most computer systems.
The autos per person regression equation is also cali-
brated outside of Submodel IV using the data suggested in
Table 10.
Nineteen seventy labor force by zone is estimated by
Submodel IV as tbe sum of 1970 non-mover and mover labor
force. Non-mover labor force is an output of Submodel II.
Mover labor force is derived in Submodel III by summing the
home trip ends from the mover work-to-home tables. Sub-
model IV then sums the mover, non-mover, and military labor
force to produce total 1970 labor force by zone.
CALIBRATION RESULTS
The results of the calibration procedures for each
SAAM submode! are documented in this section. The calibra-
tion of Submodels I and IV requires the use of regression
72
techniques which are independent of the SAAM. The calibration
of Submodels II and III is performed via the SAAM program
package, and these calibration procedures are also described
in this section.
Submode! I -- Table 11 illustrates the final equation
selected for Submode! I. Specifically, it was determined that
the 1970 percent non-movers is related to:
• The patterns of urban development intensity in the state as represented by population density
• The stabilizing influence of middle-aged popula-tion expressed in terms of the percent of popu-lation aged 45-54
• The economic status of the zone in terms of median family income
The relationship between the percent non-movers and the
independent variables is shown graphically in Figure 6. As
the population density rises, the percent non-movers drops
rather sharply. In other words, urban areas experience a
higher turnover of population than rural areas. As the pro-
portion of population in the 45-54 age group increases, the
percent non-movers also increases; i.e., middle-aged persons
are less mobile than other age groups .11 As median family
1/ The population in the 45-54 age group are less mobile than the 65+ age group because the latter often change residence upon retirement.
73
TABLE 11
1970 PERCENI' NON-MJVER REGRESSION mt.JATION--CONNB:TICUT
~O = 38.7265 - 1.1173 POPDEN60 + 1.6358 POP (45-54)70 - .0008 IN:60
where:
Cl>served standard deviation
Standard error of the estimate
Correlation Coefficient (R)
F Ratio
49.12
8.53
6.75
.62
26.93
Standard Error of Coefficient
POPDEN .1366
POP (45-54) .3107
INC .00025
!'™ = Percent non-:rrovers
POP DEN = Population density
t-value
-8.1811
5.2657
-3.1417
POP ( 45-54) = Percent of :EXJPulation age 45-54 . INC = M:!dian family incxm=
60 = 1960
70 = 1970
74 Figure 6. A Graphical Representation of the
Percent Non-Movers Relationships
100
(/) 80 a:
w > 0 ~ 60 z 0 z I- 40 z w u a: w 20 Q.
0 0 10 20 30
PERSONS PER GROSS ACRE
100
(/) 80 a: w > o. ~ 60 z 0 z I- 40 z w u a: w 20 Q.
0 0 10 20 30
PERCENT OF POPULATION
100
Cl) a: w 80 > 0 ~ z 60 0 z u.. 0 I- 40
Inc z w u a: 20 w Q.
0 0 5 10 15
THOUSANDS OF DOLLARS
75
income rises, the percent of non-movers falls, which sup-
ports the premise that high income families are more mobile than
lower income families. These results suggest that the
percent non-movers equation is a statistically significant
relationship which reflects real world phenomena.
Submodels II and III -- The calibration of Submodels
II and III is based upon a comparison of actual and estimated
mean trip length and trip length distributions. The estimated
mean trip lengths and trip length distributions are produced
by the allocation equations in Tables 2-5, based on the input
value of S (beta) . If the estimated mean trip length differs
from the actual by more than ten percent, then the user
must calculate a.new value for S (bet~ as follows:
=
where:
n+l =
= n
MTL =
MTL =
A
MTL Equation (12) MTL
the next input value for beta
the last input value for beta
the last mean trip length estimated by the SAAM submode!
the actual mean trip length for the state
76
and
B = 2/MTL 0
where:
B = The initial value of beta in Tables 2 and 3 0
MTL = An actual state mean trip length (in the measure of spatial separation chosen by the user)
When the actual and estimated mean trip lengths for the
equations in Tables 2 and 3 are within ten percent, the cali-
bration of Submode! II is completed. The final B (beta) value
for Tables 2 and 3 are then input as the initial B (beta)
values for Tables 4 and 5, respectively. If necessary, the
interpolation procedure described by Equation (12) is con-
tinued until the calibration of the allocation functions in
Tables 4 and 5 of Submodel III is completed.
The mean trip length for Connecticut's home-based short
trip purposes was used in calculating B for the retail sector
of Table 3, while the mean trip length for home-based long trip 1/
purpose was used for B in the services sector of Table 3.-
The actual and estimated mean trip lengths and estimated
trip length distributions for the allocation functions in
1/ Short trips include personal business, medical-dental, eat meal, civic-religious, shopping and other trip purposes. Long trips include related business, educational, social and recreational trip purposes. This stratification of pur-poses was chosen for convenience purposes only, since in other cases the services sector would include personal business; civic-religious and medical-dental purposes.
77
Tables 2-3 are illustrated in Figures 7-9 for the
Connecticut calibration. County sununaries of actual
and estimated population and employment distributions
and associated statistics output by Submode! III are
presented in Tables 12 and 13.
In Table i2, the largest percentage difference
between actual and estimated constrained population
levels occurs in Tolland County, while the largest
absolute difference is in New Haven County. The
underestimation of Tolland County population is
attributable to the high levels of activity in
neighboring Hartford County which has attracted an
excess of estimated population.
The overestimation of constrained population in
New Haven County is due to high levels of base year
activity as well as the potential for urban develop-
ment reflected by the 1964 holding capacities for
some New Haven area zones. That is, those areas
which are tightly constrained by the 1964 holding
capacities gave up their excess population to New Haven
County zones with high holding capacities.
78
Figure 7 Estimated Trip Length Distribution for Non-Mover Primary Labor Force
Actual Mean Trip Length = 13.0 mins. Estimated Mean Trip Length = 12.9 mins.
~ 151---+-·~·-1--~+-~~~~t--~~~-t-~~~~-t-~~~~+-~~~--t~~~~.....,
a: I-I-z w u ~ 10 ::::::::::i
~ ,. ~~ 5 1-.1.;.;.;..;.;.;..;.;..;.;~...c;;..;.;.;..;.;.;..;.;.;J,,..+~~~~+-~~~~f--~~~-+~~~~-+-~~~~
~ ; [~%> 0 Li1:11:tt21:11:1Li1:11:1LiZ22::i:::z:;=:.:==,L__~~l_~_J
0 10 20. 30 40 50 60 70 TRAVEL TIME (MINUTES)
•
U) '1.
cc f-f-z w u cc w '1.
79
Figure 8 Estimated Trip Length Distribution For Non-Mover Retail Employment
Actual Mean Trip LeA§th = 7.5 mins. Estimated Mean Trip Length= 7.4 mi.ns.
3Ql--~4-~-+~~~~+-~~~-+~~~~t-~~~-.~~~~r-~~~....,
201--4;..;"~·~~l--~~~-+~~~~t--~~~-+~~~~t-~~~-+~~~----;
10 ' \
0 ~ ilffis>~ 0 10 20 30 40 50 60 70
TRAVEL TIME (MINUTES)
(I) a.. a: t-t-z w u a: w a..
80
Figure 9 Estimated Trip Length Distribution
for Non-Mover Services Employment
Actual Mean Trip Length = 11.5 mins. Estimated Mean Trip Length = 11.5 mins.
20>----+.;.+-~-+~~~~-t-~~~-+~~~~;-~~~-r~~~~-r-~~~-t
151---+Y"~"";+--~+-~~~-+~~~~+-~~~-+~~~~-t-~~~-+~~~--t
·.·.·.·.
:11 10>--~:-~_:::~:::~:::·~.:~;-~~~-r~~~~;-~~~--r~~~~;-~~~-r~~~----.
::::::::::::::
0 10 20 30 40 50 60 70
TRAVEL TIME (MINUTES)
•
81
'mBIE 12
1970 ACIUAL VERSUS ESTIMATED CCNSTRAINED POPULATION BY COONI'Y*
Percent Absolute Cormty Actual Estimated Difference Difference
Fairfield 814,296 799,554 - 1.81 14,742
Hartford 847,141 865,041 2.ll 17,900
Litchfield 126,526 112,775 -10.87 13,751
Middlesex 89,787 79,634 -ll.31 10,153
New Haven 748,863 789,818 5.47 40,955
New IDndon 228,905 226,979 - .84 1,926
'lbllad 95,962 74,837 -22.01 21,125
Wirrlh.am 80,159 83,036 3.59 2,877
1.anal Statistics:
COefficient of Detennination • 96
!mt Mean Square Error 4919.12
Percent IMS 22.88
* sane of the Connecticut 141 transportation zones cross cxnmty bourrlaries. 'Iherefore, the actual and estimated population levels above are only roughly equivalent to actual 1970 population in these Counties
82
In Table 13, the largest percentage difference between
actual and estimated employment levels occurs in Tolland
and Windham Counties. The employment in these Counties
is overestimated because of the low number of employees per
person in these Counties. That is, many members of the
labor force in these Counties are traveling further to work
than the mean state trip length.
The largest absolute difference in Table 13 is for
Hartford County. The underestimation of employment levels
in Hartford County is based on the high number of employees
per person in the calibration year. In fact, the services
employment to population ratio for Hartford Zone 63 doubles
between the base and calibration year. Since the central
place factors are based upon base year levels of service
employment and population, the minimum services employment
for Zone 63 does not improve the SAAM estimate. A solution
to this problem would be to increase the central places
factors to calibration year levels, so that service employ-
ment in the most urbanized Hartford County Zones would be
improved. This approach would improve all of the employment
statistics in Table 13 since all other Counties except Hart-
ford are overestimated.
83
TABLE 13
1970 Actual Versus Estimated Employrrent By Connty*
Percent Absolute CO\mty Actual Estimated Difference Difference
Fairfield 307,128 307,737 .20 609
Hartford 402,679 361,793 -10.15 40,886
Litchfield 37,154 41,572 11.89 4,418
Middlesex 31,456 36,631 16.45 5,175
New Haven 295,181 302,451 2.46 7,270
New IDndon 78,449 90,511 15.38 12,062
Tollad 20,683 25,776 24.62 5,093
Windham 26,469 32,640 23.31 6,171
* Sare of the Connecticut 141 transportation zones cross county boundaries. Therefore, the actual and estimated population levels above are only roughly equivalent to actual activity levels in these Counties.
84
Submodel IV -- The only procedures in Submodel IV which
require calibration are the median family income and auto
ownership regression relationships (the net residential
density and labor force procedures require verification). A
test case was run to ensure the operationality of Submodel IV.
However, no calibration of median family income or auto
ownership relationships was undertaken with Connecticut data.
TREATMENT OF EXTERNALS
Because the boundaries of Connecticut define a political
area rather than an autonomous economic region, the state
cannot be modeled as an isolated jurisdiction. The urban
areas outside the state, which employ Connecticut residents
(and lure them to shop), and urban areas inside the state,
which employ out-of-state residents and draw out-of-state
shoppers, were identified so that the work-home and home-
shop interactions between these areas could be modeled by
the SAAM.
The criteria for selection of external zones for
Connecticut were:
• That the zones be similar in size to the Connec-ticut 129 non-city zones.
• That the areas in which the external zones lie be urban areas or be within 25 miles of an urban area in Connecticut.
85
• That the 1970 annual average traffic volumes flowing between internal and external areas be at least 15,000 vehicles/day.
On the basis of these criteria, the following New York
and Massachusetts zones have been selected for inclusion
in the Connecticut state zonal system:
The New York Counties of: Bronx Kings Nassau New York Queens Richmond Rockland Westchester
qnd the Massachusetts minor civil divisions of: Agawam Chicopee East Longmeadow Hampden Holyoke Longmeadow Southwick Springfield Westfield West Springfield
These areas are illustrated in Figure 10.
The 1960 and 1970 data required to include the New York
County zones in Submodels I-III were obtained from the 1972
County and City Data Book. Data for Massachusetts MCD's
which could not be obtained from the U.S. Census were derived
by assuming county rates for all MCD's within the county. The
calibration data required for the Connecticut externals are
86
Figure 10. Connecticut External Zone System
CONNECTICUT
0 10 20
SCALE MILES
87
presented in Table 14. The sources for externals data are
discussed more fully in Chapter VI.
The SAAM handles external zones as though they were a
part of the Connecticut zonal system until the distribution
functions in Tables 2-5 are executed. After the primary
labor force, primary employment, retail employment, or
services employment are distributed to all zones, including
the externals, the SAAM normalizes the state distributions to
state control totals. Therefore, the externals are not a·
part of the zonal system after the activity distribution
processes are executed and do not appear in the final output
tabulations of the SAAM submodels.
The next chapter contains a description of the transpor-
tation and land use policy changes assumed in the SAAM
sensitivity-test and presents the impacts of these changes
on the distribution of population and employment in
Connecticut.
88
• TABLE 14
CALIBRATION DATA REQUIREMENTS -- CONNECTICUT EXTERNALS
Analysis Data Item Year Level Source Comments
Percent non-movers 1970 MCD or County and City Input to Submode! III County Data Book, 1972
Submode! III
Labor force MCD or County and City participation rate 1970 County Data Book, 1972
Unemployment rates 1970 MCD or County and City County Data Book, 1972
Military labor force 1970 MCD or County and City Used in determining
County Data Book, 1972 non-mover primary (civilian employed)
Primary labor MCD or County and City labor force force percent 1970 County Data Book, 1972
Primary employment 1970 MCD or State planning County agencies
Population 1960 MCD or Used in distributing
County U.S. Census non -mover primary employees from
24-hour skim tree 1960 MCD or home to work County Conn DOT
Retail employment 1960 MCD or State planning County agencies
Services employment 1960 MCD or State planning Used in distributing non-mover service
County agencies employment by type 24-hour skim tree 1960 MCD or ..,___ -
County Conn DOT
Population 1960 MCD or County U.S. Census Used in distributing
24-hour skim tree 1960 MCD or mover population from County Conn DOT work to home (Table 4)
Retail employment 1960 MCD or State planning County agencies
Services employment 1960 MCD or State planning County agencies Used in distributing
24-hour skim tree 1960 MCD or mover service employ-
County Conn DOT ment (Table 5)
CHAPTER V
A SENSITIVITY TEST OF THE SAAM - CONNECTICUT
To measure the sensitivity of the SAAM to changes in
policy-controlled input, transportation inputs based on speed
and land development constraints in the form of holding
capacities were varied as shown in Table 15. State control
totals were held constant in all cases.
TEST CASE TRANSPORTATION INPUTS
A transportation policy input to the 1960-1970 SAAM
calibration for Connecticut (Scenario I) is the 1960 average
link speeds. For the purposes of the sensitivity test, the
1960 speeds were doubled for Scenarios II and V and were
decreased by one-third for Scenarios III and VI. These
drastic speed changes are not typical of real world phenomena;
they were chosen to illustrate the sensitivity of the SAAM
to extreme policy changes.
TEST CASE HOLDING CAPACITY INPUTS
The population holding capacities used in the 1960-1970
calibration were redefined for Scenarios IV-VI to reflect 1973
policy guidelines in "A Plan of Conservation and Development
for Connecticut" (State of Connecticut, 1973) . Land and Water
89
90
TABLE 15
EXPERIMENTAL DESIGN FOR SENSITIVITY TEST OF SAAM
Scenario I (calibration run)
Scenario II
Scenario III
Scenario IV
Scenario V
Scenario VI
1960 Average Link Speeds
x
2x
.67x
x
2x
.67x
Connecticut Land Use Policies
(population holding capacities)
Based on 1964 zoning policies
Based on 1964 zoning policies
Based on 1964 zoning policies
Based on 1973 land and water resource policies
Based on 1973 land and water resource policies
Based on 1973 land and water resource policies
91
Resources Policy "7C" of this report states that, "Urban
development should be staged in accordance with the cri-
teria and priorities as reflected in the Urban Development
Opportunities and Limitations map." An adaptation of this
map with a 141-zone overlay is presented in Figure 11.
The opportunity and limitation areas in Figure 11 were
translated into SAAM population holding capacities for Con-
necticut in the following manner:
Limitation Zones
The areas with "Opportunity for Expansion of Urban
Development'' in Figure 11 are characterized by "existing,
programmed and/or anticipated sewer systems with waste
tolerance levels above the design capacity of the sewerage
system."
The percentage of each zone covered by urban develop-
ment limitations was estimated and these percentages were
applied to the difference between the 1970 calibration holding
capacities, used in Scenarios I-III, and the 1970 population.
For example, if the limitation area covered an entire zone,
then the test case holding capacity for a limitation zone was
set equal to the 1970 population. Similarly, a fifty percent
....
92
l ! l I ;
. '& !
' \ . ' f. ! l
~«
.. ( ! ::> I
~
i 1 1 "l
6 i I .. ..
0 \ 1 n n ~ Q " I ~ i -
93
coverage implied that fifty percent of the"Net People' were
added to the 1970 population for that zone.
0pportunity Zones
Environmental Limitation areas in Figure 11 involve both
"Water Supply Watershed Limitations" and "Stream Quality
Limitations." Water supply watershed limitation areas have
existing, programmed, or anticipated sewer systems which are
designed to solve existing pollution problems only. Stream
quality limitation areas are tributary to streams which are
near or above their waste tolerance level despite existing,
programmed or anticipated treatment (State of Connecticut,
1973).
The total number of persons displaced from urban develop-
ment limitation zones was then added to the holding capacities
of urban development opportunity zones in proportion to the
population affected by the opportunities. For example, if
fifty percent of the area of a zone were affected by growth
opportunities and the 1970 population for that zone were one
thousand, then it was assumed that five hundred persons
were affected by urban development opportunities. Each
opportunity zone was then assigned a proportion of the total
displaced persons to be distributed on the basis of the popu-
lation of that zone affected by urban development opportunities.
94
Results
Selected output of the sensitivity-test for Scenarios
I-VI is summarized in Table 16. Population densities, employ-
ment densities and speeds for selected zones are presented
for comparison.
The two zones presented in Table 16 were selected to
represent an area with opportunity for development and one
with environmental limitations.
Zone 95, in the City of New Haven, was selected as the
urban development opportunity zone in Table 16. When speeds
are doubled in the SAAM (Scenario II), the population
density of zone 95 decreases by ten percent and the employ-
ment density increases by 11 percent~ This implies
that population is moving out of the city and into the sur-
rounding suburbs, while more residents of the suburbs are
commuting to work in the city. Conversely, decreasing the
·speed by one third results in an increase in population den-
sity of 4 percent and a decrease in employment density of
7 percent. These impacts imply that more persons working
in the city will live in the city, while more suburbanites
will find jobs in the suburbs.
- - - - -- ---····------ -·- !..., ____ .._ ------
T/\DLE 16
I A COMPARISON OF SCENARIOS !-VI FOR SELECTED ZO?\TES"'
Scenarios I II III IV v v: Bae~ Year· Percent With adjusted holding capacities
change from base yc:ir holding
Speed x 2x .67:x capacities x 2x .67x
PoEulation Density (Persons/Total Acres)
27. 2:~ . -~ 95 26.21 23.4~ +21 28.51 25.98 28.90 U1
68 1.22 1.43 1.2C -50 1.19 1.29 1.20
Employment Density (Empl~ees/Total Acres)
95 15.27 17.02 14. l:J +21 '15.57 17.17 14.40 68 0.32 0.29 0.37 -50 0.32 0.28 0.36
•zone 95: City of New Haven: urbanized area with opportur.ity for development
Zone 68: Includes MCD of Vernon and part of Ellington: suburb with environmental limitations
Areas for development and with limitations are illustrated in Figure 11.
96
The same trends in population and employment density
changes are observed when the population holding capacity
for Zone 95 is increased by 21 percent to encourage in-
creased urban development in Scenarios IV-VI (the methodology
for determining the adjusted holding capacities is discussed
in the preceding section). Because Zone 95 is tightly con-
strained by its base year holding capacity (i.e., the SAAM
estimates an unconstrained population level which is higher
than the base holding capacity), the effect of applying an
increased holding capacity for Zone 95 is to increase
population and employment densities for all speeds.
Zone 68 represents a rural area with environmental limi-
tations located in the minor civil divisions of Vernon and
Ellington, Connecticut. When the speeds are doubled, the
population density of Zone 68 increases by 17 percent, indi-
cating that more persons working in the Hartford metropolitan
area are living in Zone 68. However, the employment level
decreases slightly with the higher speeds, since residents
of Zone 68 who formerly worked in that zone are now commuting
to jobs in Hartford.
A reduction of the base speeds by one-third slightly
decreases the population density of Zone 68 and increases the
employment density by 16 percent. This implies that some
97
residents of Zone 68 who work in Hartford at base year speeds
have moved closer to Hartford when the speed is reduced,
while others have found jobs within their zone of residence.
The general impact of reducing the population holding
capacities by 50 percent for Zone 68 in Scenarios IV-VI is to
decrease population and employment densities for all trip
lengths. The most significant decrease of 10 percent is
observed for population density in Scenario V.
Figures 12 and 13 present plots of the changes in popu-
lation and employment density versus changing speeds for the
13 most urbanized zones in Connecticut. A large majority
of the zones in ~igure 12 show a trend toward decreasing
population densities with increasing speeds. The influence
of speeds on zones which do not observe this trend is off set
by the impact of their population holding capacities (for
61 and 62) or large pockets of primary employment in nearby
zones (for 6, 81, 136).
In Figure 13, the zones in the Hartford metropolitan
area follow the employment density pattern of New Haven,
as discussed above. That is, for these large employment
centers (zones 61, 62, 63, 95), employment density increases
with increasing speeds. However, the remaining urbanized
98
Figure 12. Change in Population Density Versus Speed for the Most
Urbanized Connecticut Zones
0.67 x 1960 Speeds
1960 Speeds
INCREASING SPEEDS
Key: 6-New London,.,__ __
48-Middletown 58-New Britain
~~}-Hartford 63 81-Westhaven
84 }-Bridgeport 91
· 95-New Haven 107-Waterbury 136-Stam ford 139-Torrington
Trend Areas
•
2 x 1960 Speeds
+27
t +20 ~ (/) z +15 w 0 I-z +10 w ~ >-0 +5 ...J Q. ~ w z 0 w l!) z -5 <( :c u I- -10 z w u a: w -15 Q.
-20
99
Figure 13. Change in Employment Density Versus Speed for the Most
Urbanized Connecticut Zones
~~~~~-r--~~~~..,-~-,-;:-;--;-.,-,...,:-;-r:-:-:'7':":"":"':'':':':"":'7~'7:':::::::::-::::7"'.'r763~~~~~~~---62
61
95
=--t----J~91
i:,:,.;~;.,;..;~;..;.;.~..;.;.;.;.;..;..;,~~~:-4-~~-f'~:::......~-.:::---l-~-="'-'""""'::::=-r-s8~~~.._~~~---<
0.67 x 1960 Speeds
1960 Speeds
INCREASING SPEEDS -
Key: 6-New London
48-Middletown 58-New Britain
=~ )-Hartford 63 81-Westhaven 84} -Bridgei:iort 91 95-New Haven
107-Waterbury 136-Stamford 139-Torrington
~}}}~~} Trend Areas
136,81
6
84, 139
48 107
1-Zone Numbers
2 x 1960 Speeds
•
100
zones in Figure 13 follow a similar trend to that observed
for population density: Their employment densities
decrease with increasing speeds. It may be concluded then,
that the largest employment centers are so attractive that
they draw more employees from the suburbs as speeds increase.
On the other hand, the smaller employment centers are not
as intrinsically attractive and, therefore, draw less
employees as speeds increase.
Figures 12 and 13 indicate that a 100 percent increase
in speeds will produce as much as a 25 percent change in popu-
lation or employment density. On the other hand, a 33 per-
cent decrease in speeds produces 20 percent changes in em-
ployment density and 15 percent changes in population density.
The speed changes tested with the SAAM represent extreme
values. Since the transportation policy changes used in the
sensitivity test were applied across the entire State, the
results indicate the maximum expected change of a uniformly
applied policy. Large, non-uniform changes in transportation
facilities across the State may produce a larger change in
population and employment densities than 25 percent.
The next chapter describes SAAM data requirement and
data development procedures related to the forecasting process.
CHAPTER VI
FORECASTING WITH THE SAAM
Although a SAAM forecast was not produced for Connecti-
cut, it is anticipated that states will be interested in
using the SAAM as both a policy-testing and a forecasting
device. Therefore, the first section of this chapter is
devoted to a discussion of the 141-zone input data required
in forecasting with the SAAM and approaches which might be
used to develop the required input data. The second section
addresses input data sources and requirements for external
zones.
INPUT DATA REQUIREMENTS FOR INTERNAL ZONES
The Connecticut input data required to forecast 1980
population, retail and services employment, net residential
density, median family income, auto ownership, and labor
force by 141-zones is presented in Table 17. Data supplied
to Submodels II, III, and IV by Submodels I, II, and III are
not included in Table 17. Although the following subsections
specifically address the 1970-1980 forecasting interval, the
comments may be applied equally well to the 1980-1990, 1990-
2000, etc. intervals. Only the input data items in Table 17
which require further explanation are discussed below.
101
102
TABLE 17
INPUT REQUIREMENTS FOR A Hl80 FORECAST -- CONNECTICUT 141 ZONES
Analysis Data Item Year Level Source Comments
Submode! I
Percent population age 45-54 1980 Zone See text Used in fore-
Median family incc.:n..: 1970 Zone 1960-19'l0 SAAM casting 1980 "percent non-
Population density 1970 Zone 1960-1970 SAAM movers"
Submode! II
Population 1970 Zone 1960-1970 SAAM
Labor force parti-cipation rates 1980 Zone See text Used in fore-
Military labor force 1980 Zone See text casting 1980 non-mover primary
Unemrloyment rates 1980 Zon.e See text labor force
Primary iservicc labor (civilian employed}
for~e percentages i98iJ L,oue See text by zone
Primary employment 1980 Zone See text Used in distri-
24-hour highway Derived from buting non-mover
skim tree 1970 Zone 1970 network primary labor force from home
1!1aps to work
Retail employment 1970 Zone 1960-1970 SAAM Used in fore-
Services employment 1970 Zone 1960-1970 SAAM casting 1980 non-mover retail and
24-hour highway Derived f:i;-om services employ-skim tree 1970 Zone 1970 network ment by zone
maps
Retail employment 1980 State See text Used in calculating
Services employment 1980 State See text 1980 mover retail and services employment control totals
102 ;~.
TABLE 17, Continued
Analysis Data Item Year Level Source Comments ------·- ---
Population . 1980 State See text Useci in calculating 1980 mcver popu-lation state control totals
Subrr.odel III --·----Population 1970 Zcne 1960-1970 SAAM Used in calculating
Median family income 1970 Zone 1960-1970 SAAM 1980 mover residen-tial attraction index
24-hour highway De:dved from Used in fore-sbm tree 1970 Zone 1970 network casting 1980
mr.ps mover population
Population holding 1980 Land by zone
capacities 1980 Zone Use Plan
Het.ail emnlovmcnt 1970 Zone 1960-1970 SAAM Used as the
Services employment 1971) Zone 1960-1970 SAAM mover retail and services employ-ment attraction indices
24-hour highway Derived from Used in fore-skim tree 1970 Zone 1970 network casting mover
maps retail and ser-
Retail and services vices employ-
employment-to-pcpu- ment by zone
le.lion ratios 1970 Zone 1960-1970 SAAM
Submcdd iV ---·--·-
New development densities {in persons 1960 Land used in fore-per net residential acre) 1970-1980 Zone Use Plan casting 1960
i'.~edian fa.r;1ily income 1970 Zone 1960-1870 SAAM median family income
AH other required input dat2 is supplied to sui..;moriels of the SAAi1I from preceding subrnodeln.
103
1980 Percent Non-Movers
Although the regression equation calibrated for Connec-
ticut contains the value "percent population age 45-54," this
is a rather difficult value to forecast. To take into account
changes in birth and death rates over time, it is suggested
that a cohort survival technique be employed at the state
level (this may be used in forecasting the 1980 population
control total as well}. Ten-year birth, death, and migration
rate forecasts for each state are available from the U.S.
Census and a review of cohort survival techniques is contained
in Population Forecasting Methods (U.S. Department of Com-
merce, 1964). The difference between the state percent of
population age 45-54 in 1980 versus that percent in 1970 may
then be applied.to each 1970 zonal percentage to obtain 1980
forecasts by zone. This procedure may, of course, be followed
to forecast the percentages for any age group which is found
to be significant in the "percent non-movers" regression.
An alternative approach is to calibrate the "percent non-
movers" relationship with median family income and population
density as the only independent variables. Since both of
these lagged independent variables are output by the SAAM
for preceding intervals, the "percent non-movers" is most
easily forecast in this manner.
104
1980 Labor Force Participation Rates
Labor force participation rates in terms of labor force
per person may be forecast on a zonal basis by performing
a trend line analysis of state labor force participation
rates modified by national labor force projections if neces-
sary. The difference between the forecast 1980 state labor
force participation rate and the 1970 state participation
rate would then be applied to the 1970 zonal rates to produce
1980 zonal forecasts.
1980 Military Labor Force
Military labor force estimates for the forecast years
are influenced by Federal policies related to the draft,
Federal spending, etc. Therefore, these estimates must be
made exogenously with the best current information regarding
the probable opening and closing of military bases and the
expected size of each base in the forecast year.
1980 Unemployment Rates
Unemployment rates may be estimated in a two-step
process, relating national forecasts to the state level and
state forecasts to zones. The difference between the national
105
1980 unemployment rate (generally estimated as 4 percent) and
the 1970 national unemployment rate may be applied to the
1970 state unemployment rate to obtain a 1980 state unemploy-
ment rate. The difference between the state 1970 and 1980
rate may then be applied to each 1970 zonal unemployment rate
to produce 1980 zonal unemployment rates.
1980 Primary and Service Labor Force Percentages
Service labor force percentages may be derived by a
share technique similar to that employed above. First, a
trend analysis based on census data may be performed to
estimate the share of the total labor force held by service
labor force in 1980. The difference between the 1980
service labor force percentage and the 1970 percentage may
then be added to the 1970 zonal service labor force
percentage to produce the 1980 zonal share of service labor
force. The 1980 primary labor force percentages are equal
to 100 percent minus the service labor force percentages.
1980 Primary Employment
A 1980 primary employment control total for the state
may be estimated via a state input-output model or trend
line projections by industry type. The allocation of 1980
106
primary employment to zones is more difficult to forecast.
Since primary employment, by definition, is "site-oriented"
and "growth-generating" rather than "population-serving," the
choice of location by primary industries may be quite diffi-
cult to anticipate.
However, knowledge of the location of future industrial
parks and the expected expansion of existing industrial areas
may assist in the emplacement of future primary employment.
For this reason, it is strongly recommended that the primary
employment allocations for the future be performed by econo-
mists familiar with the study area. Opti~ally, economists
would conduct surveys of large primary employers in the state
to ascertain projected employment growth, expected sites and
criteria for the changing of location.
To supplement this process (or to substitute for it, if
necessary) a mathematical relationship may be developed to 1/
allocate future primary employment.- In a supplementary
context, such a relationship might be used to allocate only
the primary employment remaining after existing stable sites
and the most probable future sites of primary employment have
1/ Experience with such relationships suggests that they may be quite inadequate.
107
been identified. The residual primary employment might then
be allocated to zones on the basis of the following:
ACCik PE.k 1 (t+l)
= (t) E ACCik
PE k(t+l)
Equation (13)
i (t)
-et .. 1] e ACC.k
1 (t) = E PEjk
j (t) Equation (14)
where:
e
t .. 1]
(t)
(t+l)
= Primary employment of type k in zone i
= Accessibility of zone i to primary employment type k
= Primary employment of type k in zone j
= Total primary employment of type k to be employed
= Base of the natural logarithm
= Calibration parameter derived from Table 4
= Travel time or cost from zones i and j
= Base year (i.e., 1970)
= Forecast year (i.e., 1980)
Alternatively, the accessibility function may involve
a negative power function (Lowry, 1964), a negative trans-
formation in logarithmic form (Goldner, et.al., 1972) or
even a gamma function (Voorhees, 1973A).
108
1980 Control Totals
The last input data items to be discussed in this sec-
tion are the 1980 population, retail employment, and ser-
vices employment control totals, which are required in fore-
casting with the SAAM. 1980 population estimates for a state
may be developed by application of a cohort-survival tech-
nique using U.S. Census forecasts of birth, death, and migra-
tion rates. 1980 retail employment and services employment
for a state may be derived from trend projections of retail
and services employment.
INPUT DATA REQUIREMENTS FOR EXTERNAL ZONES
The input data listed in Table 18 for submodels II and
III is required for SAAM forecasts with the eighteen Con-
necticut external zones. Sources for base year externals data
and simplistic methods for forecasting this data are discussed
in this section. All percentages, rates, and incomes derived
from the County and City Data Book, 1972 for Hampden County,
Massachusetts, were applied to all ten external zones within
that county. 1/
This MCD data should be available for Massachusetts from the fourth count of the U.S. Household Census. However, it was not readily available at the time of the SAAM calibrations.
109
TABLE 18 INPUT RmlJIREMENTS FOR A 1980 FOROCAST-CTNNOCTIOJT EXTERNAL ZONES
Analysis Data Items Year level Co'lnents
Sutroodel II
Percent non-novers 1980 Zone
Population 1970 1.one
Iabor force participa- 1980 Zone tian rates
Military labor force 1980 Zone Used in forcasting 1980 rx>n-nnver primary labor force
~loyrcent rates 19&0 Zone (civilian anployed) by zone
Primacy/service 1980 Zone labor force percentages
Primary arployrrent 1980 Zone Used in distributing 1980 non-m:wer service anployrrent
24-hour highway skim tree 1970 Zone demand
Petail anploym:mt 1970 Zone
Services ercploym:mt. 1970 Zone Used in distributing 1980 non-m:wer service anploy-
24-hour highway skim tree 1970 Zone m=nt demand
sutm:Xiel III
Population 1970 Zone Used in calculating 1980 nover residential attrac-
Median family incate 1970 Zone tion index
24-hour highway skim tree 1970 1.one Used in distributing 1980 m:wer population
Population oolding capacities 1980 Zone Used as 1980 :rrover retail
Petail ercployrrent Zone and service attracting imices
Services anployrrent 1970 Zone
24-hour highway skim tree 1970 Zone
Petail and services employ- 1970 1.one Used in distributing 1980 m=nt to population ratios nover retail and service
erploynent
110
Nineteen-seventy percent non-movers for the New York
externals and Hampden County were derived from the County and
City Data Book, 1972. For SAAM forecasts, it is recommended
that the percent non-movers for all external zones be held
constant.
Nineteen-sixty and 1970 population for the external
zones was derived from U.S. Census data. A straight-line
extrapolation of the past population levels will provide an
adequate estimate of future population for external zones.
Nineteen-seventy labor force participation rates, military
labor force, unemployment rates, and primary/service labor
force percentages were obtained for the externals in New York
and Hampden County from the County and City Data Book, 1972.
It is suggested that these data be held constant for all
future forecasts or be estimated as extrapolations of data
from the 1967 and 1972 County and City Data Books.
All travel time data involving external zones should
remain at base year levels for all SAAM forecasts.
Nineteen-seventy employment for external zones was ob-
tained from county statistics collected by New York and
Massachusetts State planning offices. These same offices
111
will provide 1980 employment forecasts by county which may be
divided into primary and service sectors on the basis of the
~orecast split for Connecticut. Service employment may then
be divided into retail and services types based on Connecticut
retail and services employment percentages. 11 Nineteen-sixty
and 1970 median family income may be obtained from the 1967
and 1972 County and City Data Book for the New York external
zones and Hampden County. Future forecasts of median family
income may then be based on an extrapolation of the 1960 and
1970 levels of income by county.
Population holding capacities are set arbitrarily high
for all external zones in both calibration and forecasting
modes. Retail and service employment-to-population ratios
are set to zero for all external zones for calibration and
forecasting purposes.
The next chapter summarizes the results of the SAAM
calibration and application for Connecticut and presents
recommendations related to the use of the SAAM in other states.
1/ Hampden County, Massachusetts, employment data was dis-tributed to the ten external zones on the basis of the population of that zone.
CHAPTER VII
CONCLUSIONS AND RECOMMENDATIONS
The purpose of this study has been to develop and
demonstrate the applicability of an activity allocation pro-
cedure and to develop appropriate data derivation procedures
which may be used at the state level. The expected output
of these procedures was to be: population, retail employ-
ment, services employment, net residential density, median
family income, auto ownership, and labor force, which are
required variables in the statewide trip generation package
(Voorhees, 1973A). The State Activity Allocation Model
(SAAM) has been designed so as to meet these requirements.
Chapter I has introduced the context in which operation-
al urban activity allocation models are currently being
applied and has identified the need for a similar state
model. The second section of Chapter I has provided a
description of the urban area procedures which were evalua-
ted in the process of choosing the basis for the state model.
Chapter II has discussed the major theoretical considerations
which have influenced the SAAM. The most significant single
influence on the SAAM has been the Lowry Model structure.
In addition, the SAAM contains allocation functions which
112
113
were developed by A. G. Wilson at the Centre for Environ-
mental Studies in London, and minimum service employment
thresholds which reflect tenets of Central Place Theory.
However, the SAAM differs from other operational activity
allocation models in its stratification of activity into
movers and non-movers, a concept which improves the theoreti-
cal validity of the model.
Chapter IlI has provided an overview of the SAAM struc-
ture and summaries of the four component submodels. Sub-
model I of the SAAM involves the estimation of the percent
of non-movers living in a small area at the end of the
forecast interval. Submode! II estimates small area levels
of non-mover population, labor force, primary employment,
and service employment by type and mover primary employ-
ment. Submodel III allocates mover population and service
employment to small areas and submodel IV derives small
area estimates of net residential density, media family
income, auto ownership, and labor force.
Chapter IV has described the calibration of the SAAM
for the 1960-1970 interval and 141 Connecticut transporta-
tion zones. This chapter has included descriptions of
data base requirements, sources for Connecticut data, and
calibration techniques for each SAAM submodel. The
114
statistical results of the calibration have been presented.
On a zonal level, the coefficient of determination for con-
strained population was .96 and for total employment, .98.
The percent root mean square error for population was
22.88, while for total employment this was 27.70 percent.
Although some of the calibration errors seem quite
large on a zonal basis, these errors may be attributed
to several factors. First, the 1970 data population and
employment data used in comparison with SAAM submode! III
output were allocated from minor civil divisions to the
141 zone level by a very simplistic methodology (see Appen-
dix A), which may have introduced considerable error.
Secondly, the major source of error seems to be in the small
urban area zones which have large levels of employment com-
pared with population. Central place factors may be used
to increase employment estimates in the small urban area
zones which will, in turn, improve the calibration results
for those zones for which employment was overestimated.
Although resources did not permit the detailed evaluation of
zonal results for the Connecticut calibration, such an
evaluation would be necessary in a state application and
would lead to explanations for or improvements of zonal
calibration results.
115
Once final calibration results have been obtained, the
error between actual and estimated activity levels may be
eliminated by inputing the SAAM estimated calibration
results as the base year in forecasting runs. The SAA.M
will then project activity growth which the user will add
to actual base year activity to obtain SAAM forecasts.
Chapter V has documented the sensitivity test performed
with the SAAM. Six scenarios were compared in the test; the
differences between these scenarios were based on transpor-
tation and land use policy input assumptions. Scenario I
was defined by 1960 Connecticut highway speed and 1964
holding capacity inputs. In Scenarios II and V, the 1960
speeds are doub~ed and in Scenarios III and VI, the speeds
are reduced by one-third. Scenario IV is defined by 1960
speeds and 1973 holding capacities, while Scenarios V and VI
also assume 1973 holding capacities.
The impact of these policy changes on activity distri-
bution is measured in terms of the zonal population and
employment densities output by the SAAM. Population and
employment densities in urban areas vary by as much as
25 percent with a 100 percent increase in speeds, while a
30 percent decrease in speeds produces as much as a 20 per-
cent change in employment density and a 15 percent change
116
in population density. The hQlding capacities in Scenarios
IV-VI have only a minor impact on the distribution of activity
in urban areas.
Chapter\~ has discussed input data requirements and
techniques for developing required data when forecasting
for the 1970-1980 interval with the SAAM. The 1980 input
data for which forecasting techniques are suggested include:
percent non-movers, labor force participation rates, mili-
tary labor force, u~employment rates, primary labor force
percentages, primary employment and activity control totals.
Although application of the SAAM for Connecticut has
involved use of .the mover/non-mover stratification process,
the SAAM may be applied without this process. In this case
only submodels III and IV would be used and total population
and service employment would be allocated rather than
mover population and service employment. The SAAM User's
Manual describes the procedures for by-passing the mover/
non-mover process.
Several recommendations for facilitating the applica-
tion of the SAAM in other states have arisen from experience
with the Connecticut calibration. These may be summarized
as follows:
117
• Define the SAAM small areas as minor civil divisions or groups of minor civil divisions.
• Adopt a 1960-1970 calibration interval and forecast in ten year increments from 1970 using SAAM calibration output as 1970 base data.
• Include external small areas only if there is a significant volume of work and shopping trips across state boundaries.
Further elaboration of these recommendations is presented
below.
It is recommended that states adopt an analysis zone
system which is compatible with minor civil divisions, so
that MCD's or groups of MCD's may be used as the spatial
scale for application of the SAAM. MCD's provide an excel-
lent basis for ~btaining the U.S. Census data required in
calibrating the SAAM. In addition, areas which are smaller
than minor civil divisions (approximately four to six miles
square) are less appropriate for the analysis of intrastate
economic processes, including the interactions among primary
employment, population, and service employment (simulated
by the Lowry procedure in Figure 2).
In conjmction with MCD's or groups of MCD's, it is
suggested that large cities be defined as distinct small
areas in the SAAM allocation system, so that the activity
levels in these cities may be monitored. SAAM input data
118
for cities with a 1960 population of at least 50,000 may be
obtained from 1967 and 1972 County and City Data Books pub-
lished by the U.S. Census. Since urban areas are the most
critical site of most transportation, land use, and environ-
mental problems, it is encouraged that cities be defined
as zones which are spatially independent of the MCD's to
which they belong. In addition, if city zones are defined
separately, then central place factors may be used in the
SAAM to provide minimum service employment levels for these
"market centers-." (See Chapter II for further discussion of
central place factors.)
It is recommended that a ten year calibration (1960-
1970) and forecasting interval be adopted in using the SAAM.
This recommendation is based upon the availability of census
data necessary to calibrate the SAAM for 1960 and 1970. In
addition, it is suggested that the AAM small area calibra-
tion estimates, rather than actual 1970 levels of popula-
tion and service employment by type, be input as base year
data for the 1970-1980 forecast. This will erase fore-
casting errors caused by. an imperfect calibration by allow-
ing the SAAM to project the incremental growth in population
and service employment rather than the absolute level of
activity.
119
External small areas should be defined for states such
as Connecticut which have a large volume of commuters and
shoppers with one trip end in urban areas•of other states.
In fact, all states which contain parts of the Eastern
megalopolis would be advised to include externals in the
SAAM allocation system. However, most midwest and western
states would not require external small areas in the applica-
tion of the SAAM.
It is hoped that these final recommendations may serve
to clarify and facilitate the implementation of the SAAM
by state agencies. Depending on the spatial scale which
is adopted and the number of alternatives tested, it is
estimated that the consulting fees for data refinement,
SAAM calibration, and the forecasting of several alterna-
tives would be $75,000 and $100,000 and the elapsed time
requirement approximately one year.
Of course, the SAAM may also be implemented by an
agency in-house at somewhat lower costs. While this report
has attempted to describe the theory and function of the
SAAM and its calibration for the State of Connecticut, the
· SAAM in-house user will also wish to refer to the SAAM
User's Manual. The User's Manual addresses the computer
aspects of the SAAM, such as job setup, core requirements,
120
and input data organization. Chapters I-VII of this report
and the SAAM User's Manual together should provide sufficient
reference material to support the in-house calibration and
application of the Statewide Activity Allocation Model by
state agencies.
The Connecticut calibration of the Statewide Activity
Allocation Model has demonstrated that the procedure is an
effective tool for allocating state population and service
employment to small areas. At the same time, the Connecti-
cut sensitivity test has proved that the SAAM may be applied
in a policy-making context on the state level. The latter
is of particular significance because a state is a political
jurisdiction with the power and resources necessary to
implement and enforce critical transportation and land use
policies.
121
REFERENCES
Argonne National Laboratory, Illinois River Basin Pilot Project, Appendix C, Center for Environmental Studies, January, 1973.
Batty, Michael, "Recent Developments in Land Use Modeling: A Review of British Research," Urban Studies, June, 1972.
Berry, Brian J.F., Geography of Market Centers and Retail Distribution, Englewood Cliffs, New Jersey: Printice-Hall, 1967.
Chapin, F. Stuart and Shirley F. Weiss, "A Probabilistic Model for Residential Growth," Transportation Research, December, 1968.
Garin, R. A., "A Matrix Formulation of the Lowry Model for Intra-metropolitan Activity Location," JAIP, 1966.
Goldner, William, "The Lowry Model Heritage," Journal of the American Institute of Planners, March, 1971.
Goldner, William, M. M. Reyholds, S. R. Rosenthal, and J.R. Meredith, PLUM/SD--Volume II, The Urban Development Model, developed for the San Diego Comprehensive Planning Organiza-tion, August, 1972.
Harris, Curtis C. Associates, Inc., Evaluation of Regional Economic Effects of Alternative Highway Systems, Final Report to FHWA, January, 1973.
Kilbridge, M.D., R.P. O'Block and P.V. Teplitz, "A Conceptual Framework for Urban Planning Models," Management Science, February, 1969.
King. Leslie J. "Models of Urban Land-Use Development," Models of Urban Structure, David C. Sweet, ed., Lexington Books, 1972.
Lowry, Ira. s., A Model of Metropolis, Rand Memorandum No. RM-4035-RC, August, 1964.
Pack, Janet R., The Use of Urban Models: Report on a Survey of Planning Organizations, The University of Pennsylvania, 1973.
122
Peat, Marwick, Mitchell and Company, Empiric Activity Allo-cation Model Summary, May, 1972.
Peat, Marwick, Mitchell and Company, A Review of Operational Urban Transportation Models, Department of Transportation Final Report No. DOT-TSC-496, April, 1973.
Pinkerton, James R., R.R. Campbell and F.K. Harmston, Pro-jections of Socioeconomic Data to 1967, 1975, and 1990-,~Prepared for the Missouri State Highway Department, June, 1968.
Smith, Robert H.T., E.J. Taffe, Leslie J. King, eds., Readings in Economic Geography, Chicago: Rand McNally and Company, 1968.
State of Connecticut, Department of Finance and Control, Office of State Planning, A Plan of Conservation and Development for Connecticut, January, 1973.
U.S. Department of Commerce, Bureau of Public Roads, Popula-tion Forecasting Methods, June, 1964.
Voorhees, Alan M. and Associates, Application of the Urban Systems Model to a Region - North Central Te~as, Volumes I and II. Prepared for the North Central Texas Council of Governments, October, 1972.
Voorhees, Alan M. and Associates, A Model for Allocating Economic Activities into Sub-Areas of a State, Prepared for the Connecticut Interregional Planning Program, May, 1966.
Voorhees, Alan M. and Associates, Simplified Statewide Travel Forecasting Procedures Including Supply-Demand Relationships-Final Report, March 1973A.
Voorhees, Alan M. and Associates, TRIPS-TransE2rtation Improve-ments Programming_~~tem, January, 1973B.
Voorhees, Alan M. and Associates, Statewide Travel Forecastinq Procedures Including Activity Allocation and Weekend Travel -Phase II, Quarterly Report 1, October, 1973C.
Wilson A.G., Entropy in Urban and Resional Modeling, London: Pion Limited, 1970.
Wilson A.G., "Models in Urban Planning: A Synoptic Review of Recent Literature," Urban Studies, November, 1968.
123
APPENDIX A
124
A DESCRIPTION OF TECHNIQUES FOR ALLOCATING
FROM 169 MCD's TO 141 ZONES
The allocation of activity and socioeconomic data from
169 MCD's to 141 zones was necessitated because much of the
1970 data required by the SAAM was only available by minor
civil division from the Census. The data items presented in
Table A-1 were allocated from MCD's to zones by AMV personnel.
In preparation for the allocation process, an analysis
of the land area of each MCD contained in each zone was
undertaken. Approximate area percentages were then applied
to the 1970 population of each MCD obtained from the U.S.
Cnesus to estimat~ 1970 population by 141 zones. The MCD
containing the largest portion of a zone's land area (and
population) was identified.
All 1970 data for the 12 city zones was based upon the
County and City Data Book, 1972. The proportion of the 1960
population of these 12 zones to the 1960 population of the
cities of which they were a part was used to determine the
1970 population of the 12 zones. The 1970 population of all
other zones was reconciled in these city zones in the MCD
allocation process.
Submodel I Input
1970 Percent
1970 Percent
1970 Percent
1970 Percent
1970 Percent
1970 Percent
125
TABLE A-1
MCD DATA ITEMS
Population Under
Population 24-34
Population 35-44
Population 45-54
Population 55-64
25
Population over 65
1970 Unemployment Rates
Submodel II Input
1970 Labor Force Participation Rates
1970 Unemployment Rates
1970 Military Labor Force
1970 Primary and Service Labor Force
1960 Retail Percentages and Services Employment
1970 Primary Employment
Submode! III Input
1970 Population
1960 and 1970 Retail Employment
1960 and 1970 Services Employment
126
All of the input to Submodel I in Table A-1 was developed
by applying the rate or percentage associated with the most
prominent MCD in a zone to that zone. A similar process was
used for the rates and percentages required as input to
Submode! II. The 1970 military labor force was also allocated
to zones on the basis of the largest MCD since data concerning
the zonal location of military installations was not readily
available.
Nineteen-sixty and 1970 primary employment, retail employ-
ment and services employment required as input to Submodels
II and III were obtained from the Connecticut Department of
Transportation at the MCD level. These data were allocated
to 141 zones on the basis of the percentage distribution of
MCD population in each zone.
The vita has been removed from the scanned document
THE DEVELOPMENT AND APPLICATION OF A
STATE ACTIVITY ALLOCATION MODEL
by
Cathy Digges Schlappi
(ABSTRACT)
Decisions involving statewide land use and transporta-
tion policies and pr6grams require consistent information
concerning the ':?Xpected impact o:i: these actions on the
pattern and <li:msity of development and t!:'avel demand. 'rfte
Statewide Activity Allocation Model (SAAM) is one of a set
of analytical tools which has been developed for the
Federal Highway Administration to provide this state
information.
The SAAM is a Lowry-type model which has a unique
residential mobility concept and provides information on
population and employment by analysis area and forecast
year. The model has been calibrated and subjected to
a sensitivity testing procedure for a 141 zone system
in Connecticut. The results of the calibration and
sensitivity test indicate that t.he SAAM may be useful
in evaluating the impact of alternative transportation
and land use policies at the state level.
