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Joint
Transportation
II JTRP
Research
Program
FHW A/IN/JHRP-96/l 8 -©I Final Report
AN INTEGRATED TRANSPORTATION LAND USE MODELING SYSTEM FOR INDIANA Parti
Andrew Ying-Ming Yen Jon D. Fricker
August 1998
Indiana
Department of Transportation
Purdue University
8
Report
Final
FHW A/IN/JHRP-96/1 AN INTEGRATED TRANSPORTATION LAND USE MODELING SYSTEM FOR INDIANA PARTI by
Andrew Ying-Ming Yen Research Associate
and Jon D. Fricker Professor of Civil Engineering
Purdue University School of Civil Engineering
JOINT TRANSPORTATION RESEARCH Project No. File
Prepared
in
PROGRAM
C-36-54ZZ
No. 3-3-52
Cooperation with the
Indiana Department of Transportation and the
U.S. Department of Transportation Federal
The contents of this
Highway
Administration.
report reflect the views of the authors,
the accuracy of the data presented herein.
who
The contents do not
are responsible for the facts and
necessarily reflect the official
views or policies of the Indiana Department of Transportation or the Federal Highway Administration. This report does not constitute a standard, specification, or regulation.
Purdue University
West Lafayette IN 47907-1284 August 1998
Digitized by the Internet Archive in
2011 with funding from
LYRASIS members and Sloan Foundation;
Indiana Department of Transportation
http://www.archive.org/details/integratedtranspOOyena
8
8
Ill TECHNICAL REPORT STANDARD TITLE PAGE Report No.
1.
2.
Government Accession No.
3.
Recipient's Catalog No.
FHWA/IN/JHRP-96/1 4. Title
and Subtitle
Report Date
5.
August 1998
An Integrated
Transportation Land
Use Modeling System
for Indiana,
Performing Organization Code
6.
Part 7.
I
and Part
II
Authors)
Performing Organization Report No.
8.
Andrew Ying-Ming Yen and Jon D.
FHWA/IN/JHRP-96/1
Flicker
Performing Organization Name and Address Research Program 1284 Civil Engineering Building Purdue University West Lafayette, Indiana 47907-1284
10.
9.
Work Unit
No.
Joint Transportation
Sponsoring Agency
12.
11.
Contract or Grant No.
13.
Type of Report and Period Covered
HPR-2107
Name and Address
Indiana Department of Transportation
Final Report
State Office Building
100 North Senate Avenue
IN 46204
Indianapolis,
Sponsoring Agency Code
14.
Supplementary Notes
IS.
Prepared in cooperation with the Indiana Department of Highways and Federal Highway Administration.
16.
Abstract
The principle objective of this research was
to
develop an integrated model to represent the interrelationships between land use
ISTEA of 1 99 1 and the CAAA of 990. The integrated model includes two major parts: a land-use allocation module and a travel demand module. An interface module has also been built to transform data between these two modules. The land-use allocation module consists of a residential location model, an employment and transportation, subject to the requirements of the
1
location model, a land use potential model, and a land consumption model.
One unique
feature of the residential and
employment location models is that they simultaneously estimate passenger movement by work-to-home, home-to-shop and work-to-shop trips between zones before entering the travel demand module. Then the TRANPLAN-based travel demand module
stages for estimating home-based school, home-based other, non-homeThe land consumption model, which is significantly different from the LANCON procedure of DRAM/EMPAL, is based on micro-economic theory to simulate the profit-maximizing behavior of housing or landowners over time. The major purpose of the land consumption model is to satisfy the need to reach a balance between demand and supply in the housing market during each time period. The land consumption model is also influenced by Anas's work in CATLAS, which did not deal with employment location, but simultaneously considers housing location and employment location. The integrated model can be used to evaluate land use policies and transportation policies. Tests run for the Lafayette area have demonstrated that the model can be used to quantify positive and negative effects of long range carries out trip generation
and
trip distribution
based, external-internal and external-external
transportation and land
The
final report
use plans.
has two parts. Part
I is
the technical report that describes
System (ITLUMS) was developed. Part
ITLUMS, 17.
trips.
the sequence in
II is
which the programs must be
run,
18. Distribution
demand, integrated models, land use
allocation,
Unclassified
Form
DOT F 1700.7 (8-69)
No restrictions.
Use Modeling
FORTRAN programs that make up
files
needed by the
ITLUMS programs.
Statement
This document
is
available to the public through the National
Technical Information Service, Virginia, 22161
land use potentials
19. Security Classif. (of this report)
Indiana Transportation Land
and the format of the input
KeyWords
land use, travel
how the
a separate user's guide, which describes the
20. Security Classif. (of this page)
Unclassified
21. No. of Pages Part
I -
Part
II
28
-158
22. Price
51
TABLE OF CONTENTS
Page
LIST OF TABLES
vi
LIST OF FIGURES
CHAPTER
1.
viii
INTRODUCTION
CHAPTER 2. LITERATURE REVIEW
CHAPTER 3. MODEL STRUCTURE AND METHODOLOGY 3
.
3.2 3.3
3.4 3
.
3.6
Framework Land-Use Allocation Module Land Use Potential Study 3.3.1 Land Suitability Analysis 3.3.2 GIS Database Land Consumption Model Interface Module Travel Demand Module 3.6.1
Simultaneous Location and Trip-distribution Procedures
16 18
26 27 28 28 38 38 38
3.6.3 Trip Distribution
43
Modal
Model
Split
43
Assignment
46
Calibration
CHAPTER 4. DATA REQUIREMENTS AND ANALYSIS 1
16
40
3.6.5 Traffic
4.
5
3.6.2 Trip Generation
3.6.4
3.7
1
Data Requirement
52
66 66
1
Page
CHAPTER 5.1
5
CASE STUDY
Tippecanoe County, Indiana 5.1.1
5.1.2 5.1.3
5.1.4
Land Use Allocation Module Land Use Potential Study Land Consumption Model Travel Demand Model
5.1.5 Policy Test
1
-
5.1.6 Policy Test 2
-
5.1.7 Policy Test 3
-
Improvements of highway network for 20 1 Changes in land use pattern Improvements of highway network for 2015
CHAPTER6 CONCLUSIONS AND RECOMMENDATIONS 6.
Conclusions and Recommendations
76 76 78 85
87 88 91
93
94 119
119
6.2 Future Research
123
6 3 Implementation
124
LIST OF
REFERENCES
Appendix A. Land-Use Potential Study - Scoresheet System Approach Appendix B. Dempster-Shafer Evidence Theory
125
132 135
1
LIST
OF TABLES
Page
Table
3.1
Lot area (square
feet) per dwelling unit,
3.2 Tippecanoe County, Indiana: 1994 data
by
60
district
on auto occupancy
44
5.1
Summary ofthe
Lafayette area in 1970, 1980, 1990,1993,2000
76
5.2
Summary of the
Lafayette area by districts in 1980, 1985, 1990, 1993
98
5.3 Calibrated parameters
ofthe land use allocation module on 1980,
1990 and 1993 data 5.4
The average
99
rents in Tippecanoe
County townships
in
5.5 Estimated coefficients for the existing housing supply in the
5.6
990
100
submodel 100
Lafayette area
Year 2010 population
5.7 Differences in
5.8
1
Year 2010
Year 2010 population forecasts
Retail
5.9 Differences in
forecasts for Policy Test
101
1
for Policy Test
employment forecasts for Policy Test
Year 2010
retail
employment
101
1
102
1
forecasts for Policy Test
5.10 Comparisons of estimated average travel time based on Policy Test
102
1
1
and
base case
5.1
Peak hour Volume/Capacity based on Policy Test 1
103
ratios
on old
US
231
in
1993 and
in
2010 103
Vll
Page
Table 5.12 Year 20 10 Population forecasts Policy Test 2 5.13 Year
2010
Retail
employment forecasts
5.14 Peak hour Volume/Capacity ratios on
104
for Policy Test 2
SR 26
in
1993 and
104
in
2010
based on Policy Test 2
105
5.15 Year 2015 Population forecasts for Policy Test 2
105
5.16 Differences in population forecasts for Policy Test 3
106
5.17 Year 2015 Retail employment forecasts for Policy Test 3
106
5.18 Differences in Year 20 1 5
retail
employment forecasts
107
for Policy Test 3
5.19 Comparisons of estimated average travel time based on Policy Test 3 and
base case
1
5.20 Peak hour Volume/Capacity ratios on Northwestern in
A.
1
B.l
1993 and
Land use
in
2015 based on Policy Test
Avenue and US 52 108
3
134
potential decision-making matrix
Some common
139
evidential intervals
B.2 Probability measures for assessing land
08
suitability
(Dempster-Shafer Theory)
.
145
B.3 Calculation of lower probability
149
B.4 Calculation of upper probability
1
49
LIST
OF FIGURES
Page
Figure
3.1
Framework of Land-Use/Transportation Model
62
3.2 Order of model operation for simulating the dynamics of interaction
between Land use and Transportation 3.3 Structure
3.4
63
of land use potential model
64
The framework of land consumption model
4.1 Forested Land,
65
Tippecanoe County, IN
71
4.2 Distance to Sanitary Sewer System, Tippecanoe County,
4.3
&
Airports, Tippecanoe County,
4.5 Current and Expected
73
IN
74
Land Use, Tippecanoe County, IN
Tippecanoe County, IN
Order of model operation
75
109
5.2 District System, Tippecanoe County,
5.3
72
Road System, Tippecanoe County, IN
4.4 Rail Lines
5.1
IN
IN
for simulating the
110
dynamics of interaction
between Land use and Transportation, Tippecanoe County, IN 5.4 Current and Expected
5.5 Point
Land Use, Tippecanoe County, IN
System Method, Tippecanoe County, IN
77 Ill
1
12
Page
Figure 5.6 Dempster-Shafer Theory, Tippecanoe County,
5.7 Policy Test
5 8
Changes
in
1,
IN
Tippecanoe County, IN
114
the road network by 2000, Tippecanoe County,
5.9 Policy Test 2, Tippecanoe County,
5.10 Policy Test
113
3,
IN
IN
115
116
Tippecanoe County, IN
117
5.11 Changes in the road network by 20 1 0, Tippecanoe County,
IN
118
A evidence
140
B.2 The probability assignment based on
B
140
B.3 The probability assignment based on
A and B
B.
1
The
probability assignment based
on
evidence
evidences
140
CHAPTER 1 INTRODUCTION
Recent
(CAAA)
of 1990 and
Surface Transportation Efficiency Act (ISTEA) of 1991
has placed
legislation in the
the Intermodal
form of the Clean Air Act Amendments
increased emphasis on the use of travel
The
planning analysis.
CAAA
demand simulation models
demands
in
environmental and
that air quality forecasting
must consider the
interaction
between land use and transportation and requires regional land use
mitigating
congestion and
transportation plans to
quantify impacts on land use.
attainment areas need to indicate whether
impacts on
air
The ISTEA
environment impacts.
quality (Wegener,
1994).
new
policies for
long range
requires
For example,
MPOs
These groups believe
that current
non-
transport projects will have negative
The conventional
travel
demand
simulation
processes have, however, received strong criticism from environmental groups 1992).
in
modeling practice overstates the
(NARC,
air quality
emissions benefits of highway improvements by showing speed increases without the
induced
additional
(Hawthorn,
1991).
travel
that
may
result
improved
from
highway
infrastructure
This induced travel would be generated from trips previously
foregone, relocation of activities over a wider area, or
new growth
within the urban area
responding to the improved transportation system performance.
(Neuburger,
1971;
Putman, 1983,1991; Orski, 1989;Wachs, 1989; Mackett, 1993)
The
CAAA
of 1990 and the
ISTEA of
transportation programs and practices.
The
1991
CAAA
transportation planning and project development
Ambient Air Quality Standards programs
in
for
unquestionably will affect ongoing
of 1990 in
will
have a major impact on
areas not meeting the National
ozone and carbon monoxide. The federal-aid highway
those areas will be revised as a result of the
new
law's provisions for
sanctions, conformity, and transportation/air quality issues (Hawthorn, 1991).
of 1991 also in
will
place a greater emphasis on the use of travel
demand
highway
The ISTEA
simulation models
environmental and planning analysis. These two acts will have a profound effect on the
future of land use and transportation interactions.
One of
the most visible elements of public investment in recent decades has been the
enormous expenditures on new highway witnessed large-scale
shifts in population,
This same period
construction.
both from rural areas to urban areas, and within
the urban areas from city center to automobile-oriented suburban development. it
has proven
difficult to establish clear,
Although
complete, and explicit quantitative definitions of
the causal relationships between these developments, exist.
has also
it
is
clear that these relationships
(Putman, 1991; Mackett, 1993; Wegener, 1994; Giuliano, 1995; Waddell, 1995)
Land use covers
a variety of activities, including residing, working and shopping;
physical infrastructure such as workplaces and homes; and the outcomes of market
processes, such as property and land values.
changes
in transport.
Urban theory
also
All these activities can
shows us
be influenced by
that people locate their houses and
workplaces by trading off housing and commute costs and other factors schools, etc.).
Commuters choose
their residential locations
by considering both housing
needs and workplace access. Likewise, employers choose work
sites that are accessible to
employees with tolerable time and monetary costs (Giuliano, 1995). transportation planning requires a
urban
activities (land use).
Most
good
accomplished by predicting
often, this is
employment data
it
good
how
land use
Typically, the analyst will
for the study area, then allocate these area
totals to subareas, such as traffic analysis zones.
the area-wide control totals, but
Therefore,
forecast of the type, magnitude, and location of
patterns will change with respect to base year conditions. predict future population and
(e.g., amenities,
This allocation
is
must also conform to zoning
not only considered by restrictions
on type of
land use in each subarea and reflect the characteristics associated with each subarea that affect land use location decisions.
The
effects
of a change
living in an area
in
the level of activity
on the number of
improved transport
link
on the
trips
level
of
—
for example, the
made and activity
—
number of residents
the impact of a significant are observable
new
phenomena.
or
The
influence of changes in land use pattern on travel pattern tends to be easier to observe than
the converse relationship, because (a) travel patterns are affected primarily
by land use patterns, while
.
(b) land use choices are influenced
The
effects
by many
of land use on transport can be modeled
levels using well-established travel trip distribution,
modal
split,
and
demand modeling
traffic
one of which
factors, only
assignment.
and generally accepted way to model the converse
at
is
transportation.
both aggregate and disaggregate
techniques, such as trip generation,
There
is,
however, no
relationship.
common view
(Putman, 1983; Mackett,
1993)
To
address the above issues, the principal objective of this research
is
to develop an
improved integrated land-use/transportation model to represent the two-way relationships
between land use and transportation, subject
to the following constraints:
1
The requirements of the ISTEA of 1991 and the
2.
The
acquisition of a statewide license by Indiana
(INDOT) 3.
CAAA of 1990.
demand modeling software TRANPLAN.
for the travel
Metropolitan Planning integrated
model
Department of Transportation
Organizations
(MPOs) and
other
potential
users
of the
not have (or could not reasonably be expected to collect) land
will
use and economic data
in
a form or in the level of detail that land use models
previously-developed need as input.
Therefore,
it
may be
travel patterns resulting
necessary to create a feedback mechanism to account for
from changes
in the
development pattern and the converse.
mechanism, where a land use allocation step generation, trip distribution, modal
discussed in
more
detail in
Chapter
Chapter 2 contains the
split
3,
literature
and
is
new This
integrated with the usual four-step (trip
traffic
assignment) travel
demand model,
is
"Model Structure and Methodology".
review for this research project and identifies the
strengths and weaknesses of the current integrated Land-use/Transportation models.
Chapter 3 describes the overall structure of the integrated Land-use/Transportation
model developed and the methodologies adopted
in this research.
Chapter 4 describes data requirements and the process of analytical quantitative analysis.
Chapter
5
is
a case study from Tippecanoe County, Indiana.
Chapter 6 contains the conclusions and recommendations from suggestions for further research.
this research, as well as
.
CHAPTER 2 LITERATURE REVIEW
Conventional four-step travel demand models, whether aggregate or disaggregate, cannot adequately represent the long-term impacts of changes use/transport policies (Putman, 1983; Mackett, 1993).
approach
is
in transport
supply or land-
In land use planning, a
common
the Delphi process, which relies heavily on local planners or experts.
approach does not
explicitly identify the interaction
This
between land use and transportation
and does not systematically evaluate the impact of transportation on land use or the converse, because
The
it
is
based on judgment rather than analytical quantitative approaches.
application of land-use/transportation models has evolved over
ISTEA and
CAAA
the
have accelerated
this evolution.
use/transportation models can be grouped into
Wegener (1994) mentioned meaning least
that they
two
classified
and disaggregate.
land-use/transportation models must be operational,
that
(For a more detailed review of operational models, see Waddell,
Models based on Lowry-type model
DRAM/EMPAL (Putman,
HLFM II + (Horowitz,
1983,1991)
1993)
(Mackett, 1983)
POLIS
(Prastacos, 1986)
Models based on Input/Output economic model
MEPLAN (Echenique et al., TRANUS
(de
KIM (Kim,
la
of
using a modification of Waddell's classification
1995 and Wegener, 1994.)
LILT
set
at
operational land-use/transportation models in use today can be
into the following groups,
system (Waddell, 1995).
2.
types, aggregate
have been calibrated, implemented and used for policy analysis for
The major
ITLUP,
The
In general, the integrated land-
one metropolitan region. This excludes theoretical models presented only as a
equations.
1
two decades.
1990)
Barra, 1989)
1983,1990)
3.
Models based on Random
CATLAS 5-LUT
Utility/Discrete
Choice theory
(Anas, 1985)
(Martinez, 1992)
Hamerslag(1994) Waddell(1995)
4.
Models using microsimulation techniques
NBER-HUDS
(Kain, 1985)
MASTER (Mackett,
5.
1990)
IRPUD
(Wegener, 1986; Wegener
Models
integrated with GIS.
et al.,
1991)
CUFM(Landis, 1993) Batty (1992)
Models based on Lowry-type model
The Lowry-Garin model (Lowry,
1964; Garin, 1966), a spatial interaction approach,
has been applied to study a number of policy issues relevant to fast-growing regions.
These include new transportation changes inability
in
facilities,
increased
labor-force
zoning regulations. However, the analysis of transportation
and
participation, is
hampered by the
of the model to account for endogenous congestion and route choice, or to
provide a basis for measuring the value of benefits produced (Berechman, 1988; Putman, 1983,1995).
grounding 1995).
in
Furthermore,
the
spatial
interaction
approach lacked any appropriate
terms of economic theories of activity location (Wegener,
1
994; Waddell,
Hence, Cochrane (1975) developed a "location surplus" notion to provide
satisfactory theoretical underpinning for
Garin type model.
The
economic theories of activity location
in a
a
Lowry-
derivation indicates that the trips that provide the trip-maker with
the greatest net benefit are the ones chosen.
the multinomial logit model
(MNL)
Furthermore, Anas (1983) demonstrated that
derived from
random
utility
maximization
is,
at
an
equal level of aggregation, equivalent to the entropy and gravity models proposed by
Wilson (1967, 1970).
Although the basic Lowry model circles, variations
on
it
is
called
decades old and
continue to be used
model with widespread application
employment
is
ITLUP
in
not accepted in
newly-developed software packages.
in
(Integrated Transportation
A
Land-Use Package) (Harvey and
ITLUP combines two
land-use model and a transportation network model.
separate components: a
model
In a later project, the land use
revised by improving calibration techniques and by modifying the spatial-allocation
formulae (Putman, 1991 and 1996). submodels:
EMPAL
descriptions, and data
The
model component includes two major
land use
on the current location of employment and population, the
trends, transportation facility descriptions, and data
EMPAL's
business,
developers,
traffic
is
congestion and
and government
based on random
utility.
in
it
In order to
EMPAL
these calculated that will
demand
match the land
METROPELUS, limitations
is
sum of land used available
for
a procedure
the actual change in the
is
1994).
overcome ITLUP 's lack of
demand by household.
be used by each demand category. category, the
their
(LANCON)
to
modified to calculate location by employers,
calculation of location
demands and estimates
model
permits consistent treatment of
calculate land consumption.
DRAM's
DRAM
making decisions about
Putman (1995) incorporates
followed by
Taking regional
not realistically reflect the role of
the land market mechanism,
is
EMPAL
location and investment (Waddell,
a definite improvement because is
facility
on the current location of population,
ITLUP does
respective choice in development process:
However, ITLUP
several types.
forecast of the future location of employment, the
forecasts the future location of households.
household,
(Disaggregated
Beginning with regional trends, transportation
model forecasts the future location of employment of
along with
DRAM
(EMPloyment ALlocation model) and
Residential Allocation Model).
to
some research
the U.S. used to distribute residential population and
Deakin, 1993; Putman, 1974 and 1983).
was
is
LANCON takes both
amount of land, by zone,
After the calculations are done for each
adjusted, using an increase/decrease in densities,
such uses.
The new
release
of ITLUP,
one of the few successful urban models (Wegener, 1994).
of Lowry-type models, including
DRAM/EMPAL,
are:
called
Some
Workplace and housing
1)
they
may be jointly
determined (Waddell, 1995).
The models only consider
2)
choices.
assumed to be sequentially determined. Actually,
location are
They ignore
the
(or
demand
make
side
of
and employment location
residential
a crude representation of) the supply process of
housing and workplace choices.
The models do not
3)
simulate the dynamic process (e.g., the bidding action for house or
building) of changes in land prices or housing rents.
The models do not
4)
realistically reflect the role
of households, businesses, developers,
or governments in making decisions concerning the development process, for example, location choices and investment (Waddell, 1995).
The data 1)
required for
DRAM/EMPAL
3-5 household categories, defined
income groups) by zonal 2)
consist
Employment
is
level,
in
of the following items:
terms of income
whose parameters
whose parameters
3)
Total land area for each zone
4)
Vacant developable land
5)
The percentage of developable
6)
Ratio of the amount of household type n (n
7)
over the study
in the
for each
employment type k to the 1,2,..., 8)
retail,
are individually estimated.
in
the study area
land already developed for each zone.
total
=
1,2,..., 5)
number of employees
in
who
are employees in
employment type k (k =
area.
number of households over
in
employment type k (k =
1,2,..., 8) to
Amount of land
that can
9)
Amount of land
that can be used for
be used for residential development by zonal
employment type k (k =
level.
1,2,..., 8)
development
level.
O-D zone
10)
Impedance
1
A network consists of streets and intersections in the study area.
(e.g., travel
the total
the study area.
8)
1)
manufacturing and
study area.
zone
Ratio of the number of employees
by zonal
are individually estimated.
divided into 4-8 categories (for example,
other employment) by zonal level,
middle, and low
(e.g., high,
time or travel cost) between each
pair.
.
Another Lowry-Garin type model
Model
11+) (Horowitz,
is
called
HLFM
1993).
urban area owing to improvements
in the
HLFM 11+
(Highway Land-Use Forecasting
11+ helps identify developmental impacts in an
highway and
transit systems.
the Lowry-Garin land-use model by permitting constraints on the total
may be
HLFM 11+ extends amount of land
allocated to various activities, by allowing for the possibility for agglomeration in
services,
and by representing constraints on population and service employment
district.
The
Traffic/Land
procedures
traffic forecasting
Quick Response System
Use
for
II
in
HLFM
Windows (QRS
equilibrium (or stabilized
)
HLFM
II).
solution.
five
(e.g.
disadvantages
years,
years
ten
or
more).
in
any
11+ are identical to those of the
The
11+ can find a combined
stabilized condition
there are no variations in activity locations and transportation costs within the
period
that
However,
of other Lowry-derivative models noted
HLFM
earlier.
explanation of the stabilized situation between land use and
11+
A
means
that
same time
also
has
the
more complete
transportation
will
be
described in Chapter 3
The required data 1)
for
One household ,basic
HLFM 11+ consist of the following items: category in the study area. Employment
and service (or
retail)
employment, by zonal
is
divided into 2 categories
level.
2)
Ratio of population to the total number of employees over the study area.
3)
Ratio of the number of service employees to the total population over the study area.
4)
Ratio of the number of service employees to the total number of employees over the study area.
5)
Amount of land
that can
be used for
6)
Amount of land
that can
be used for service development by zonal
7)
Land
8)
Persons per dwelling
9)
Value of time.
10)
Impedance
1
A network consists of streets and intersections in the study area.
1)
residential
development by zonal
level.
level.
area required for each service employee. unit.
(e.g., travel
time or travel cost) between each
O-D zone
pair.
10
The LILT (Leeds
Integrated Land-use Transport) model (Mackett, 1983)
developed for application to the split
city
stages of conventional travel
of Leeds.
It
combines the
demand model with
modes of transport
(car, public transport
trip distribution
a land-use model based
type theory to locate housing and economic activity. three
was
originally
and mode
on Lowry-
The model was disaggregated by
and walk), three socioeconomic population
groups, and twelve industrial sectors (manufacturing, transport and communications,
LILT
construction and so on).
employment (or economic shop
trips
uses processes similar to
activity)
between zones. Trips
ITLUP
to allocate population and
and to calculate the journey-to-work and journey-to-
for other purposes are calculated after the distributions of
population and economic activity have been found, by applying trip-generation and attraction rates based
on the interzonal
use/transportation model.
It
cost.
The LILT model
it
an aggregate land-
is
cannot explicitly represent the links between decision
processes of individuals (for example, choice of transport mode, as
trip-
home
location) over time,
represents population and employment associated with a set of cross-section zonal decisions over time
data, without identifying the various changes to the individuals'
(Mackett, 1990).
The
Projective Optimization
Land Use Information System (POLIS) of the San
Francisco Region, developed by Prastacos for the Association of Bay Area Governments, is
a mathematical programming formulation of a Lowry-type model based on random
utility
same
POLIS
and the given location of basic employment (Prastacos, 1986). limitations as other
shares the
Lowry-type models.
Models based on Input/Output economic model
Two
well-known models based on Input/Output economic analysis are
(Echenique
et al.,
Partners, and
MEPLAN
1990; Hunt and Simmonds, 1993), developed by Marcial Echenique and
TRANUS
(de
la
Barra, 1989), developed by
modeling, these two models use Input/Output structure and linkages of
market and capture the
economic
effect
activities.
Tomas de
la
Barra.
In land use
economic techniques to capture the
They
reflect the
operation of the land
of transportation improvements on land
prices, land use
and
11
development more
realistically
Once
mechanism.
than Lowry-derivative models, which lack a land market
the equilibrium stage of a land use
model
reached,
is
MEPLAN
transforms the resulting flows of labor, service and goods into physical flows of person trips
conventional transport model to do the model
model and the
traffic
The
restraint.
change
MEPLAN
work, to shop, or to school) and goods movements.
(to
transport model
iterated until convergence, that
is
from one
iteration to the next.
of the transport model are fed back in
the next time period.
has been applied
more than
in
by a hierarchical multinomial
logit
assignment by a multi-path probabilistic approach under capacity
in transport costs
of activities
split
uses a
is,
The generating
until there is
no
costs (disutilities)
into the land use model, thus influencing the location
MEPLAN
the second successful urban model and
is
a dozen countries in the world, including Greater
London
(Wegener, 1994).
Furthermore,
Kim
(Kim, 1983 and 1990;
Rho and Kim, 1989) proposed
transportation-land use model incorporating goods
demand
endogenously determined together with
is
of production and resulting
network
is
given.
efficient
The model
is
KIM
which zonal
analysis,
travel
congestion costs, optimal amounts
of land uses, once the transportation
random
utility
programming
and bid-rent theory.
It is
worth
model determines a general equilibrium between transportation
and location based on the
demand with endogenous
link
in
integrated into a consistent mathematical
framework based on input/output noting that only the
densities
movements
a combined
strict
economic sense of equilibrium between supply and
prices (Wegener, 1994).
KIM's approach, however, does
model physical stock, such as workplace (non-residential building such as
not
factories,
shopping centers and so forth) and housing, and land use development.
Models based on Random
The
attractiveness
Utility/Discrete Choice theory
of a discrete choice framework based on random
has increased since the contributions of McFadden (1973) and (1975).
Analysis
utility
maximization
Domencich and McFadden
of mode choice can be done using the standard techniques of
multinomial probit, multinomial logit and nested logit models (Ben-Akiva and Lerman,
12
1985).
Logit and nested logit approaches have also been applied to the choice of
residential location (Martinez, residential location
1992a and 1992b), the joint choice of
travel
mode and
by Lerman (1977), McFadden (1978), and Anas (1981, 1982, 1985),
and the joint choice of
residential location,
workplace and housing tenure by Waddell
(1995).
The Chicago
Area
Use
Transportation/Land
System
Analysis
(CATLAS) was
developed by Anas (Anas and Duann, 1985) and was applied to Chicago.
economic urban simulation model
that
contains a
location and on rent
in transportation policies
mode
implementation
difficulties that
long-term forecasting. 1)
Some of its
The assumption
that
of workplace
unrealistic.
is
may
on
residential
travel
and location choice
an elegant approach, but
it
has
some
development for short-term and
limitations are described below.
workers choose
The model does not
is
limit its potential
their residential location
based on a prior choice
Actually, Waddell (1995) and Giuliano (1995) mentioned
that housing location and workplace
2)
It
prices,
can be viewed as a hybrid of the land
and land use models (following Alonso, (1964)) with the
model (following McFadden, (1973)).
an
designed to evaluate the
It is
on housing and land
CATLAS
choice patterns.
is
simultaneous equation system to
estimate housing and land values and achieve equilibrium.
impact of changes
CATLAS
deal with
may be jointly
employment
determined.
location.
Hence, the validity of the
predictions of land price impacts on changes in land use or transportation strategies will
be questionable. In general, households and businesses compete for location, and
businesses often outbid households for location where they compete (Waddell, 1995). 3)
The mathematical formulation of
the model
is
exceedingly complex, requiring that a
system of hundreds of simultaneous equations be solved for equilibrium.
The
approach creates a large computational burden. 4)
The model
is
estimated
implementation.
in
aggregate form because of the simultaneous equations in the
Further disaggregation would probably substitute a microsimulation
approach for the approach adopted within the
CATLAS.
The microsimulation
procedure would require the development of a different model (Waddell, 1995).
The 5-LUT (5-Stage Land-Use Transport) model Santiago de Chile (Martinez, 1992a).
demand model with
developed by Martinez for
is
Martinez extends the conventional four-step travel
a residential location choice (logit form) as the
The model
fifth level.
integrated the bid-rent theory and discrete-choice approach for residential location choice. It
also has
many of
the
model warrants further
A Dutch
same problems discussed with respect to
C ATLAS.
But
this
attention for potential extension and application.
approach uses a general-equilibrium model
that includes land use,
employment
and residential location, and highway and public transport networks (Hamerslag, 1993 and
The model
1994).
is
based on micro-economic theory under budget and time constraints.
how
The model
identifies
interaction
between transport
the dynamics of land use development are influenced by the infrastructure and land use development,
and provides
forecasting and sensitivity testing of policies for changes in highway and public transport
networks.
This
micro-economic
approach
offers
overcoming existing land-use/transportation model
the
greatest
limitations
opportunities
for
and may warrant further
research and investigation.
Models using microsimulation techniques Aggregate land-use/transportation models cannot the decision processes (housing choice, individuals over time.
For
mode
explicitly explain the links
between
choice, route choice and so forth) of
this reason, the application
of disaggregate microsimulation
approaches to land-use/transportation models becomes
attractive,
and
a
computing
approach based on microsimulation using a large sample of households becomes more efficient
The the
than one based on aggregate data (Waddell, 1995).
NBER
HUDS
(National Bureau of
Economic Research) model (Ingram
et al.,
1972) and
(Harvard Urban Development Simulation) model (Kain and Apgar, 1985) are
economic urban simulation models, which have been applied to policy questions concerning the housing market.
The
NBER-HUDS
models were developed to evaluate
the impacts of spatially housing improvement programs (Kain and Apgar, 1985).
NBER-HUDS
The
models employ a disequilibrium framework to obtain housing choices and
14
location rents within 50 distinct housing markets using a linear
One major weakness of
NBER-HUDS
the
models
is
programming approach.
the assignment of households to
housing units following the disequilibrium process rather than the better-established
market clearing procedures
in
CATLAS
(Anas and Duann, 1985).
The
NBER-HUDS
models, moreover, do not consider the interaction between transportation, land use and the housing markets
MASTER
(Micro- Analytical Simulation of Transport, Employment and Residence) has
been developed
in the
U.K. by Roger Mackett (1990).
It
was
developed
originally
because models such as LILT could not satisfactorily represent the complexity of responses to changes
in
developed by Wegener
at the Institute
(IRPUD) (Wegener,
Another microsimulation model was
the transport system.
Wegener
1986;
of Spatial Planning et
al.,
1991).
at
the University of
The IRPUD model
Dortmund
starts
aggregate data, but uses microsimulation approaches with endogenous sampling
housing market submodel.
with in its
The major shortcomings associated with the microsimulation
techniques are: (Waddell, 1995) 1)
Many
assumptions about individuals' decision processes must be made. This limits
its
credibility.
2)
The
errors involved in the aggregation of microsimulation
model behavior are not
easily identified.
3)
Disaggregation of key actors
computing
cost, although this
(e.g.,
households and businesses) produces a high
problem continues to diminish..
Models integrated with GIS Geographic Information Systems (GIS) are computer-based systems that are used to store and manipulate geographic information. essential tool for the effective use
1970s,
GIS has evolved
as a
This technology has been touted as an
of geographic information (Aronoff, 1989).
means of assembling and analyzing diverse
and Estes, 1990; Laurini and Thompson, 1994). ability to build
improves the
and maintain the
It
spatial data (Star
has greatly enhanced the planner's
spatial database for planning
ability to visualize the land
Since the
and
analysis.
GIS
also
use and transportation planning environments
at
15
the urban, regional, state, and national levels of government.
have started to developed
at
utilize
GIS
techniques.
the Institute of
California
Urban Futures Model (CUFM) was
Urban and Regional Development of the University of
California at Berkeley as a disaggregate first
The
Some new urban models
model of housing development, and
urban models to take advantage of GIS capabilities (Landis, 1993).
not a general purpose land use forecasting model, but benefits
from
integrating
(Waddell, 1995).
GIS
techniques
Another model using GIS
is
into
it
the
is
The
land-use/transportation
one developed by Batty (1992).
Their efforts are exploratory and simplistic
The model, however, does not transportation.
yet
CUFM
is
demonstrates significant potential
exploration, calibration, prediction, and the display of results from the urban entirely dealt with within GIS.
one of the
models
The data model are
at this stage.
consider the interaction between land use and
lt>
CHAPTER 3
MODEL STRUCTURE AND METHODOLOGY
3.1
Framework
Figure 3
.
1
shows the
model developed
in
this
overall
framework of an integrated Land-use/Transportation
research.
It
illustrates
The
forecasting and transportation system modeling. activities
of the markets for land use and transport.
area, the
model estimates the equilibrium housing
the
demand
the relationships between land integrated
use
model simulates the
For each zone within a metropolitan rents (or price of land) resulting
from
created by the activities in the zone and the supply of land or housing units (or
floorspace) at any one time.
In a similar
way, the model estimates the equilibrium
generalized cost of transport, including travel time and costs, that reflects the interaction
between the demand for (or accessibility)
is
travel
and the supply of transport
fed back to the land use
module
at
any time. The transport cost
in the
next time period, thereby
affecting the equilibrium rents of housing units or price of land and the location of activities.
The
integrated
of which
is
model allows comparison between two runs of the integrated model, one
a do-nothing case against which a policy can be tested.
to evaluate land use policies such as
new
industrial
The model can be used
or commercial construction and
transportation policies such as the improvement of the road network. period, the integrated stabilized situation
A
model
will
be iterated
between the land use
means
until
convergence, that
allocation
module and the
no
significant
population and employees over the study area
in the land
stabilized situation
significant
change
that there
is
change
is,
During each time
the model reaches a
travel in
demand module
the distribution of
use allocation module, and no
in transport costs (or travel time) in the travel
demand module from one
iteration to the next.
Figure 3.2 (Echenique
et al.,
land use and transportation.
1990) shows a dynamic process of interaction between In general,
the changes in the land use patterns will
17
Thus, the changes
immediately affect the distributions of travel patterns. activities (or trips
by purpose) resulting from the changes
demand module
as inputs in the travel
Changes
allocation module.
influence
the
accessibility)
spatial
produced
in the travel
module during the next time
The travel
integrated
of land
land use pattern will be used
same time period as
Therefore,
use.
demand module
for the land use
will
transport
the
be used
in the
disutility
(or
land use allocation
period.
model includes two major
demand module.
economic
network, however, will take a longer time to
in the travel
patterns
the
in
in
in
a land-use allocation
parts:
There are interface links (or modules)
module and
a
built to transform data
between these two modules
1)
The land-use
module:
allocation
employment location model,
contains
It
a
residential
a land use potential model,
model. The purpose of this module
is
location
2)
to estimate the spatial pattern
between zones before entering the
The
travel
travel
demand module: This module
for
home-based
estimating
and external-external
modes and then
assigns the vehicle trips
home-based
trips.
It
on the
splits
links
other,
was acquired by
The
TRANPLAN
of network being analyzed
as the basis for the travel
demand module
allocation module. allocation
It
It
on the routes and
Because
the Indiana Department of Transportation
interface module: This
travel
non-home-based,
the trip matrices into individual
considers the behavior of individual stochastic route choice.
3)
simultaneously
contains trip generation and trip distribution
includes capacity restraint on these links to represent congestion
study used
It
demand module.
school,
external-internal
license
of households (or
movement by work-to-home, home-to-shop and work-to-shop
trips
stages
an
and a land consumption
population), employment, and density of occupation and floorspace.
estimates the passenger
model,
a statewide
(INDOT),
this
demand module.
module converts the generalized costs produced from the
into the accessibility
between zones for use
in the land-use
operates in a reverse way, transforming output from the land-use
module such
as the flows of activities
between zones
into the physical flows
of person
trips, e.g.,
the peak-hour trip matrices by purpose, used in the travel
demand
module.
3.2
Land-Use Allocation Module
One major concern of interaction used
to
the land-use allocation
model should incorporate
economic
at least the
It
(3)
It
should reflect the changes
employment
Any such
activities in a region.
should help predict the impact of a change
location
in
employment opportunities
(e.g., a
upon the redistribution of population.
in accessibility to transportation services.
should recognize the importance of transportation costs and nontransportation
attributes (e.g.,
housing needs and neighborhood surrounding)
choice of household (4) It
analysis of spatial
the
following properties.
plant opening, expansion or closing) (2)
is
forecast the likely direction of population growth,
locations and the distribution of
(1) It
module
in
an individual's
site.
should obey population (or housing) and employment capacity constraints that are
either determined the natural
The
by fixing
residential
and employment densities or are affected by
topography of the region.
spatial interaction structure
of land-use allocation module
origins in entropy-maximizing theory (Wilson,
lacked an appropriate grounding 1995).
in
the
in this
its
1967 and 1970). However, Wilson's work
economic theories of
activity location
(Putman,
Consequently, a 'surplus' notion was developed by Cochrane (1975) to provide a
satisfactory theoretical basis for
gravity type model.
The
economic theory of
derivation of 'surplus'
is
activity location in a
explicitly discussed
Furthermore, Anas (1983) asserts that the multinomial logit model
random
research has
utility
maximization
is,
at
Lowry-Garin
by Cochrane (1975)
(MNL)
derived from
an equal level of aggregation, equivalent to the entropy
and gravity models proposed by Wilson.
19
The model developed
research uses a multivariate attractiveness function and a
in this
two-parameter travel deterrence function
Tanner's function, f(^
(i.e.,
=
) ;
A
analogous to Putman's (1995) equation forms. to
specific
satisfy
employment capacity and employment
strategies.
module includes two components: the
residential
exp(-/?/^.)),
consistent constraint procedure
population
including
constraints,
activity
a
f
The core of location
housing)
(or
is
used
capacity,
the land-use allocation
model and the employment
location model.
The
model
residential location
Following the 'surplus' concept proposed by Cochrane, a "location surplus" notion was developed by Putman (1995).
assumed
location model,
it
1995).
assumed
It
is
is
between the
difference
deterministic trip cost
that the
that
exponential in the upper
In order to derive the functional
tail
number of zones
the underlying
ur
distribution
trip.
The
cost
including direct travel payment and travel time cost and so on.
given as ^v probability
=
ja.
-
q
of the surplus
is
's',
given
all
is
approximately defined as the trip,
Therefore, the surplus
we
1) lag.
The amount of new housing constructed and
old stock demolished in a given time period depend on decisions
The land consumption model
in
CATLAS
(e.g.,
made
in last
time period
of a number of equations to
consists
simultaneously for each time period
work
or demolishing old ones
5 years).
These equations,
be
solved
similar to Anas'
(Anas and Duann 1985), are written as follows (equations (3.22)-
(3.30)).
n
I Q
E; wr
:
t,« ex P (-$"
tv )
1
where n
Q ;'=ZS, E?
(3.23)
n
k
=
&;
and and
ytf
=
(Lwrtf^(rp;t
ij
(3 - 24)
)r
X? X f ...X™
(325)
2
where the i
g;'
:
nJ
JJ
:
number of housing
units
of household type n
offered to those employees working in zone
the
number of housing
units
j
at
of household type n
(e.g., single-family) in
time period in
zone
i
at
time period
the probability that a housing unit of household type n in zone
i
at
J :
J :
t
J
be offered for renter occupancy, given the ongoing average rent ffl the probability that a housing unit of household type n in zone i at time period will
J^
t.
time period
will
JJ"
zone
t.
be offered for owner occupancy, given the ongoing average rent
fi£*.
the average monthly rent of housing units of household type n in zone
time period
t.
i
during
t
.
30
x:
a vector of the zone's characteristics related to the supply side, such as the age of
:
an existing housing
~jj
77
unit.
a set of empirically calibrated parameters on the supply side for renter occupancy.
:
a set of empirically calibrated parameters on the supply side for
:
owner
occupancy. :
J?**
time period
at
£
:
f
yn
:
ni :
number of employees
the
in
employment type k
the attractiveness of residential zone
"
,B
=
zone j
i
a
t,
are the attributes of zone
?
,
oc\,
X"
1
+
for population living in household type n at
i
and
households or housing
sr
in
number of households for household type n to employees in employment type k over the study area at time period t the disutility (travel time or travel cost or both) of travel between zone and j.
X?,XX?,...,X
B
who work
the ratio of the
time period
"
(e.g., retail)
t.
i,
such as vacant available land, the number of
units, the
average rent of housing units and so on.
al, ..., an. empirically calibrated parameters on the demand
side.
cr Dr
-i 0,3K
(3-34)
)
.
34
where J
J£"
:
the supply side zone characteristics of housing units of household type n in zone i
during time period
such as the location of the housing unit and the percentage
t,
of developed land. 77 Im
's
are the coefficients to be estimated.
Thus, the probabilities renter
and
JJ"''r
JJ"''o that
an existing housing unit
be offered for
will
occupancy and owner occupancy can be derived using the following two
approaches.
Linear regression method
1
UZ=T]
rfi
K^t
TJrM
m=l
u:: =
t] oo
j k; +
±
lom
m=\
and
XZ+g
(335)
xz+£
(336)
satisfy
uz + uz
+
=
uz
i
°
(3-37)
where
TV*
:
the probability that a housing unit of household type n in
zone
i
at
time period
t
J
be offered for renter occupancy, given the ongoing average rent fl£ the probability that a housing unit of household type n in zone i at time period
will
TV * 1
:
t
be offered for owner occupancy, given the ongoing average rent J£' the probability that a housing unit of household type n in zone i will remain
will
TV*
:
vacant at time period Tj
,77
,7]
nJ
7
p
and-p"- are
2)
Logit model
and
7]
random
,7]
t.
,
,
7]
are empirically estimated coefficients.
error terms.
Ul
UZ
=
(338)
Ul + U2 + U3
35
U2
+U2
Ul
+ U3
U3
UZ=
(
34 °)
Ul + U2 + U3 where
ui=exP (77r0 2r + E
Tlrm
X;D
77^+1 7M
B
m=l
U2=exp(
m=
l
Equations (3.38)-(3.40) comprise the multinomial 77
,77
,..,77
,77
,
and 77
,77
,..-,77
logit
model, where 77
,77
are empirically estimated coefficients
The housing stock adjustment submodel
The adjustments of housing stock
from one time period to the next
are performed
Only the construction of new dwellings on vacant land and the demolition of old dwellings
Anas (Anas and Duann, 1985) mentioned
are considered. crucially
on "present value of profit" (PVP)
Suppose the average
remaining lifetime.
average age
is
rental decision
q.
.
now
Then (time
(K,
that can
lifetime
-
depend
be calculated from a dwelling over
of a dwelling
the present value of profit,
t) until
that these decisions
in
(PVP)
,
zone
i
is
m years
and
its
its
can be obtained from a
the end of a dwelling's lifetime
MUOJl
+ U\,
)
+
(-
AfiuXi-
Ul U'J -
m
CPVP)
-
X
(3-41)
(1
+!)-«
36
If a dwelling can be constructed
on vacant land
in
zone
i,
then the profit accrued from
construction will be represented as follows.
RSji^r
A,,, =(PVP) ai +
C,
-
+
£u
(3-42)
where
RSim
l
(2it
the current construction cost for the dwelling in zone
'
p
random
a
:
the present value of situation will
A,„ = where \Z
is ;
(PVP)
.,,
in
all
be written
Vt,
+
=
profit,
^.
under
£
(
the land price and g.
is
a
random
equation (3 42) can be rewritten
+UI
r
error term.
The present value of
this
3
-
43 )
profit,
as:
(Mk, M\,uW\, -
)
r
+ U'.J
-
MU
m
Z
+
S=\
I
(3-44)
5=1
(1+r)^
The
The
as:
(& W\, ) ; ,,.
i.
be equal to the land price, which incorporates
future taxes and other expenses.
m
PVP
i.
error term
If the land remains vacant, the profit will
(
m years from now in zone
tne resa e value of a dwelling unit
differential profit
1
(1+r)
5
'
between the decision to construct a new dwelling versus keeping
the land vacant can be described as:
N
m
a,„
-
a,,, =
+ziz:;
x
m=
5=1
(1
+
rr
1
\
+
si
-
si
(3.45)
.
37
The term
V m=
Xtln stands for the second summation
_^
may
but these data
Thus
not always be available.
are used to represent these quantities. /L,---,/L
the above assumptions, the probability of a
vacant land
C
C/;-
in
in
equation (3 44) plus ~y.
,
\
zone
i
Under
are coefficients to be estimated
new
can be computed by a binary
a function of the supply side variables
dwelling that will be constructed on
logit
model.
T~
m
N
—
|_
5=1
m=l
_]
I
= m
N
—
l_
5=1
m=l
_|
(346)
I—
1
In a similar way, the probability of demolishing the average old dwelling in
be derived by a binary
logit
zone
i
can
model.
1
UT=
= L
(3-47)
J
m=1
*=a
where
y ,...,y
are empirically estimated coefficients.
Market clearing equilibrium during each time period
The equation
K2
^
•••>
i^']'
(3.22),
'
s
which
is
solved for the market clearing rent vector
J?"
=
tne core of land consumption model during each time period.
iff'
Anas
(1982) has demonstrated that the system of equations (equations (3.22)-(3.30)), given
Q
£
max y =
Ej^Ej
i
-
(i.e.,
constraint
to adjust values
of
find
Z
Ej^Ej
(3
-
68)
j
r ^ mm e < r mod.e
subject to J
employment location model would be run
^ 2 '-' and ^k to
solution for the
and yk (see equation (3.13)), within acceptable
can then be solved to satisfy the second goodness-of-fit criterion
(3.69)).
trip cost is
•
*s
< r ^ max e
(3.69) v '
where jj5"
:
p
:
£ max e C m0 d e r nun e
:
the observed employees working in zone
*-*
by the integrated model.
mean home-to-shop
trip cost.
the lower limit of mean home-to-shop r trip r cost.
Another goodness-of-fit calibration and Rubinfeld, 1991),
employees
j
the upper limit of mean home-to-shop trip cost. tne es timated
:
j.
the estimated employees working in zone
in
will
criterion,
RMSE
(root-mean-square error) (Pindyck
be used to compare the estimated and observed population and
the study area. In the residential location model,
RMSE w -JO/JV)2(i5-^)
3
where
RMSE
po/)
Pi
p N In the
:
:
:
:
the root-mean-square error for population.
the observed population living
in
the zone
the estimated population living in the zone the
number of zones
in the
employment location model,
study area.
i.
i
by the integrated model.
56
RMSE
frai
=
J(1/A0X (Ej-EjY
where
RMSE^
:
J?.
:
p
'
N
the root-mean-square error for employment. the observed employees working
the
:
in
the zone
i.
the estimated employees working in the zone
number of zones
in
i
by the integrated model.
the study area.
Gradient search method
The approach used models
is
to calibrate parameters in the residential and
gradient search technique (Bazaraa
to the nonlinear equations
et. al.,
1993).
employment location
This procedure
is
appropriate
of the two models, and to the non-normal distribution of the
data.
In the residential location model, equation (3.4) can be rewritten in the following
general form.
Z
=
Pi
Ej Bj
m
W tf t
(370)
ex P (-/? f ) f
and
where
p. J? f
the population living in zone
:
the
:
yy.
in
zone j
the disutility (travel time or travel cost or both) of travel between zone
:
.
i
number of employees working
:
B ,B
the residential attractiveness, such as vacant available land, the
households or dwelling
units, the
for population living in
zone
,
o.
:
The term employed
at
i
and
j.
number of
average monthly rent of housing
units,
i.
empirically calibrated parameters.
Q
2
Wi" t/
zone j
will
ex P(-/?
choose to
/, )
live in
represents the average probability of a
zone
i.
commuter
.
57
The of \y
model
calibration processes used in the residential location
B
equation (3.66)) with respect to the parameters
(i.e.,
,
maximize the value
to
B, and or
are derived using
the following steps.
Step
0: Initialization
Choose and Step
1:
set
the starting values for /?(t)
=
t
B(t) and
a(X), pick stopping tolerance £
>
0,
0.
Gradient
Compute function
By
,
the gradient, Vv)/(x(t))
Vj/(x(t))
=
v|/
(/?(t),
/?
(t),
= {dxfldB,
a(t)),
and
its
norm
the chain rule for the derivative, the gradient of
d\y
dp
d\\i
dyldB 1
1
,
dylda), of
V\j/(x(t))
1
1
with respect to
vj/
P
d P>
A
*fi
the likelihood
= t^{dy/ 1 ekjf
B
is
derived:
I ep
jfi
dp x
i
\
/ p,
-
z
S \EjBjA, \\Bj(L p
UAg)-t )
(3.72)
/
\
where
A
fi
'
Wi'tSa&rfij,)
In a similar way, the
