Transportation Planning for Your Community - System Planning Appendix
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PREFACE
This publication is part of a series entitled Transportation
Planning for Your Community and is designed to acquaint officials
and planners with transportation planning for communities of from
25,000 to 200,000 population.
The series consists of two guides that explain the concepts of
transportation planning and five technical manuals that describe
techniques for carrying out transportation planning programs. The
guides are: A Guide for the Decisionmaker and The Manager's Guide
for Developing a Planning Program. The five technical manuals are
titled:
Traffic Planning
Transit Planning
System Planning
Monitoring and Forecasting
Programing Projects
A Guide for the Decisionmaker describes the importance of
urban transportation and the benefits of transportation planning.
It includes a review of how transportation planning works, and the
role of city, county and town officials in transportation planning.
The Manager's Guide for Developing a Planning Program
describes the principles of transportation planning and is directed
to those engineers, planners and administrators who are charged
with the responsibility of organizing and administering the
transportation planning program.
The individual technical manuals describe transportation
planning techniques appropriate for small communities. The manuals
also include references to other publications that describe
appropriate planning techniques.
The Traffic Planning manual is a reference of basic traffic
engineering techniques a nd their potential for improving traffic
flow and traffic safety of urban arterial streets and highways.
The manual identifies the traffic engineering measures appropriate
for consideration in development of transportation improvement
plans and programs.
The Transit Planning manual includes techniques for estimating
transit patronage, service options, and operating requirements.
Also included are procedures for evaluating the need for
specialized services for the elderly and handicapped.
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For sale by the Superintendent of Documents.
U.S. Government Printing Office Washington, D.C. 20402
The System Planning manual details the steps required, for the
functional classification of streets and highways, the estimation
of future traffic, the estimation of the impacts of future traffic,
and the estimation of street and highway system requirements. An
Appendix includes alternative methods for forecasting traffic.
The Monitoring and Forecasting manual provides instructions
for assembling inventories of transportation and land activity. It
describes methods for monitoring the performance of the
transportation system and general community development and methods
for forecasting information needed in urban transportation
planning.
The Programing Projects manual contains procedures for
development of the transportation improvement program. Included
are procedures for identification of candidate improvement
projects, determination of the plan to fund candidate improvement
projects, assignment of priorities to candidate improvement
projects, budget allocation and project scheduling, and monitoring,
adjusting and evaluating the programs.
This series was prepared by the COMSIS Corporation and the
Highway Users Federation for Safety and Mobility under a grant from
the Federal Highway Administration with the aid of a "steering
committee" made up of the following officials:
Dan C. Dees
Illinois Department of Transportation
Springfield, Illinois
James Echols
Tidewater Transportation Commission
Norfolk, Virginia
David D. Grayson
Automobile Club of Southern California
Los Angeles, California
John J. Holland
Cumberland County Planning Board
Bridgeton, New Jersey
F.W. Landers
Department of Public Works
Worcester, Massachusetts
Marion R. Poole
North Carolina Department of Transportation
Raleigh, North Carolina
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The principal investigators were:
Arthur B. Sosslau
COMSIS Corporation
Wheaton, Maryland
Marshall F. Reed, Jr.
Highway Users Federation for Safety and Mobility
Washington, D.C.
Other principal authors were Maurice M. Carter of COMSIS
Corporation and Woodrow W. Rankin of the Highway Users Federation.
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TABLE OF CONTENTS
Page
APPENDIX A USEFUL DATA (DEFAULT VALUES) FOR MANUAL AND COMPUTER
APPLICATIONS . . . . . . . . . . . . . . . . . . A-1
APPENDIX B APPLICATION OF THE MANUAL TRIP DISTRIBUTION
PROCEDURE. . . . . . . . . . . . . . . . . . . . B-1
APPENDIX C TRIP INTERCHANGE MODAL SPLIT MODEL . . . . . . . C-1
Model Development. . . . . . . . . . . . . . . . C-1
Data Required for Application. . . . . . . . . . C-4
Application of the Manual Modal Choice Estimation
Procedures . . . . . . . . . . . . . . . . . . . C-8
Single Purpose Modal Split Model . . . . . . . .C-23
APPENDIX D GUIDE TO UTPS PROGRAMS FORMING SIMPLIFIED CHAIN FOR
FOUR-STEP TRANSPORTATION PLANNING. . . . . . . . D-1
Program RR . . . . . . . . . . . . . . . . . . . D-1
Program UROAD (Time Matrix Preparation). . . . . D-2
Program SCAGM (Small City Trip Generation and
Gravity Model) . . . . . . . . . . . . . . . . . D-2
Input Files. . . . . . . . . . . . . . . . . . . D-3
SYSIN File . . . . . . . . . . . . . . . . . . . D-5
J1 File. . . . . . . . . . . . . . . . . . . . . D-5
P and A Files. . . . . . . . . . . . . . . . . . D-5
F File . . . . . . . . . . . . . . . . . . . . . D-5
K File . . . . . . . . . . . . . . . . . . . . . D-8
ZONAL1 File . . . . . . . . . . . . . . . . . . D-3
ZONAL2 File . . . . . . . . . . . . . . . . . . D-8
PRATES File . . . . . . . . . . . . . . . . . .D-14
PRATES File Format. . . . . . . . . . . . . . .D-14
J9 File. . . . . . . . . . . . . . . . . . . . .D-19
Trip Attraction Rates. . . . . . . . . . . . . .D-19
Internal-External Trips. . . . . . . . . . . . .D-19
Auto Driver Trips. . . . . . . . . . . . . . . .D-20
Truck Trips. . . . . . . . . . . . . . . . . . .D-20
External-External Trips. . . . . . . . . . . . .D-21
Program UMATRIX. . . . . . . . . . . . . . . . .D-21
Program UROAD (Traffic Assignment) . . . . . . .D-22
APPENDIX E DETAILS OF TRAFFIC ESTIMATION BASED ON GROUND COUNTS
MANUAL APPLICATION . . . . . . . . . . . . . . . E-1
Input Requirements and Steps in Application. . . E-1
An Example Application . . . . . . . . . . . . . E-5
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TABLE OF CONTENTS (Continued)
Page
APPENDIX F COMPUTER PROGRAMS FOR GROUND COUNT FACTORING. . F-1
UROAD - Application (1). . . . . . . . . . . . . F-1
UROAD - Application (2). . . . . . . . . . . . . F-3
Program UMCON. . . . . . . . . . . . . . . . . . F-3
APPENDIX G EXAMPLE OF REDISTRIBUTION OF ASSIGNED VOLUMES AMONG
AVAILABLE FACILITIES . . . . . . . . . . . . . . G-1
APPENDIX H DETAILS OF THE PARTIAL MATRIX TECHNIQUE (PMT). . H-1
Theory of the PMT. . . . . . . . . . . . . . . . H-1
Computational Steps for Application of the PMT . H-4
REFERENCES. . . . . . . . . . . . . . . . . . . . . . . . . . . I-1
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LIST OF FIGURES
Figure
Number Title Page
A-1 Airline Distance vs. Travel Time vs. Distribution Factors
by Trip Purpose: Urbanized Area
Population = Under 100,000 . . . . . . . . . . . . . . . .A-12
A-2 Airline Distance vs. Travel Time vs. Distribution Factors
by Trip Purpose: Urbanized Area
Population = Under 100,000 . . . . . . . . . . . . . . . .A-13
A-3 Airline Distance vs. Travel Time vs. Distribution Factors
by Trip Purpose: Urbanized Area
Population = Under 100,000 . . . . . . . . . . . . . . . .A-14
A-4 Airline Distance vs. Travel Time vs. Distribution Factors
by Trip Purpose: Urbanized Area
Population = Under 100,000 . . . . . . . . . . . . . . . .A-15
A-5 Airline Distance vs. Travel Time vs. Distribution Factors
by Trip Purpose: Urbanized Area
Population = Under 100,000 . . . . . . . . . . . . . . . .A-16
A-6 Airline Distance vs. Travel Time vs. Distribution Factors
by Trip Purpose: Urbanized Area
Population = Under 100,000 . . . . . . . . . . . . . . . .A-17
A-7 Airline Distance vs. Travel Time vs. Distribution Factors
by Trip Purpose: Urbanized Area
Population = Over 100,000. . . . . . . . . . . . . . . . .A-18
A-8 Airline Distance vs. Travel Time vs. Distribution Factors
by Trip Purpose: Urbanized Area
Population Over 100,000. . . . . . . . . . . . . . . .A-19
A-9 Airline Distance vs. Travel Time vs. Distribution Factors
by Trip Purpose: Urbanized Area
Population = Over 100,000. . . . . . . . . . . . . . . . .A-20
A-10 Airline Distance vs. Travel Time vs. Distribution Factors
by Trip Purpose: Urbanized Area
Population = Over 100,000. . . . . . . . . . . . . . . . .A-21
A-11 Airline Distance vs. Travel Time vs. Distribution Factors
by Trip Purpose: Urbanized Area
Population = Over 100,000. . . . . . . . . . . . . . . . .A-22
A-12 Airline Distance vs. Travel Time vs. Distribution Factors
by Trip Purpose: Urbanized Area
Population = Over 100,000. . . . . . . . . . . . . . . . .A-23
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LIST OF FIGURES (Continued)
Figure
Number Title Page
B-1 Map of Study Area: Hypothetical City (Step 1). . . . . . . B-2
B-2 Manual Trip Distribution Worksheet, Enter Production
and Attraction Trip Ends (Step 9). . . . . . . . . . . . . B-3
B-3 Enter District-to-District Travel Times and Distribution
Factors (Step 3) . . . . . . . . . . . . . . . . . . . . . B-4
B-4 Calculate Attraction Factors, Accessibility Index and
Production Index - Iteration #1 (Step 4):
Calculate Trip Interchanges - Iteration #1 (Step 5). . . . B-6
B-5 Recalculate Attraction Factors, Accessibility Index,
Production Index - Iteration #2 (Step 6);
Recalculate Trip Interchanges - Iteration #2 (Step 7). . . B-9
B-6 Summary Flowchart of the Manual Trip Distribution
Procedure. . . . . . . . . . . . . . . . . . . . . . . . .B-12
C-1 Nomograph for Conversion of Airline Distance to
Average Operation Speed. . . . . . . . . . . . . . . . . . C-7
C-2 Flowchart of the Manual Mode Choice Estimation
Procedure. . . . . . . . . . . . . . . . . . . . . . . . . C-9
C-3 Mode Choice Analysis Worksheet A . . . . . . . . . . . . .C-10
C-4 Nomograph for Conversion of Airline Distance to Total
Impedance-Transit: (Access Mode=Walk). . . . . . . . . . .C-12
C-5 Nomograph for Conversion of Airline Distance to Total
Impedance-Transit: (Access Mode=Auto). . . . . . . . . . .C-13
C-6 Nomograph for Conversion of Airline Distance to Total
Impedance-Auto; Operating Cost: $0.05/Mile . . . . . . . .C-14
C-7 Nomograph for Conversion of Airline Distance to Total
Impedance-Auto: Operating Cost: $0.10/Mile . . . . . . . .C-15
C-8 Nomograph for Conversion of Airline Distance to Total
Impedance-Auto: Operating Cost: $0.15/Mile . . . . . . . .C-16
C-9 SLM Mode Choice Model Trip Purpose = HBW. . . . . . . .C-17
C-10 SLM Mode Choice Model Trip Purpose = HBNW . . . . . . .C-18
C-11 SLM Mode Choice Model Trip Purpose = NHB. . . . . . . .C-19
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LIST OF FIGURES (Continued)
Figure
Number Title Page
C-12 Mode Choice Analysis Worksheet B . . . . . . . . . . . . .C-22
C-13 Nomograph for Conversion of Airline Distance to Total
Impedance-Transit; Single Purpose Model. . . . . . . . . .C-27
C-14 Nomograph for Conversion of Airline Distance to Total
Impedance-Auto; Single Purpose Model
Operating Cost: $0.05/Mile . . . . . . . . . . . . . . . .C-28
C-15 Nomograph for Conversion of Airline Distance to Total
Impedance-Auto; Single Purpose Model
Operating Cost: $0.10/Mile . . . . . . . . . . . . . . . .C-29
C-16 Nomograph for Conversion of Airline Distance to Total
Impedance-Auto; Single Purpose Model
Operating Cost: $0.15/Mile . . . . . . . . . . . . . . . .C-30
C-17 SLM Mode Choice Model - All Purpose Trips. . . . . . . . .C-31
D-1 Sample Zone Production and Attraction Data . . . . . . . . D-6
D-2 Sample Production Zone Activity Input Data . . . . . . . .D-10
D-3 Sample Production Zone Activity Input Data--Income Not
Input. . . . . . . . . . . . . . . . . . . . . . . . . . .D-11
D-4 Sample Production Zone Activity Input Data--Single
Areawide Income and Auto Ownership . . . . . . . . . . . .D-12
D-5 Sample Attraction Zone Activity Input Data . . . . . . . .D-15
E-1 Computation of the Average Growth Factor by Highway Section
Using Base Year and Future Year Productions and
Attractions. . . . . . . . . . . . . . . . . . . . . . . . E-4
E-2 Flowchart Representation of the Traffic Estimation Method
Based on Ground Counts . . . . . . . . . . . . . . . . . . E-7
E-3 Map of Study Area Showing Districts and Highway Network
Selected for Analysis (Step 1) . . . . . . . . . . . . . . E-8
E-4 Base Year I-E, E-E Vehicle Trip Matrix (Step 3). . . . . .E-10
E-5 Assignment Worksheet Showing Base Year I-E, E-E Vehicle
Trips (Step 3) . . . . . . . . . . . . . . . . . . . . . .E-11
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LIST OF FIGURES (Continued)
Figure
Number Title Page
E-6 Base Year All Purpose I-I Vehicle Trip Distribution
Using the Gravity Model (Steps 5, 6, 7). . . . . . . . . .E-14
E-7 Base Year All Purpose I-I Vehicle Trip Matrix (Step 7) . .E-15
E-8 Future Year All Purpose I-I Vehicle Trip Distribution
Using the Gravity Model (Steps 8, 9, 10) . . . . . . . . .E-16
E-9 Future Year All Purpose I-I Vehicle Trip Matrix
(Step 10). . . . . . . . . . . . . . . . . . . . . . . . .E-18
E-10 Assignment Worksheet Showing Base Year and Future Year All
Purpose I-I Vehicle Trips by Link (Steps 11, 12) . . . . .E-19
E-11 Growth Factors for Districts and External Stations
(Step 14). . . . . . . . . . . . . . . . . . . . . . . . .E-20
E-12 Average Growth Factors for District/External Station Trip
Interchanges (Step 15) . . . . . . . . . . . . . . . . . .E-22
E-13 Future Year (Expanded) I-E, E-E Vehicle Trip Matrix
(Step 17). . . . . . . . . . . . . . . . . . . . . . . . .E-23
E-14 Assignment Worksheet Showing Future Year I-E, E-E
Vehicle Trips (Step 18). . . . . . . . . . . . . . . . . .E-24
E-15 Summary of Base Year and Future Year Vehicle Trips
by Link. . . . . . . . . . . . . . . . . . . . . . . . . .E-26
F-1 Program Chain for Computerized Traffic Estimation Based on
Ground Counts. . . . . . . . . . . . . . . . . . . . . . . F-2
G-1 Cutlines of Screenline A-A for Redistribtuion Analysis
Within the North-South Corridor. . . . . . . . . . . . . . G-2
G-2 Comparison of Capacity and Base Year, Future Year and
Redistributed Traffic Volumes for Highway Links Crossing
Screenline A-A . . . . . . . . . . . . . . . . . . . . . . G-6
H-1 Hypothetical Study Area and Trip Movements . . . . . . . . H-2
H-2 Map of Study Area: Hypothetical City (Step Al) . . . . . . H-9
H-3 Partial Average Daily Vehicle Trip Matrix Resulting from
Trips Observed at the Cordon and Screenline Interview
Stations (Step A2) . . . . . . . . . . . . . . . . . . . .H-10
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LIST OF FIGURES (Continued)
Figure
Number Title Page
H-4 PMT Worksheet Showing Partial Production and Attraction
Trip Ends (Step A2), and District-District Travel Times
and Distribution Factors (Step A3) . . . . . . . . . . . .H-11
H-5 PMT Worksheet Showing Computations for Step Bl through
Step B7. . . . . . . . . . . . . . . . . . . . . . . . . .H-13
H-6 PMT Worksheet Showing Computations for Step B8 through
Step B13 . . . . . . . . . . . . . . . . . . . . . . . . .H-16
H-7 PMT Worksheet Showing Computations for Step B14 through
Step B19 . . . . . . . . . . . . . . . . . . . . . . . . .H-17
H-8 PMT Worksheet Showing Computations for Steps C1,
C2 and C4. . . . . . . . . . . . . . . . . . . . . . . . .H-19
H-9 Comparison of Trip Interchanges Obtained from the PMT
and from a Full-Scale FM . . . . . . . . . . . . . . . . .H-21
H-10 Completed Trip Matrix Resulting from the Use of the PMT. .H-22
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LIST OF TABLES
Table
Number Title Page
A-1 Detailed Trip Generation Characteristics
Urbanized Area Population; 25,000-50,000 . . . . . . . . . A-1
A-2 Detailed Trip Generation Characteristics
Urbanized Area Population; 50,000-100,000. . . . . . . . . A-2
A-3 Detailed Trip Generation characteristics
Urbanized Area Population; 100,000-200,000 . . . . . . . . A-3
A-4 Trip Generation Parameters:
Part A - Trip Production Estimates . . . . . . . . . . . . A-4
Part B - Useful Characteristics for Trip Estimation. . . . A-5
Part C - Trip Attraction Estimating Relationships. . . . . A-6
A-5 Assumptions Used in Developing Conversion
Charts for Urbanized Areas . . . . . . . . . . . . . . . . A-7
A-6 Speed Values (MPH) by Facility Type by Subregion by
Urbanized Area Population. . . . . . . . . . . . . . . . . A-8
A-7 Distribution Factors by Urbanized Area Population and
by Trip Purpose. . . . . . . . . . . . . . . . . . . . . . A-9
A-8 Average Daily Auto Occupancy Rates (1976) by
Urbanized Area Population and Trip Purpose . . . . . . . .A-10
A-9 Average Daily Auto Occupancy Rates (1976) by Urbanized
Area Population and Land-Use at Trip Destination . . . . .A-11
C-1 SLM Calibration Exponents. . . . . . . . . . . . . . . . . C-3
C-2 Input Data Elements Required for Mode Choice Analysis. . . C-5
C-3 Impedance Variables for Single Purpose SLM . . . . . . . .C-24
D-1 Files for SCAGM. . . . . . . . . . . . . . . . . . . . . . D-4
D-2 Distribution Factors by Urbanized Area Population and
by Trip Purpose. . . . . . . . . . . . . . . . . . . . . . D-7
D-3 Production Zone Activity Data Format . . . . . . . . . . . D-9
D-4 Attraction Zone Activity Data Format . . . . . . . . . . .D-13
D-5 Default PRATES1 (Person Trips) . . . . . . . . . . . . . .D-16
D-6 Default PRATES2 - Population 50,000-100,000. . . . . . . .D-17
xii
LIST OF TABLES (Continued)
Table
Number Title Page
D-7 Default PRATES3 - Population 100,000-200,000 . . . . . . .D-18
G-1 Traffic Data for Highway Links Within the North-South
Corridor and Crossing Screenline A-A . . . . . . . . . . . G-3
G-2 Worksheet for Redistributing Future Year Ground Counts . . G-4
xiii
APPENDIX A
USEFUL DATA (DEFAULT VALUES) FOR
MANUAL AND COMPUTER APPLICATIONS
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A-1
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A-2
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A-3
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A-4
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A-5
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A-6
TABLE A-5
ASSUMPTIONS USED IN DEVELOPING CONVERSION CHARTS
FOR URBANIZED AREAS WITH POPULATION 100,000 AND ABOVE:
Central
CBD City Suburb
Terminal time (mins.) 6 3 1
Local street distance (miles) 0.0625 0.1875 0.5000
Local street speed (mph) 11 15 25
Local street time (mins.) 0.34 0.75 1.20
Total terminal timeb 6.34 3.75 2.20
(terminal+ local street time) (mins.)
FOR URBANIZED AREAS WITH POPULATION LESS THAN 100,000:
Central
CBD City Suburb
Terminal time (mins.) 4 2 1
Local street distance (miles) 0.0625 0.1875 0.5000
Local street speed (mph) 14 20 29
Local street time (mins.) 0.27 0.56 1.03
Total terminal timeb 4.27 2.56 2.03
(terminal + local street time) (mins.)
FOOTNOTE:
a. Source: Various urban transportation studies.
b. This time represents the total terminal time at either
the origin end or the destination end of a trip.
Therefore, to obtain the total O-D terminal time for a
trip originating, say, in the CBD and terminating in the
suburb, this time is 6.34 + 2.20 = 8.54 mins. (for an
urbanized area population of 100,000 and above).
A-7
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A-8
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A-9
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A-10
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A-11
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A-12
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A-13
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A-14
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A-15
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A-16
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A-17
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A-18
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A-19
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A-20
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A-21
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A-22
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A-23
APPENDIX B
APPLICATION OF THE MANUAL TRIP DISTRIBUTION PROCEDURE
Five districts in a hypothetical urban area of 60,000
population are to be analyzed for all purpose trips, i.e., HBW +
HBNW + NHB trips. Productions and attractions for each district
(and for all three purposes) are provided from the trip generation
phase. The method proceeds in the following manner:
STEP 1: Map of Study Area. Lay out a map showing the five
districts, district centroids and subregion boundaries (Figure
B-1). A map showing major arterials and freeways is useful.
A highway road map is usually suitable for this purpose.
STEP 2: Enter Production and Attraction Trip Ends - Pj, Aj
These trip end totals (for all purpose trips) are entered in
the trip distribution worksheet along with other
identification features such as headings, district numbers,
etc. (Figure B-2). Thus, for example, district #2 produces
10,400 all purpose trips and attracts 11,600 trips, The total
number of all purpose trips for the 5 districts amounts to
100,000 trips.
STEP 3: Enter District-to-District Travel Times and
Distribution Factors Fij Although it is only the distribution
factors that are to be used in the computation of trip
interchanges, it is useful to enter and retain the travel
times - these times will enable the user to better relate and
perceive the spatial separation between the districts (Figure
B-3).
Helpful Aids and Notes of Caution:
1. Since the construction of the travel time/distribution
factor matrix entails repetitive steps, it is important
that the user build up and maintain some kind of "mental
rhythm" particularly when there are a large number of
interchanges involved. This results in some time
savings. One efficient approach is exemplified below:
Steps User Response
i. Identification of origin- "2 to 5, central city to suburb."
destination subregions
ii. Scaling of airline distance "Figure A-5: 1.6 mile central
and reading off travel time city @ 20% arterial...in-vehicle
from appropriate graphs. travel time = 2.6 mins."
"Figure A-6: 1.1 mile suburb @
100% arterial...in-vehicle
travel time = 1.4 mins."
iii. Total 0-D terminal times Central city to suburb = 6.0
mins."
iv. Total travel time "2.6 + 1.4 + 6.0 = 10.0 mins."
v. Distribution factor (all "1.70"
purpose) @ 10 mins.
B-1
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B-2
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B-3
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B-4
And so on. This series of operations can be performed very easily
on the desk calculator. A calculator with paper tape could prove
handy in that travel time for the various portions of the trip
interchange can be saved for later checking should the need arise.
Note that in Figure B-3, the distribution factors are not from
Appendix A, but have been fabricated for the example.
2. Although the time matrix is triangular, it is helpful to
enter all the interchange cells with their respective travel time
and distribution factors,
3. Caution should be exercised when making judgments on the
freewayarterial percentage mix for any interchange, since distances
on a map can be visually deceptive especially when a small map
scale is used.
STEP 4: Calculate Attraction Factors (AiFij), Accessibility
Index on Index (Ri) - Interation #1 : Except for Ri, the terms
AjFij and äAjFij are calculated to the nearest 100 (Figure B-4).
- Attraction factor from district i = 2 to district j = 5 is;
A F = 8,000 x 0.17 = 1,400
j ij
- Accessibility index for district i = 2 is:
5
ä A F = 14,400 + 6,100 + 4,700 + 6,000 + 1,400
j=1 j ij
= 32,600
- Production index for district i=2 is:
P
i
R = _________ = 10,400/32,600 = 0.319018
i 5
ä A F
j = 1 j ij
And so on for all rows and columns.
Helpful Aids and Notes of Caution:
1. As a time saving measure, the attraction factors (AjFij)
can be computed by columns instead of rows. For instance, for
column 5, the attraction (Aj = 8,000) can be stored as a constant
in the desk calculator; the attraction factors (AjFij 's) from i =
1 to 5 can be calculated by entering the respective Fij in the
calculator and obtaining the product.
STEP 5: Calculate Trip Interchanges (Tij) - Iteration #1 :
The trip interchanges are calculated using Tij = RiAjFij, The
production and attraction totals at the end of iteration #1 are
also obtained
B-5
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B-6
(Figure B-4). Thus:
- Trip interchange for district i=2 and district j=5 is;
T = R A F = 0.319018 x 1,400 = 400
ij i j ij
- Production total for district i=2 is:
5
P = ä T = 4,600 + 2,000 + 1,500 + 1,900 + 400
i j=1 ij
= 10,400 (which matches the desired P )
i
- Attraction total for district j=5 is:
5
A = ä T = 300 + 400 + 2,100 + 1,000 + 4,500
j i=1 ij
= 8,300
(Unbalanced. +4% difference from desired A )
j
At this point, due to the structure of the Gravity Model
formulation which constrains the production values, the production
total for each district will equal the true production trip ends.
The attraction totals, however, will not necessarily match their
input values. To refine the calculated interchanges, attraction
totals are adjusted prior to application in iteration #2.
The adjustment is made as shown below:
- Adjusted attraction total for district j=5 for use in
iteration #2 is:
A
2 1 5 8,000
A = A (_____) = 8,000 x _________ = 7,700
5 5 1
C 8,300
5
1
where: C = Column 5 total for iteration #1.
5
And so on for all columns (Figure B-4).
Helpful Aids and Notes of Caution.
1. A time saving can be realized by storing Ri as a constant
in the calculator and then computing Tij by entering AjFij for j=1
to 5.
2. There must be production balance: if not, an error may
have been introduced in the preceding calculations, However, if the
balance is off only slightly, it may be due to rounding errors
which may be ignored.
B-7
3. It is wise to compute the percent differences between the
attraction total at the end of iteration ill and the desired
attractions. This will indicate the magnitude of deviations,
4. It should be noted that the trip matrix is not
triangular, i.e., trips from i to j not = to trips from j to i;
therefore, interchanges for all cells must be calculated.
STEP 6: Recalculate Terms as in Step 4 - Iteration #2 : This
step (Figure B-5) is a repetition of Step 4, but using the adjusted
attraction totals out of iteration #1. Thus:
þ Attraction factor from district i=2 to district J=5 is;
A F = 7,700 x 0.17 = 1,300
j ij
- Accessibility index for district i=3 is:
5
ä A F = 14,800 + 6,500 + 4,300 + 6,000 + 1,300
j=1 j ij
= 32,900
- Production index for district i=2 is:
P
i
R = __________ = 10,400/32,900 = 0.316109
i E
ä A F
j=1 j ij
And so on for all rows and columns.
STEP 7: Recalculate Terms as in Step 5 - Iteration #2 : This
step is a repetition of Step 5, but using the new attraction
factors (A Fij) and the new production index (Ri) computed in Step
6. The production and attraction totals are also calculated by rows
and columns respectively (Figure B-5). Thus:
- Trip interchange from district i=2 to district j=5 is:
T = R A F = 0.316109 x 1,300 = 400
ij i j ij
- Production total for district i=2 is:
5
P = ä T = 4,700 + 2,100 + 1,400 + 1,900 + 400
j=1
= 10,400 (which matches the desired P )
i
B-8
Click HERE for graphic.
B-9
- Attraction total for district j=5 is:
5
Aj = ä T = 300 + 400 + 2,100 + 1,000 + 4,400
j j=1 ij
= 8,200
(+3% difference from desired Aj)
At the end of this iteration, the new attraction totals should
have converged very close to the desired attraction totals. If
this is not the case and it is desired that trip interchanges be
refined further through an additional iteration (#3), the adjusted
attraction totals can be computed as follows:
- Adjusted attraction total for district j=5 for use in
iteration #3 (if desired) is:
A
3 2 5 8,000
A = A (____) = 7,700 x _________ = 7,500
5 5 2
C 8,200
5
And so on for all columns. Note that at the end of iteration
#2, all of the attraction totals are within ñ3% of the desired
attraction totals which is sufficiently accurate in nearly all
applications. Generally, a third iteration is not recommended.
Finally, the average trip time (ATT) of the all purpose trips
can be calculated, if desired, quite simply by using:
5 5
ä ä T * t
i=1 j=1 ij ij
ATT = ________________________
5 5
ä ä Tij
i=1 j=1
Where:
Tij = trip interchanges from area i to area j
tij = travel time for trip interchange ij
i.e.:
(3100 x 5) + (700 x 6) +...+(6800 x 8) + (4400 x 6)
ATT = ______________________________________________________
100,000
= 7.0 minutes
B-10
At this juncture, it is advisable to conduct a systematic
checking of the various calculations to confirm the validity of the
figures, If no errors are detected, the 5x5 district trip
distribution is then considered complete.
These interchanges represent the all purpose trips; if
required, the HBW or HBNW or NHB trip interchanges can also be
calculated in a similar fashion. Note, however, that for the HBW,
HBNW and NHB trips, the district-to-district travel times remain
the same as those calculated initially; only the distribution
factors will be different,
In some cases where a quick and rough trip distribution matrix
is to be developed, one need only perform the distribution
computations for the HBW trips, and then factor these to arrive at
the total (all purpose) trip distribution. Thus, the HBNW and NHB
trip distributions could be avoided altogether. These "expansion"
factors are provided in the Users Guide, (6), Chapter 6, "Time of
Day Characteristics," and for more details refer to the Users
Guide, (6), Chapter 10, "Scenario for Site Development Impact
Analysis: Boise, Idaho."
The manual trip distribution procedure described above is
summarized diagrammatically using the flowchart in Figure B-6.
B-11
Click HERE for graphic.
B-12
APPENDIX C
TRIP INTERCHANGE MODAL SPLIT MODEL
Model Development
The Simplified Logit Model (SLM) was developed through an
analysis of the UTPS UMODEL default modal split model and
distribution factor curves for gravity type trip distribution
models.
The mode choice model contained in the UTPS program UMODEL 7/
simultaneously performs the trip distribution and modal split
functions. The mathematical form of the model is:
-éI
m(i,j)
A * e
j
T = P * ____________________________
m(i,j) i -éI
m(i,j)
ä ä A * e
j m j
Where:
Tm(i,j) = Trips from i to by mode m
Pi = Productions at i (home end)
Aj = Attractions at i (destination end)
e = 2.71828
é = A calibrated constant that varies by trip purpose
Im(i,j) = A measure of impedance by mode m equal to:
(1.0 x in-vehicle time) +
(2.5 x excess time) + trip cost)/
(0.33 x income per minute)
Research indicates that it is possible to state the impedance
variable in the same form as time is displayed in the Gravity Model
equation. That is, e-éI can be replaced with I-b where I is equal
to a measure of trip impedance and b is an exponent of the trip
impedance, dependent on the trip purpose. Thus, substituting the
expression for time, the equation becomes.
-b
A * I
j m(i,j)
Tm(i,j) = Pi * ___________________
-b
ä ä A x I
j m j m(i,j)
The form of the above equation is still such that distribution
and modal split are accomplished simultaneously. The rate
transformation was accomplished by dividing transit trips by auto
trips and converting the ratio into an actual fractional market
share quantity as follows:
C-1
T
t(i,j)
r = ______________
T
a (i, j)
where:
r = ratio of transit trips to auto trips
. r
. . ms = __________
t(i,j)
1 + r
where:
mst(i, j) = fractional market share of trips estimated to
use the transit t(i,j) mode.
Thus, the SLM model is reduced to the following equation:
b
I
a(i, j)
ms = ______________________
t(i,j)
b b
I I
a(i,j) t(i,j)
In other words, the fractional market share for the transit
mode is equal to the quotient of the auto impedance raised to a
power of "b" and the sum of the transit impedance and auto
impedance each raised to a power of "b."
It has been found that t he calibration exponent, b, can be
determined by calculating the slope of the distribution factor
about the point of intersection with the average trip length.
Default calibration exponents for small urban areas are shown in
Table C-1.. Nomographs for modal split were prepared using b values
for cities in the greater than 100,000 population category (Figures
C-9 through C-11).
The level of detail at which the mode choice procedure is
applied is a function of time availability. One should not
hesitate to apply the procedure to large analysis areas (e.g.,
districts) if time constraints are stringent.
There are two major outputs of the mode choice analysis:
- Interchanges of transit person trips
- Interchanges of auto person trips.
The transit person trips will probably be summarized by the
user to show transit travel by either large analysis areas or
corridors and may be input to other transit system analyses.
The auto person trips will most likely be subjected to an auto
occupancy analysis to convert the person trips into auto driver
trips as preparation for further analysis of the highway system.
C-2
TABLE C-1
SLM CALIBRATION EXPONENTS
b values
TRIP PURPOSE POPULATION < 100,000 POPULATION > 100,000
HBW 2.15 1.99
HBNW 2.67 2.71
NHB 2.78 2.68
C-3
Data Required for Application
The data required for mode choice analysis vary depending upon
previous work undertaken for the study area. It is recommended,
where possible, that the user make every effort to take advantage
of models and values that are specific to the study area. For
those areas with a minimal history of transportation planning,
default values have been incorporated into the modal choice
procedures and can be used without further manipulation.
Table C-2 lists the data elements required for application of
the mode choice procedures. The user can quickly distinguish
between those input elements which must be supplied and those that
are already available.
1. Highway Airline Distance. The highway airline distance
can be obtained from several sources. If the analyst has used the
trip distribution procedures described in the System Planning
manual, the analysis area-to-analysis area airline distances might
already have been developed.
2. Transit Airline Distance. For analysis area pairs that
have direct transit service, the highway airline distance can be
used to represent transit airline distance for estimating transit
demand of radially oriented trips. For area pairs where transit
service is indirect, the user must exercise great caution. In
those cases, the transit patron will probably be required to travel
in a radial direction to a transfer point, change direction and
continue to the final destination. It is recommended that the
transit airline distance for indirect trips be determined in
components to account for indirect routing by: a) measuring from
the production analysis area centroid to the transfer point, b)
measuring the distance from the transfer point to the final
destination area and, c) summing (a) and (b) as the transit airline
distance. The user will need to invoke careful interpretation of
airline distance in those instances.
Some area pairs may not be accessible by transit. Those areas
without service can be quickly identified using a graphic
representation of the transit system routes (data element 11) and
can be immediately eliminated from any further mode choice
analysis.
3. Transit Fare. The user will be required to supply area-
to-area transit fare. If the user is studying an alternative with
a flat fare system, this task becomes trivial in terms of the level
of effort. On the other hand, an alternative that has an elaborate
zone or graduated fare structure will require additional effort to
organize the fare data between analysis areas.
4. Auto Operating Cost. The cost being considered is
actually the out-ofpocket cost to the auto user. Over the years,
modal split models have been calibrated with a wide range of
assumed values for out-of-pocket operating costs. Currently, most
modeling efforts are estimating these costs to be approximately
five cents per mile in 1970 dollars. Other values of cost are
available to the user in the mode choice procedures and the final
responsibility for selecting a cost rests with the analyst. It
should be observed that it is possible to assess mode choice under
an assumption of varying auto operating costs. For example, the
user may wish to analyze the magnitude of a shift to transit if
auto operating costs were to double.
C-4
TABLE C-2
INPUT DATA ELEMENTS REQUIRED FOR MODE CHOICE ANALYSIS
SOURCE
INPUT DATA ELEMENTa Default User Supplied
1. Highway Airline Distance x
2. Transit Airline Distance x
3. Transit Fare x
4. Auto Operating Cost x
5. Attraction End Parking Cost x
6. Average Highway Speed x
7. Impedance Exponent (b) Values x
8. Median Income x
9. Access Time x
10. Person Trip Table x
11. Graphical Display of Transit
System x
FOOTNOTE:
a. Input data elements 1,2,3,6 and 10 are by analysis
area pairs (e.g., district-to-district).
Input data elements 5,8 and 9 are by the appropriate
analysis area (e.g., data element 5 for the attraction
district).
Input data elements 4 and 11 are by the study area.
Input data element 7 is by trip purpose (HBW, HBNW or
NHB).
C-5
5. Attraction End Parking Cost. The user will be required
to develop estimates of parking cost in order to use the highway
impedance nomographs (exhibited later in this chapter). Parking
costs will be necessary for each trip purpose since trip duration
varies between the work and non-work purposes. As a guide, the
user can assume a duration of nine hours for the HBW trip and two
hours for the HBNW and NHB trip purposes. The parking costs shown
in the highway impedance nomographs represent the full parking
charge associated with a trip. For the purpose of demand analysis
it is appropriate to consider onehalf of the actual parking changes
associated with a round trip. The curves contained in the highway
impedance nomographs represent a consideration of onehalf the mid-
range parking costs as described by each highway impedance nomo-
graph. In preparing the estimates of parking costs by analysis
area, the analyst is cautioned to develop the cost based on all
available parking (free and paid) for the particular trip purpose
under consideration.
6. Average Highway Speed. Area-to-area average highway
speed can be determined from previous efforts of the user or as a
special exercise. To determine average auto operating speed using
the manual trip distribution nomographs contained in the System
Planning manual:
a. Locate the appropriate "Airline Distance vs. Travel Time
vs. Distribution Factors" graph.
b. Determine the mix of highway facilities (i.e., between
freeways and arterials) the trip will traverse.
C. Enter the appropriate graph (Figures A-1 through A-11) at
the appropriate airline distance and read across to the
facility mix desired and down to the travel time.
d. Subtract from the travel time the terminal time (if
included) shown for that graph and convert the new time
to an operating speed using the nomograph shown in Figure
C-1.
7. Impedance Exponent (b) Values. Impedance exponents for
the general modal choice model are supplied for the user in the
form of transit modal choice nomographs (Figures C-9, C-10 and C-
11) for three trip purposes - HBW, HBNW and NHB. Those nomographs
can be used if the analyst elects to employ the SLM in a manual
mode. The "b" values shown in Table C-1 can be incorporated into a
computerized application procedure. The results obtained for the
manual and computerized applications will be comparable.
8. Median Income. The mode choice analysis procedures
assume a median family income of $9,000/year for converting travel
cost items into equivalent minutes. Median income (by each
analysis area) is referenced since most landuse forecasting
procedures produce the number of households within an income range.
However, average household income values may be used if they are
available. Income is applied to all impedance components dealing
with trip costs to convert each to equivalent minutes. If the user
wishes, the default impedance curves may be adjusted to take into
account varying median income values.
C-6
EXAMPLE:
If the centroid-to-centroid airline distance between two analysis
areas = 10 miles and the corresponding in-vehicle time = 30
minutes, then the average operating speed = 24 mph.
Click HERE for graphic.
C-7
9. Access Time. Access time is that quantity of time from
leaving the origin point to getting into the vehicle (bus or auto)
plus the time between exiting the vehicle and reaching the trip
destination. For transit trips, it may also include time to
transfer between transit vehicles. It is also referred to as out-
of-vehicle time plus, if appropriate, in-vehicle time not
associated with the line haul part of the trip, For calculating
transit impedance, access time represents an important segment of
the total impedance value. In the manual procedure, the transfer
time is assumed to be zero. Trip interchanges which involve a
transfer can have an impedance adjustment by adding 2.5 times the
transfer time to the impedance read from the nomograph. Transfer
time can be estimated as one-half the headway of the transit line
being transferred to.
10. Person Trips. The user is required to supply area-to-
area person trips for each trip purpose (maximum of three
purposes - HBW, HBNW and NHB). Trips may be used as developed from
the trip distribution procedure or, the user may elect to use a
computer developed trip table if one is available. With regard to
the separate application for each trip purpose, if the user de-
sires, only modal choice analysis for the HBW trip purpose may be
conducted and then the number of transit trips derived doubled to
estimate Annual Average Weekday (AAWD) transit passenger movements.
Also, see information relative to an all purpose model later in
this Appendix.
11. Graphical Display of Transit System. The user will need
a graphic representation of the existing or proposed transit system
to overlay the analysis area boundaries for determining those
interchanges with and without transit service. Movements without
transit service may be eliminated from the modal choice analysis,
and it can be assumed that all trips for those interchanges are
made via auto (auto driver and auto passenger). The analyst can
assume specific areas.. use the transit system via Park-n-ride or
Kiss-n-ride access. Care should be exercised, though, or an over-
estimation of this type of trip will result. If transit service
differs significantly between the peak and offpeal, periods in the
specific study area, separate peak and off-peak descriptions will
be required. As a general rule, the peak system applies to the HBW
trip purpose travel while the remaining two trip purposes (i.e.,
HBNW and NHB) should be associated with the off-peak system.
Application of the Manual Modal Choice Estimation Procedures
A generalized flowchart of the manual modal choice procedure
is shown in Figure C-2. The procedure shown must be completed once
for each trip purpose subjected to an analysis. There are three
main steps required with application of the modal choice procedure
as follows:
STEP 1. Determine Auto and Transit Impedances. The first and
most difficult task confronting the user is determining area-
to-area impedances. (NOTE: The user is directed to Figure C-3,
"Modal Choice Analysis Work Sheet A for application of the
procedures.) To minimize the level of effort required, it is
recommended that the user consider two-way trips; e.g., assume
the travel characteristics between i and j equal j to i and
sum the trips to get a total movement between i and j. This
simplification should be fully satisfactory except in
localized transit service areas
C-8
Click HERE for graphic.
C-9
Click HERE for graphic.
C-10
where inbound transit service differs markedly from outbound
service. For example, where a substantial peak commuter bus
operation is provided in the peak direction, separate peak
direction and off-peak direction calculations may be appropriate.
The analyst must supply the following information for each
analysis area pair (See section entitled, "Input Data Elements"
above.):
INPUT SOURCE
- Highway distance - Map of study area
- Transit distance - Equal to highway distance except
where trip requires additional
trip distance due to transfer
location. In those cases the
airline distance is equal to the
airline distance from origin to
transfer point to destination.
- Highway operating - User judgment
speed
- Transit fare - Local transit system
- Parking cost - User knowledge of study area
Additionally, the user must determine the access mode (walk or
auto) for each production analysis area. (See asterisk in Figure C-
3.) It may be assumed the access mode is the same for each cell of
a particular row on the analysis work sheet.
For those analysis areas without transit service, the user can
simply record "0%" transit in the appropriate space on "Work Sheet
A" and analysis of those areas can be considered complete.
The above informatio on should be recorded on "Work Sheet A"
for each analysis area pair. When Work Sheet A is completed, the
technician will be prepared to determine the market share from the
appropriate mode choice nomographs (Figures C-9 through C-11) and
prepare the modal person trip estimates.
To determine the transit and auto impedances, the user is
directed to the "Transit and Auto Total Impedance Nomographs"
(Figures C-4 and C-5 for transit, and Figures C-6 through C-8 for
auto). The transit impedance nomographs for walk access have an
assumed walking-plus-waiting time at the production end of the trip
of fifteen (15) minutes before weighting. The user may desire to
alter that assumption.. To change the assumption the user should
subtract 2.5 times 15 minutes (37.5 equivalent minutes) from the
impedance quantity and add 2.5 times the desired access time. The
user may wish to keep the assumed walk time (5 minutes) and modify
the wait time to equal one-half (1/2) the headway in the analysis
area. To
C-11
Click HERE for graphic.
C-12
Click HERE for graphic.
C-13
Click HERE for graphic.
C-14
Click HERE for graphic.
C-15
Click HERE for graphic.
C-16
Click HERE for graphic.
C-17
Click HERE for graphic.
C-18
Click HERE for graphic.
C-19
modify the default auto access time of 3 minutes (Figure C-5), the
user is cautioned that it is not, and should not be, weighted since
it is an invehicle travel time. Likewise, the user may wish to
adjust the default walking time at the attraction end of the trip.
The default destination walk time of 5 minutes can be adjusted by
subtracting 5 times 2.5 (12.5 equivalent minutes) from the
impedance and adding 2.5 times the desired destination walk time.
Further modifications can be made to the impedance nomographs
for transit trips requiring a transfer. These default curves
assume no transit-to-transit transfer. It is customary to
incorporate a waiting time equal to one-half the headway of the bus
line being "transferred to" The user is encouraged to make these
adjustments where appropriate for transit trips in order to prevent
an over-estimation of non-radial transit travel. As a default
condition, the user can assume an additional 30 equivalent minutes
(10 minutes unweighted transfer time) for trips of this type. When
incorporating this transfer trip modification, the user can simply
add the transfer penalty to the values determined from the transit
impedance nomographs since it causes a constant vertical shift to
the default curves.
Two transit nomographs are provided, one for walk access. and
the other for auto access the curves within each nomograph are
stratified by transit fare. Auto total impedance nomographs are
categorized by out-of-pocket auto operating costs and actual
parking cost at the attraction end of the trip; the curves within
each nomograph are stratified by highway operating speed.
By looking up the airline distance on the appropriate
nomograph and curve, the total impedance for either mode can be
read off the y axis and recorded on "Work Sheet A' (i.e., It for
transit and Ia for auto).
The user should be aware of all the assumptions that have
entered into the development of the total impedance curves for
transit and auto trip paths.
The assumption used in the above reference to convert highway and
transit airline distance to actual miles of route was 1.27 (the
circuity factor). Other assumptions are as follows:
- Parking Costs:
PARKING COST STRATA VALUE REPRESENTED 1/2 PARKING COST
0 - $ .75 $0.37 $0.185
$ .75 - $1.40 $1.07 $0.135
$1.41 - $2.50 $1.95 $0.975
Over - $2.50 $3.00 $1.500
- Total auto origin and destination terminal time = 5 minutes or
12.5 disutility equivalent minutes,
C-20
- Average Transit Access Times (mins.):
IN-VEHICLE OUT-OF-VEHICLE (unweighted)
Auto Origin Transfer Destination
Access Walk & Wait Wait Walk
Walk Access 0 5 10 0 5
Auto Access 3 1 0 7 5
- General Impedance Equation:
Total Impedance = In-vehicle Time + 2.5 (out-of-vehicle time)
+ [Costs (cent)/2.5]
The cost conversion factor (2.5) assumes an average income of
$9,000 per year.
STEP 2. Determine Market Share. The next step in determining the
market share and completing "Work Sheet A" is accomplished using
the appropriate mode choice nomographs shown in Figures C-9 through
C-11 (HBW, HBNW, NHB).
Using the determined highway and transit impedance for each
analysis area pair and the appropriate trip purpose modal choice
model, the user can determine the percentage of trips occurring
between the analysis area pair that can be expected to use transit.
To determine modal split, the appropriate nomograph is entered on
both the x and y axes using the determined highway and transit
impedances respectively; then, the intercept will show the percent
of trips by transit (mst). The user will, most likely need to
interpolate between the curves supplied on the nomograph. The mst
result should be recorded on "Work Sheet A" and "Work Sheet B"
(Figure C-12). "Work Sheet A" will now be complete and the user
can, with a calculator, proceed to complete "Work Sheet B."
STEP 3. Determine Transit and Auto Person Trips. The compressed
(triangular) person trips for each analysis area pair of the trip
purpose under investigation should be recorded on "Work Sheet B."
Multiplying the trips by the percent transit market share (mst)
will yield the number of transit person trips anticipated to occur
between the analysis areas. Subtracting transit person trips from
the total person trips for that particular interchange yields the
number of auto person trips for the interchange.
The completion of "Work Sheet B" finishes the mode choice
analysis for the trip purpose. The procedure can be repeated for
all trip purposes to be analyzed. Upon completion of the analysis
of all trip types, the transit and auto person trips, by purpose,
can each be summed to obtain total transit and total auto person
trip tables.
C-21
Click HERE for graphic.
C-22
For an example of the application of the above procedure to
estimates for selected transit route possibilities, the reader is
referred to Chapter Ten of the Users Guide 6/.
Single Purpose Modal Split Model
Chapter Two describes procedures which permit the development
of a single purpose (combining home-based work, home-based non-work
and non-home based) person trip table. Should the user elect to
invoke that technique as part of a transportation planning process,
the model and nomographs presented here may be used to continue the
mode choice analysis.
The model described here is of the Simplified Logit (SLM)
described previously. Charts and nomographs are supplied to assist
in the manual application of the model. The user is required to
code the specific FORTRAN routines for input to the UTPS program
UMODEL which will be specific to the input parameters established,
The calibration exponent used for the single purpose SLM has
been calculated to be 2.6. Thus, the mathematical expression of the
model becomes:
1
ms = __________________
t(i,j)
2.6
I
t
1 + __________
I
a
(i,j)
where:
mst(i,j) = Market share of person trips estimated to
travel via transit between two analysis
areas
It = Impedance (in equivalent minutes) to
travel by transit between two analysis
areas
Ia = Impedance (in equivalent minutes) to
travel by auto between two analysis areas.
Impedance is further defined as:
o 2.5(out-of-vehicle time) + (In-vehicle travel time)
+ Travel cost/(1/3 x Income)
The single purpose mode choice model is shown in Figure C-17.
The graphical model can be used manually, as previously described.
Input variables. and their values, used in developing the
impedance charts are found in Table C-3.
C-23
TABLE C-3
IMPEDANCE VARIABLES FOR SINGLE PURPOSE SLM
OFF-PEAK
VARIABLE PEAK PERIOD PERIOD WEIGHTED AVG.
Out-of-vehicle
Time
Walk Time 10 mins. 10 mins. 10 mins.
First Wait Time 10 mins. 15 mins. 14 mins.
Second Wait Time -0- -0- -0-
Terminal Time 5 mins. 5 mins. 5 mins.
In-Vehicle Time
Bus (Varies by trip length; Peak - Off-Peak)
Auto (Varies by trip length and speed; Peak = Off-Peak)
Travel Costs
Auto operating Cost:
5› /mile 5›/mile 5›/mile 5›/mile
10›/mile 10›/mile 10›/mile 10›/mile
15›/mile 15›/mile 15›/mile 15›/mile
Parking Cost
< 75›/day 37› 19› 23›
75›-$1.40/day $1.07 54› 65›
$1.40-2.50/day $1.95 98› $1.17
> $2.50/day $3.00 $1.50 $1.80
C-24
TABLE C-3 (Continued)
VARIABLE PEAK PERIOD OFF-PEAK PERIOD WEIGHTED AVG.
Fare:
0› 0› 0› 0›
25› 25› 17› 19›
50› 50› 33› 36›
75› 75› 50› 55›
$1.00 $1.00 67› 74›
$1.25 $1.25 83› 91›
$1.50 $1.50 $1.00 $1.10
C-25
Using the general impedance relationship and the impedance
variable values found in Table C-3, the auto and transit impedance
nomographs (Figure C-13 through Figure C-16) were developed,
The procedure for applying the single purpose model, including
the layout of the work sheets for manual analysis, is identical to
the SLM presentation in the previous section. The only change
would be to enter total person trips on "Work Sheet B" (Figure C-
12),
In order to simplify the application procedures of the single
purpose SLM, several assumptions are necessary regarding input
parameters and relationships between the peak period and off-peak
period transit services, It is assumed the analyst will define the
transit system in terms of peak period requirements. The impedance
charts are expressed in terms of peak service characteristics -
including the cost functions of transit fare and parking cost, The
parking charge stratification is stated as the full cost associated
with the work trip.
It is also assumed that the peak period characteristics are
associated with the work purpose and off-peak characteristics are
associated with the nonwork trip purposes. The trip generation
procedures describe the total residential person trip estimate to
be comprised of 20% work trips and 80% non-work trips. Each
impedance variable, where average variable values differ between
peak and off-peak periods, have been weighted by the 20/80 ratio to
properly reflect their contribution to this single purpose modal
split model.
Other assumptions include:
- Off-peak parking cost = 1/2 peak parking cost
- Off-peak average transit fare = 2/3 peak average transit
fare
- Average bus speed (peak and off-peak) = 15 m.p.h.
- Average household income = $9,000/year
- All transit access is via a walk trip
- Actual distance = 1.27 x airline distance
C-26
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C-27
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C-28
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C-29
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C-30
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C-31
APPENDIX D
GUIDE TO UTPS PROGRAMS FORMTNG SIMPLIFIED CHAIN FOR
FOUR-STEP TRANSPORTATION PLANNING
The four-step transportation planning process has been
assembled into a string of appropriate UTPS programs that
incorporate the procedures and default tables discussed in this
report. The relationship of the various programs and inputs is
shown in Figure 4. Descriptions of each component with necessary
inputs and suggested program options follow.
Program HR
This program is used to produce a "historical record" from
user coded link data cards. This data set is input to program
UROAD to produce skim trees and for traffic assignment purposes.
The reports and plots produced by program HR are useful in editing
and debugging the coded network.
Parameters (Default)
ZONES (400) Highest zone number
NODES (400) Highest node number
MAXSPD (9.99) Highest permissible link speed
MAXDST (99.99) Longest permissible link
All of the above parameters must be user specified to conform
to the network coded. The network coding will produce link data
cards in a format prescribed in the HR program documentation.
The basic information which the user must provide on a link-
by-link basis is:
A-node
B-node
Distance
Time or Speed
Optional data which may be required for various assignment options
or special summaries include;
Count
Number of Lanes
Future Additional Lanes
Parking Code
Land-Use
Facility Type
Area Type
Facility type and area type are required for the automatic capacity
restraint feature of UROAD.
D-1
It is suggested that the network editing function of HR be
utilized to uncover coding problems prior to continuing through the
process.
The reader is directed to the FH14A document, PLANPAC/BACKPAC
General Information 8/ for additional information related to
developing a network for assignment purposes.
Program UROAD (Time Matrix Preparation)
This program is used twice during the procedure outlined, In
this application, UROAD is used to produce a matrix of travel
times. The required input is the historical record produced by
prograra HR as previously discussed.
Parameters (Default)
TFIELD (0) Field containing initial link travel
time for tree building
Options
TIME (F) Option to have a time matrix file
written
In order to produce a time matrix which can be used for trip
distribution, the user must code both of the above fields. The
sample below illustrates this coding:
&PARAMT TFIELD=32 &END
&OPTION TIME=T &END
UROAD is informed that only the time matrix output is desired
by not providing an input dataset containing a trip table. The
specification of TFIELD=32 informs the program that observed travel
time is to be used for tree building.
Program SCAGM (Small City Trip Generation and Gravity Model)
This is a special UTPS program for users wishing to implement
the methods of this report with a minimum of complexity. As
described more fully in the following pages, it includes the
following general functions:
1. Terminal time and intrazonal time updates to an input
highway travel time matrix.
2. Trip generation using rates as shown in this manual by
three purposes, and three city size groupings
3. Regional balancing of attractions to equal productions
D-2
4. Trip distribution using friction factors as shown in this
manual by three purposes, and two city size groupings.
The SCAGM program is a modified version of the standard UTPS
program AGM. The SCAGM user must study the full UTPS AGM
documentation for program control (parameters, options, etc.), file
formats and reports. The SCAGM user would normally be concerned
with only the following (subset) of the full A9.1 control;
Parameters (Default)
ZONES off input skims Highest zone number
DISTS 0 Highest district number
AITER 1 Maximum iteration on attractions
DELA 0.1 Criterion to stop iteration on
attractions
MAXT 60 Highest time on F-factor cards
SKIMS 101 Table number of time matrix
TABOUT 1 Number of output trip tables
NAME (N) - Names for output trip tables
UPARMS(l) 1.7 Attraction Factor 1 (See Trip
Attraction section for
explanation.)
UPARMS(2) 10.0 Attraction Factor 2
UPARMS(3) 0.5 Attraction Factor 3
UPARMS(4) 1.0 Attraction Factor 4
UPARMS(5) 2.0 Attraction Factor 5
UPARMS(6) 2.5 Attraction Factor 6
UPARMS(7) 0,5 Attraction Factor 7
UPARMS(8) Trip generation run only if
UPARMS(8)=99999.
Input Files
Table D-1 shows the files necessary to use program SCAGM, A
complete description of these files,and their use is found in the
UTPS AGM program write up.
D-3
FILE NAME D D NAME CONTENTS OR FUNCTION
SYSIN FT05FOOl PROGRAM CONTROL CARDS
J1 FT11FOOl TIME MATRIX (FROM UROAD)
P A1 PRODUCTIONS (Optional Special
I A A2 ATTRACTIONS Generator
Overrides)
N F A3 FRICTION FACTORS (Default Files
are on UTPS Tape)
P
U K A4 "K" FACTORS (Optional)
T ZONAL1 A5 ZONAL TYPE 1 DATA
ZONAL2 FT44F001 ZONAL TYPE 2 DATA
PRATES FT46FOOl TRIP PRODUCTION RATES (Default
files are on UTPS Tape)
__________________________________________________
O
-- FT06FOOl PROGRAM REPORTS AND MESSAGES
U
J9 FT19FOOl TRIP TABLES (To UROAD)
T
P
U
T
TABLE D-1
FILES FOR SCAG14
D-4
SYSIN File
This is a standard AGM card file containing the training UTPS
program control information (i.e., parameters, options, etc.).
These are discussed elsewhere in this description and in the UTPS
AGM documentation.,
J1 File
This is a standard UTPS time matrix as output, in this case,
by UROAD. It contains zone-to-zone autQ travel times in whole
minutes, including times for external stations. It does not
include intrazonal times (the diagonal of the matrix is zero) or
terminal times (getting to and from the car at each end). These
will be added in SCAGM. [Users desiring to input a time matrix from
other than UTPS software (e.g., PLANPAC) should refer to the UTPS
program UMCON documentation for conversion information.]
P & A Files
The P and/or A files are optional in SCAGM and values are
coded only where the internally computed productions and/or
attractions (by purpose) are to be overridden as for special
generators or external stations. Leave out the zonal card entirely
or leave any purpose blank (not zero) where it is desired to use
internally computed productions and attractions. Use only the
first three values on the standard AGM P & A formats for HB14, HBNW
and NHB, respectively (as shown in Figure D-1), See the UTPS AGM
documentation for this format.
Note that any override is done prior to balancing of regional
productions so output values may be different than those input.
Note that non-home-based productions for each zone are set equal to
non-home-based attractions internally so overrides of thesd would
also logically be equal on input.
F File
The F file is required in SCAGM if both trip generation and
trip distribution are to be performed (See parameter "UPARMS(8).").
Use only the first three values on the standard AGM F file format
for HBW, HBNW and NHB, respectively. See the UTPS AGM
documentation for this standard format.
There are two such files on the UTPS tape, one for each
population group. The user may pick one or edit one to change the
friction factors and time intervals, if desired. These files on
the UTPS tape are named:
POP(OOO) DSNAME
25 - 100 URD.FFACS1
100 - 200 URD.FFACS2
Table D-2 shows the default values contained on the above files.
D-5
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D-6
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D-7
K File
The K file is optional in SCAGM. K-Factors are zone-to-zone
(or districtto-district) adjustment factors. Use only the first
three values on the standard AGM K-factor format for HBW, HBNW and
NHB, respectively. Read the AGM write up carefully for how to
input these, if desired.
ZONAL1 File
The ZONAL1 file is not a standard AGM file but is Mandatory
for SCAGM. It is for the input of income, auto and dwelling unit
data used primarily in the trip production model. It is quite
flexible in that zonal averages of income and/or autos may be input
as may categories of either or both of these. Where income or
autos is not known at all, a special "nines" value is provided.
Output accuracy will, of course, vary with input detail and the
user must be the judge of adequacy of his/her data.
Each ZONAL1 data card has fields for up to four dwelling unit
categories with income and autos for each category (See Table D-
3.), All four need not be used on any card. If more than four
categories per zone are needed, additional ZONAL1 cards may be used
as long as these follow immediately after the first card for the
zone.
On the ZONAL1 card(s) for the first zone, the income and auto
fields must be completed for each dwelling unit field used even if
only "nines" are used for income or autos. For subsequent zones,
the income and auto fields need not be coded as long as the
categories, and their sequence on the cards, are the same as for
the immediately preceeding zone. Thus, as an extreme example, if
all 20 categories are being used (5 income times 4 auto), then 20
dwelling unit fields, with complete income and auto information for
each, would appear on five ZONAL1 data cards for zone 1. For each
subsequent zone, five cards would also be input with 20 dwelling
unit fields filled out for each zone but blank (not zero) income
and auto fields. The sequence of dwelling unit categories for each
zone after the first must, of course, be the same as for the first
zone. Users of multiple cards per zone are required to place a
sequence number in column 71 on the ZONAL1 cards and all cards must
be in ascending sort sequenced by zone number (primary) and by card
sequence number (secondary).
ZONAL1 data cards need not be provided for external stations
or special generators where P's and A's for all purposes are input
on the special generator P and A cards. Where the ZONAL1 data
cards are not input for a zone, employment data, if present on the
ZONAL2 data card, will be ignored and all P and A data taken
directly from the P and A cards, The example card set ups (Figures
D-2, D-3, D-4) following will clarify these points.
ZONAL2 File
The ZONAL2 file is not a standard AG14 file but is mandatory
for SCAGM. It is for the input of employment data used in the trip
attraction model and for intrazonal and terminal times (See Table
D-4.). One card per zone is input, including external stations, For
external stations and other special generators the employment
figures may be left blank since attractions should be
D-8
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D-9
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D-10
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D-11
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D-12
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D-13
input in the special generator A file, A sample of the coding for
this file is shown on Figure D-5.
PRATES File
The PRATES file is not a standard AGM file but is mandatory
for SCAGM. It contains the person trip production rates per
dwelling unit stratified by purpose, income and autos owned.
Default tables by three population groups shown in Tables D-5, D-6
and D-7 are included on as the UTPS tape and may be used as shown
or edited by the user. The income is in 1970 dollars. The
production rates for income = 99999 and Autos = 9.9 are weighted
averages for use where either one or the other is not known. The
"3 or more" auto category is represented by the average of 3.1
autos for this group.
The user is not restricted to the income and auto categories
shown since interpolation will be performed for input values other
than these, Thus, inputs may be zonal averages (e.g., autos =
1...7) or categories other than these and interpolation will
approximate the correct production rates. For input values beyond
the range of the table, no extrapolation is performed, rather the
lowest or highest appropriate category is used.
NHB productions, while computed on a zonal basis, are used by
SCAGM only as a regional control total. NHB attractions are
factored to equal productions regionally and these attractions are
used at the zonal level for both productions and attractions.
PRATES File Format
Users who wish to edit the default production rates will need
to recognize the PRATES file format. It consists of a group of six
cards for each of three trip purposes (HBW, HBNW, NHB), each group
separated by a blank card. Each of the six cards represents a
different income level (3000, 6500, 10,000, 14,000, 20,000, and
99,999) and these levels cannot be changed in SCAGM. On each card,
the first two columns are left blank then five fields, each ten
columns wide, follow where each field contains the trips Der
dwelling unit (in an F10.2 format) for each of the five auto
ownership groups (0.0, 1.0, 2.0, 3.1, 9.9) and these cannot be
changed in SCAGM.
There are three such files on the UTPS tape, one for each
population group, and the user may pick one or edit one to change
the rates (but not the categories). These files on the UTPS tape
are named:
POP (000) DSNAME Default Values
25 - 50 URD.PRATESl See Table D-5.
50 - 100 URD.PRATES2 See Table D-6.
100 - 200 URD.PRATES3 See Table D-7.
D-14
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D-15
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D-16
TABLE D-6
DEFAULT PRATES2
Population: 50,000 - 100,000
TRIPS/HH
CARS 0.0 1.0 2.0 3.1 9.9
INCOME/ D.U.
0.48* 1.58 2.73 3.04 1.29
3,000 1.31* 4.28 7.41 8.26 3.51
0.51* 1.65 2.86 3.19 1.35
0.53 2.10 2.73 3.28 2.01
6,500 1.86 7.44 9.78 11.58 7.11
0.71 2.85 3.75 4.44 2.73
0.91 2.32 2.88 3.87 2.49
10,000 3.48 8.84 10.98 14.76 9.47
1.31 3.33 4.14 5.57 3.57
6.87 2.10 2.67 3.57 2.47
14,000 3.84 9.30 11.78 15.81 10.97
1.49 3.60 4.56 6.12 4.25
0.78 1.69 2.57 2.99 2.37
20,000 3.72 8.06 12.28 14.26 11.30
Do Not 1.50 3.25 4.95 5.75 4.56
Extrapolate
Beyond This
Category
Use rates
Shown
0.74 2.02 2.75 3.42 2.26
99,999 2.81 7.69 10.49 13.05 8.60
1.06 2.90 3.96 4.92 3.24
* Values in each cell represent trip rates for HBW, HBNW and
NHB, respectively.
D-17
TABLE D-7
DEFAULT PRATES3
Population: 100,000 - 200,000 TRIPS/HH
INCOME/ CARS 0.0 1.0 2.0 3.1 9.9
D.U.
0 .33* 1.82 2.59 3.26 1.24
3,000 0.95* 5.21 7.39 9.31 3.56
0.30* 1.65 2.34 2.95 1.13
0.89 2.53 3.16 4.14 2.39
6,500 2.59 7.34 9.16 11.99 6.93
0.98 2.78 3.47 4.55 2.63
1.22 2.98 3.48 4.53 3.13
10,000 3.65 8.94 10.45 13.59 9.40
1.54 3.76 4.40 5.72 3.96
1.33 3.04 3.55 3.88 4.75
14,000 3.92 8.96 11.42 14.00 10.47
1.75 4.00 5.10 6.25 4.68
1.31 2.70 3.78 4.59 3.62
20,000 4.02 8.25 11.55 14.03 11.07
Do not 1.97 4.05 5.67 6.88 5.43
extrapolate
beyond this
category. Use
rates as shown.
1.08 2.74 3.68 4.48 2.90
99,999 3.08 7.81 10.49 12.77 8.26
1.24 3.15 4.23 5.15 3.34
* Values in each cell represent trip rates for HBW, HBNW and
NHB, respectively.
D-18
J9 File
This is a standard AGM output file and will contain three trip
tables in sequence by purpose (HBW, HBNW, NHB) in the production to
attraction format.
Trip Attraction Rates
The default trip attraction model is as follows:
HBW = 1.7 (Total Employment)
HBNW = 10.0 Retail + 0.5 Non-Retail + 1.0 Dwelling
Emloyment Employment Units
NHB = 2.0 Retail + 2.5 Non-Retail + 0.5 Dwelling
Employment Employment Units
The user can override the seven multipliers above by use of
the UPARMS(1) through UPARMS(7), respectively, in sequence as shown
above. For example, UPARMS(6) controls the multiplier on Non-
Retail Employment for NHB attractions and defaults to 2.5.
Internal-External Trips
The default production rates include internal-external person
trips by internal residents. The external station end of these
person trips should be estimated by purpose for each station and
input on the A file as attractions for the external station.
For internal-external person trips by external residents, an
estimate should be made by purpose for each external station and
input on the P file as productions for the external station. The
process of estimating these external trip ends by purpose is
described below as well as referenced elsewhere in the System
Planning manual.
Internal-external travel is quite variable by area, dependent
upon the characteristics and size of the area as well as its
geographic location and relation to major highway facilities. The
most appropriate means to obtain the travel at external stations is
through the use of a previously collected external travel survey,
or when necessary, a new one. The data required for external
station locations are productions and attractions for internal-
external travel, to allow use of SCAGM. External-external trips
should be developed separately through a factoring of known through
trips, or by some means such as described in Chapter Three of the
System Planning manual. (See the "Non-Computer Techniques" section
and Table A-4, Part B.)
When using external survey data, trips made by internal
residents crossing the cordon are treated by SCAGM as attractions
at the stations. Trips made by persons living outside the area are
treated by SCAGM as productions at the cordon stations. This
assumes external-external travel has been removed and will be
handled by a factoring process.
D-19
Where an older external survey is available, it is advisable
to take current counts at the external station locations and apply
the knowledge regarding through travel and resident and non-
resident external-internal travel to these to obtain productions
and attractions at the external stations. More detailed discussion
of this is provided in Chapter Two of the System Planning manual,
in the "External Travel" section.
The default person trip attraction rates include all
attractions from whatever source (internal or external) and thus
need not be adjusted to work with the above external station
treatment.
Note that intrazonal times for external stations (input on the
ZONAL2 file) should be very high to eliminate unrealistic
intrastation trips between the P's and A's at each station as
described above.
Auto Driver Trips
The trip tables resulting from SCAGM default trip rates are
person trips. From these, auto driver trips must be estimated for
assignment. Two methods for doing so are as follows:
1. Multiply person trip tables (by purpose) by the factors
below using UMATRIX:
POPULATION Auto Driver Factor
(000) HBW HBNW NHB
25 - 50 0.71 0.54 0.69
50 - 100 0.70 0.54 0.68
100 - 200 0.64 0.54 0.66
2. Use locally developed mode choice/auto occupancy factors
as from a mode choice model or from "what if" policy type
assumptions as to mode choice and auto occupancy.
Truck Trips
SCAGM does not directly estimate truck trips. Two methods of
doing so are as follows:
1. Multiply auto driver trip tables, using UMATRIX, by the
factors below to expand to an approximate total vehicle trip table
prior to assignment;
D-20
POPULATION TRUCK MULTIPLIER
(000)
25 - 50 1.30
50 - 100 1.27
100 - 200 1.17
2. If a separate truck trip table is known, it can be input
to UMATRIX and added to the other trips prior to UROAD assignment.
External-External Trips
These cannot be estimated in SCAGM but should be developed
externally and combined with the other trip tables using UMATRIX
prior to UROAD assignment.
Program UMATRIX
A UMATRIX run will usually be necessary prior to assignment
with UROAD. This UMATRIX run would be to perform one or more of
the following functions:
1. "Split" the person trips (HBW, HBNW, NHB) from the
production-attraction format of SCAGM to the origin-
destination format ior assignment in UROAD.
2. Convert person trips to auto driver trips using methods
discussed elsewhere in this manual.
3. Factor auto driver trips to include truck trips or bring
these in from an external source as discussed elsewhere
in this manual.
4. Bring in external-external trips from another source as
discussed elsewhere in this manual.
5. Add all of the above together prior to assignment.
The parameters and options for UMATRIX are few and are shown
in the UMATRIX documentation. The COMBIN(N) statement on the &PARM
card is of particular interest as it determines how input tables
will be combined. An example relevant to processing SCAGM output
is given below.
The example assumes that the three purpose (HBW, HBNW,NHB)
person trip tables output from SCAGM are Tables 101, 102 and 103,
respectively, Through trips (external-external) are on Table 201.
Factors shown elsewhere are to be used to convert person trips to
auto driver trips and to adjust for truck trips. Population
50,000-100,000 is assumed.
D-21
1. Factor to auto driver by purpose and add;
COMBIN1 =' .70*T101 + .54*T102+.68*T103'
2. Split 50-50 from P and A to O and D daily trip table:
COMBIN2 =' .50*T901 + TR(.50*T90l)'
3. Factor up to truck-trips and add through trips;
COMBIN3 = ' 1.27*T902 + T20l'
This would output three tables, one for each COMBIN(N)
statement, although only the last (T903) would be of further use.
The above statement could be reduced to one for greater efficiency
but less clarity in presentation.
As an alternative to Step #1, which uses default assumptions
of mode choice and auto occupancies, policy levels of these could
be tested. For example, it what if" mode choice for CBD work trips
was 25% transit and auto occupancy for CBD work trips was 2.0 while
default rates apply to other destinations? The CBD is Zones 1, 2
and 3. Thus:
1. Factor work trips to auto driver:
COMBIN1 ='IF J=1 OR J=2 OR J=3 THEN .75*T101/2.0 ELSE 70*T101'
Many other policies or simple modal choice models can be
applied similarly with knowledge of UMATRIX,
Program UROAD (Traffic Assignment)
This program was described previously in its function as a
means of obtaining a skim tree dataset for use in trip
distribution. In this phase of the process, program UROAD is used
to combine a historical record (produced by program HR) with a trip
matrix (produced by program AGM) to obtain simulated traffic
volumes on each link. The method of assignment can be selected by
the user from among the following:
1. All-or-Nothing
2. All Shortest Paths
3. Probabilistic Multipath (Stochastic)
4. Capacity Restraint (Iterative or CATS Incremental)
D-22
Parameters (Default)
SPLIT1 (1.0,O) Origin-Destination factors for Trip
Table 1. Since the input trip tables
will be in production-attraction
format, this parameter should be
coded SPLIT1=.5,5. If additional trip
tables are input, this parameter is
coded SPLIT2, SPLIT3, SPLIT4.
TABLES (0,0,0,0) Trip table numbers (up to 4) to be
factored, summed and assigned.
THETA (0,-1,...,-1) Assignment diversion parameters used
to specify the number and type of
iterations to be performed. Up to 9
values for THETA may be specified
with the following meaning:
-1 = Do nothing for this iteration
0 = Perform all-or-nothing
assignment
O.OHERE for graphic.
E-4
The second method for obtaining link growth factors is based
upon the use of a one-purpose (i.e., HBW + HBNW + NHB trips)
gravity model for the internalinternal portion of the link volumes.
A one-purpose model is applied using current year productions and
attractions and assigned to the network (manually or by computer).
The one-purpose model is also applied using future productions and
attractions and assigned to the network. The ratio of future
assigned volume for each link to present assigned volume for each
link is the growth factor to be applied to the internal-internal
count. To the factored internal-internal count is added the
external assigned volume and the internal-external assigned volume.
This could also be done using a spiderweb network for aggregation
and to reduce assignment errors to individual facilities.
To obtain the trip productions and attractions for each zone,
local data or the default values provided in this manual may be
used. Also provided in the "Default Value" section are the
friction factors to be used in the gravity model application. If
work is to be done manually, the user is referred to the report,
Quick-Response Urban Travel Estimation Manual Techniques and
Transferable Parameters--A Users Guide 6/. A manual gravity model
application is described in Chapter Three of the Users Guide 6/. A
manual traffic assignment is described in Chapter Seven of the
same.
Where conditions are appropriate, the count procedures may be
further simplified. Where little growth in population and
employment is anticipated, less than about one-half percent per
year, and where any growth is expected to be uniform throughout
much of an area, an average "growth" factor may be applied to the
internal-internal portion of the ground count. That is, a single
growth factor for the entire area would be developed based upon
anticipated increase in travel due to the small growth, and
increase in trip making anticipated based upon increased income and
auto ownership, if expected. Further, if through trips and
internal-external travel are expected to also grow in approximate
proportion to the internal-internal traffic, and a quick estimate
of potential problem areas is desired, the actual ground counts can
be factored by the anticipated total average growth to arrive at an
estimate of future traffic volumes. These would be evaluated to
assess the emergence of any congestion problems.
In order to enable the transportation planner to manually
apply the traffic estimation methodology described above, an
illustrative example is provided below.
An Example Application
Suppose that the future ground counts are to be estimated on
the highway network for a small urban area with a population of
60,000. It is anticipated that this area will undergo a low to
moderate growth. Input information such as that described below is
available.
Input Information. Essentially, the input data consists of
the following items:
E-5
1. A map of the study area showing the layout of the
analysis areas and their respective centroids, boundary
limits of the CBD, central city and suburban subregions,
and a highway map delineating the freeway and major
arterial network. The outer limit of the sururban
boundary can also be considered to form a cordon for the
study area, and external stations are considered to be
located wherever this cordon intersects the highways.
(See Step 1 below.)
2. The base year average daily vehicle ground counts for
each link of the highway network. (See Step 13 below.)
3. The base year external trip matrix, i.e., a trip matrix
for the average daily internal-external (I-E) traffic and
the average daily externalexternal (E-E) through traffic.
(See Step 2 below.)
4. The base year all purpose (i.e., the HBW, HBNW and NHB
trip purposes combined) internal-internal (I-I) average
daily vehicle productions and attractions by analysis
area. (See Step 5 below.)
5. The base year analysis area-to-area travel time matrix
and the corresponding all-purpose friction factors. (See
Step 6 below.)
6. The future year all purpose I-I average daily vehicle
productions and attractions by analysis area. (See Step 8
below.)
7. The future year analysis area-to-area travel time matrix
and the corresponding all-purpose friction factors. (See
Step 9 below.)
8. The traffic growth factors (from base to future year) at
the external stations located on the cordon.
This information then constitutes the input data required for
the traffic estimation technique, and is utilized as described
below.
Methodology. The traffic estimation technique based on ground
counts is applied in a step-by-step manner as follows and as
depicted in the flowchart shown in Figure E-2.
STEP 1: Lay Out Map of Study Area. A part of the study area
in question is illustrated in Figure E-3 which displays the 5
districts and the highway network selected for analysis. Also
shown are the subregional boundaries and the 6 external stations at
the cordon (A through F). The freeway links (16 in number) in the
network are numbered consecutively from #101 onwards, and the
arterial links (17 in number) from #117 onwards.
STEP 2: Tabulate Base Year Ground Counts by Link. The base
year ground counts (which must be available as input) are shown
tabulated in the summary table shown later in the text in Figure E-
15, column a. The computational use of these counts does not occur
until Step 4.
E-6
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E-7
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E-8
STEP 3: Assign Base Year I-E, E-E Vehicle Trip Matrix to the
Base Year Highway Network. The base year external trip matrix
(which must also be available as input) for the study area is shown
in Figure E-4. The matrix indicates that the study area and its
external environs generate a total of 20,000 vehicle trips in the
base year, of which 15,100 (i.e., 7,200 + 7,900) are I-E-1 trips
and 4,900 are E-E trips.
The actual trip assignment entails the use of the commonly
used "all-or-nothing" procedure described in the Users Guide 6/.
Figure E-5 exhibits the assignment worksheets--trip interchanges
and the corresponding trip volumes form the left-hand columns of
the worksheets, whereas the highway link numbers are arranged
across the top. The tick marks indicate the "minimum" highway path
followed by a particular trip interchange. Thus, for example, the
trip interchange from district #4 to external station B and back
(i.e., 4-B-4) corresponds to a trip volume of 200 + 300 = 500
vehicles (Figure E-4). The highway path followed by this trip
interchange is judged to be via link numbers 127 and 113 (Figure E-
5). The tick marks are then inserted in the appropriate cells in
the assignment worksheets. Note that it is assumed that the
"minimum" highway path is the same for trips from area i to area j,
as it is (in reverse order) from j to i and is determined visually
from a map.
When all the trip interchanges and volumes have been inserted
in the proper cells, the marked cells are summed vertically for
each link to obtain the total traffic on that link. For instance,
freeway link #115 carries 400 + 300 + 300 + 300 + 300 + 300 = 1,900
vehicles or I-E and E-E traffic (Figure E-5). The base year
external traffic by link is tabulated in Figure E-15, column b.
STEP 4: Subtract Base Year I-E, E-E Vehicle Trips from Base
Year Ground Counts by Link to Obtain Base Year I-I Vehicle Trips by
Link. This subtraction is undertaken on a link-by-link basis and
the resultant I-I trips are recorded in Figure E-15, column c.
Hence, for freeway link #115, the base year I-I trips are given by:
30,100 - 1,900 = 28,200 vehicles.
The next 15 steps are necessitated in order to generate the
traffic growth factors for I-I trips by link (Steps 5 through 19),
and the growth factors by analysis area (Step 14). Steps 5 through
12 include vehicle trip generation, trip distribution and trip
assignment for both the base year and future year conditions.
STEP 5: Generate the Base Year All Purpose I-I Vehicle
Productions and Attractions by Analysis Area . The trip generation
procedures employed are those described in Chapter Two. By using
the base year socioeconomic characteristics (such as household
size, income and auto ownership) for each of the 5 districts in the
study area, the average daily person trips per household (and
thence by district) are estimated. Then, by employing auto
occupancy rates and a transit estimate, the average daily vehicle
productions (P's) and attractions (A's) are calculated. These P's
and A's are then entered into the appropriate locations in Figure
E-6. District #4, for example, produces 18,200 all purpose I-I
vehicle trips and attracts 17,600 trips on an average daily basis.
In all, the 5 districts generate a total of 100,000 I-I vehicle
trips.
STEP 6: Develop the Base Year Analysis Area-to-Area Travel
Times and All Purpose Friction Factors. The travel times and the
corresponding all purpose friction factors are developed by using
the "Airline Distance vs. Travel Time vs. Friction Factor" graphs
contained in Appendix A (for this example, for urbanized areas with
less than 100,000 population). The use of these graphs has been
documented in the Users Guide 6/. The basic input to these graphs
E-9
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E-10
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E-11
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E-12
is the centroid-to-centroid airline distance and the corresponding
mix of travel by highway facility (arterial or freeway). Note that
it is assumed that the travel time (and therefore the all purpose
friction factor) is the same for trips from area i to area j, as it
is from j to i.
NOTE: The Friction Factors for the example used in this
Appendix are not from Figures in Appendix A, but were
fabricated for the example presentation.
The travel times and friction factors are inserted in the
appropriate locations in Figure E-6. For instance, the trip
interchange between districts #4 and #3 entails a travel time of 10
minutes and the corresponding all purpose friction factor is 0.17.
(The same condition is assumed to hold true for the #3 to #4 trip
interchange.)
Having entered all the area-to-area travel times and the
friction factors in Figure E-6, the user is now ready to distribute
the base year trips between the 5 districts.
STEP 7: Distribute the Base Year All Purpose I-I Vehicle
Trips. The trip distribution is accomplished by applying the
manual trip distribution (Gravity Model) method described in
Appendix B. The Gravity Model is applied for two iterations at the
end of which the P's and the A's should be "balanced." All the
computations necessary to conduct the trip distribution are shown
in Figure E-6. Figure E-7 summarizes the base year all purpose I-I
vehicle trip matrix. Thus, 1,700 vehicle trips result from
district #4 to #3, and 2,900 trips from #3 to #4. A total of
100,000 vehicle trips have been distributed between the 5
districts.
STEP 8: Generate the Future Year All Purpose I-I Vehicle
Productions and Attractions by Analysis Area. This step is
identical to Step 5 except that the P's and A's now represent the
trip generation potential for the study area for the future year.
These P's and A's are entered in the appropriate locations in
Figure E-8. Due to the anticipated growth in the study area, it
can be observed that the district #4, for example, will produce
19,000 all purpose I-I vehicle trips and will attract 18,000 trips
on an average daily basis. In all, it has been estimated that the
5 districts will generate a total of 110,000 I-I vehicle trips, an
increase of 10% over the base year condition.
STEP 9: Develop the Future Year Analysis Area-to-Area Travel
Times and All Purpose Friction Factors. This step is identical to
Step 6 except that the travel times and the corresponding all
purpose friction factors are developed for the future year. It
must be pointed out that since the centroid-tocentroid airline
distances between the 5 districts will remain unchanged, the
"Airline Distance vs. Travel Time vs. Friction Factor" graphs
will exactly generate the base year travel times. For this
example, however, travel times have been altered from those in the
base year simply to account for some hypothetical future year
conditions--such as congestion and therefore increased travel times
on some links, and traffic improvement programs and therefore
decreased travel times on other links. The alterations in base
year travel times have been made on a purely judgmental basis.
E-13
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E-14
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E-15
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E-16
The travel times and friction factors developed are recorded
in the appropriate locations in Figure E-8. For instance, the trip
interchange between districts #4 and #3 now entails a travel time
of 12 minutes and the corresponding all purpose friction factor is
0.12. (The same condition is assumed to hold true for the #3 to #4
trip interchange.)
After entering all the area-to-area travel times and friction
factors in Figure E-8, the future year trips can then be
distributed between the 5 districts.
STEP 10: Distribute the Future Year All Purpose I-I Vehicle
Trips. This step is conducted in a fashion identical to that of
Step 7, i.e., by using the manual trip distribution (Gravity Model)
method described in Appendix B. All computations carried out for
this step are shown in Figure E-8 and Figure E-9 summarizes the
future year all purpose I-I vehicle trip matrix. It can be ob-
served from these two figures that 1,400 vehicle trips result from
district #4 to #3, and 2,200 trips from #3 to #4 (in both cases, a
decrease in the number of trips as compared to the base year
trips). A total of 110,000 vehicle trips have been distributed
between the 5 districts.
STEP 11: Assign the Base Year All Purpose I-I Vehicle Trip
Year Highway Network. As before, using the "all-or-nothing"
assignment procedure documented in NCHRP (1) and the base year
highway network graphically represented in Figure E-3, the base
year all purpose I-I trip matrix (Figure E-7) was assigned on the
assignment Worksheet shown in Figure E-10. Thus, freeway link #115
carries 15,000 + 4,600 + 7,800 = 27,400 vehicles of base year all
purpose I-I traffic. This traffic (by link) is tabulated in Figure
E-15, column d.
STEP 12: Assign the Future Year All Purpose I-I Vehicle Trips
to the Future Year Highway Network. Since there are a few changes
in the highway network attributes as compared to the base year (See
Step 9.), the future year assignment is assumed to be identical to
that of Step 11, except that the future year all purpose I-I trip
matrix (Figure E-9) is assigned. The actual assignment is also
accomplished in Figure E-10. Thus, freeway link #115 now carries
15,700 + 3,600 + 8,500 = 27,800 vehicles of future year all purpose
I-I traffic. This traffic (by link) is tabulated in Figure E-15,
column e.
STEP 13: Divide Future Year All Purpose I-I Vehicle Trips by
Base Year All Purpose I-I Vehicle Trips by Link to Obtain Growth
Factors by Link. This division is underataken on a link-by-link
basis and the resultant growth factors are recorded in Figure #115,
column f. The growth factor for freeway link #115, for instance, is
given by 27,800 ö 27,400 = 1.01. Note that where there is no (zero)
traffic on a link for both the base and future years, the growth
factor is considered to be 1.00.
STEP 14: Divide the Sum of Future Year All Purpose Productions
and Attractions by the sum of the base Year All Purpose Productions
and Attractions to Obtain Growth Factors by Analysis Area. This
step is accomplished for the five districts and the necessary
computations are exhibited in Figure E-11. The
E-17
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E-18
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E-19
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E-20
base year P's and A's for district #4, for example, sum up to
35,800 vehicle trip ends and those for the future year to 37,000,
thus yielding a growth factor of 37,000 -'.- 35,800 = 1.03. Figure
E-11 also contains the growth factors for traffic at the external
stations (A through F): these factors are readily available for
most study areas.
STEP 15: Compute Average Growth Factors for District/Station
Trip Interchanges. These factors are merely the arithmetic mean of
the growth factors at the origin and destination ends of the trip
interchanges. So, for the district #4 to Station B interchange,
the average growth factor is given by (1.03 + 1.15) ö 2 = 1.09. The
average growth factor matrix is tabulated in Figure E-12.
The next two steps involve the application of the growth
factors developed in Steps 13 and 15 to expand (respectively) the
base year I-I trips by link output from Step 4, and the base year
I-E, E-E trip matrix used in Step 3. The result of these expansions
is the future year I-I, and I-E, E-E vehicle trips by link.
STEP 16: Expand Base Year I-I Vehicle Trips by Link. This
expansion is accomplished in Figure E-15, where the product of
column c (the base year I-I trips by link) and column f (the growth
factors for I-I trips by link) constitutes the future year I-I
trips by link (column g). As an example, the 28,200 base year I-I
trips on freeway link #115 are multiplied by the corresponding
growth factor of 1.01 to produce 28,500 future year I-I trips. All
future year I-I trips are recorded (by link) in Figure E-15, column
g.
STEP 17: Expand the Base Year I-E, E-E Vehicle Trip Matrix.
This expansion is conducted by multiplying the base year I-E, E-E
trip interchanges in the matrix (Figure E-4) by the corresponding
average growth factors shown in Figure E-12. Therefore, for the
200 base year I-E, E-E trips from district #4 to Station B, say,
the product with the corresponding average growth factor of 1.09
yields the future year I-E, E-E trips equal to 218 (or 200, if
rounded to the nearest 50 trips). The future year I-E, E-E trip
matrix is exhibited in Figure E-13.
The future year I-E, E-E trip matrix indicates that there are
a total of 22,850 vehicle trips, an increase of 2,850 trips over
the base year condition. The I-E-1 trips constitute 17,150 trips
and the E-E trips add up to 5:700 trips.
STEP 18: Assign the Future Year I-E, E-E Vehicle Trip Matrix
to the Future Year Highway Network. Again, since there are a few
changes in the highway network attributes in the future year (See
Step 9.), this assignment is assumed to be identical to that
undertaken in Step 3. Further, the :minimum" paths are assumed to
stay the same as those for the base year. So, for the trip
interchange from district #4 to external station B and back (i.e.,
4-B-4), the "minimum" path, as before, is via link numbers 127 and
113 (Figure E-5); however, the 4-B-4 interchange in the future year
has a magnitude of 550 vehicle trips (as opposed to 500 vehicle
trips in the base year). The trip assignment Worksheet is
displayed in Figure E-14.
E-21
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E-22
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E-23
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E-24
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E-25
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E-26
As noted before, the vertical summation by link results in 'he
total traffic assigned to that link. Thus, for freeway link #115,
the total I-E, E-E traffic is given by 500 + 350 + 300 + 350 + 350
+ 350 = 2,200 vehicles (as opposed to the 1,900 vehicles in the
base year). The future year external traffic by link is tabulated
in Figure E-15, column h.
STEP 19: Add the Future Year I-I Vehicle Trips to the Future
Year I-E, E-E Vehicle trips by link to Obtain the Future Year
Ground Counts. The summation of the future year I-I trips by link
(Figure E-15, column g) and the future year I-E, E-E trips by link
(Figure E-15, column h) is performed and recorded in Figure E-15,
column i. For freeway link #115 then, the future year ground count
is given by 23,500 + 2,200 = 30,700 vehicles.
On observing the base year and future year ground counts in
columns a and i, respectively, in Figure E-15, it can be seen that
except for arterial link numbers 120, 122, 123 and 133, all other
links show an increase in the future year ground counts. Link #118
exhibits the highest growth in traffic (+26.5%), with link numbers
130 and 131 following with +21.9% and +21.3%, respectively. The
lowest increases occur on link numbers 115, 116 and 119 (+2.0%,
+0.6%, and +1.0%, respectively).
In absolute terms, the highest volume of freeway traffic
occurs on link numbers 103, 104, 115 and 114 (in descending order
of magnitude). For arterial traffic, the larger volumes occur on
link numbers 118, 132, 130, 131, 122 and 123 (in descending order
of magnitude).
in general, it appears that the future ground counts are
consistent with the anticipated growth in the study area. At this
point, all high-growth or high-magnitude links would be subjected
to a capacity analysis to check whether or not the future year
traffic can be accommodated at some level of service. Critical and
over-loaded links or corridors would be candidates for system im-
provements. (See Chapter Three, System Planning manual.)
E-27
APPENDIX F
COMPUTER PROGRAMS FOR GROUND COUNT FACTORING
The chain of programs that could be used to accomplish the
count factoring process is shown in Figure F-1. The programs shown
are not the only software that will accomplish the task. These
programs were selected because; (1) they make use of previously
described UTPS software that incorporates default conditions and
(2) all programs are included in the UTPS package, which saves the
user from having to obtain, install and learn other software
packages.
The program flowchart shown in Figure F-1 is effectively two
parallel paths. Each path consists of obtaining both internal and
external trip matrices and assigning these trips to a network using
program UROAD. Internal travel is obtained by using the default
model built into program AGM and previously discussed. Base year
external travel is obtained from an external O-D survey. Forecast
year external travel is obtained by using growth factors which can
be applied with program UMCON.
Two assignments are performed using program UROAD. UROAD
application (1) produces a historical record containing the basic
link data and the base year assigned volumes. It should be kept in
mind that the assigned volumes produced are based on a single
purpose model not adjusted to the area and should only be used to
obtain factors for the expansion of the around counts.. UROAD
application (2) assigns the forecast year trips and by utilizing a
user-coded subroutine, factors and the ground counts and prints a
report showing forecast year volumes.
The programs used in this process have been previously
discussed, The following discussion will cover areas that are
unique to the link count factoring process.
UROAD - Application (1). Two trip matrices are input to the
assignment process. Assuming that these matrices are each Table 1
on two separate datasets, the TABLES parameter would be coded as
follows:
TABLES=101,201
This implies that the trip matrices will be specified on
DDCARDS FT11FO0l and FT12F001. In order to achieve assigned
volumes that are in balance directionally (i.e., consistent with
the counts) it is necessary to utilize the SPLITn parameters. They
are coded as follows; SPLITl=.5,.5,SPLIT2=.5,.5. Since an updated
historical record is necessary for UROAD application (2), the user
should code the WIELD parameter as follows:
VFIELD=O
This implies that the assigned volume would be appended to the
historical record immediately after the last word in the input
record, The updated historical record will be output on a dataset
defined on DDCARD FT03F001. A complete example of a parameter card
would be:
F-1
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F-2
&PARAM TABLES=101,201,VFIELD=O,SPLIT1=.5,.5,SPLIT2=.5,.5 &END
UROAD - Application (2). Once again, two matrices are input
to the assignment process in the same manner as in UROAD
application (1). The UROAD program which is used in this case is
one that has the user-coded subroutine (supplied with the program
tape) incorporated into the program, The historical record produced
in UROAD application (1) (FT03F001) is used as input and is defined
on DDCARD FT02F001.
The parameter card coding for this application is similar to
UROAD application (1) but does not contain the VFIELD
specification;
&PARAM TABLES=101,201,SPLIT1=.5,.5,SPLIT2=.5,.5 &END
Program UMCON. Program UMCON is used to apply growth factors
to the base year external trip matrix to produce forecast year
external trips. Two options exist for applying growth factors.
The user can supply a card for each external zone coded as follows:
4-8 Zone number
9-16 Required Zonal Productions
17-24 Required Zonal Attractions
UMCON will scale the input trip matrix to achieve the desired
productions and attractions. Alternately, the user can code growth
factors to be applied to each external zone. The growth factors
are coded (with decimals) in place of the production and attraction
fields shown above. The program is informed that these values are
growth factors rather than desired trip totals by coding the FACTOR
option on the &OPTION control card. This is accomplished as
follows:
&OPTION FACTOR=T &END
F-3
APPENDIX G
EXAMPLE OF REDISTRIBUTION OF
ASSIGNED VOLUMES AMONG AVAILABLE FACILITIES
Consider the north-south corridor delineated in Figure E-3 for
redistribution analysis; the corridor is also shown on an expanded
scale in Figure G-1. Redistribution is to be performed across
screenline A-A. The redistribution technique requires that it be
conducted across cutlines (i.e., subdivisions of screenlines)
intercepting at least 3 highway links. So for illustrative pur-
poses only, assume that the corridor under consideration (Figure G-
1) has, in addition to the original links (#'s 103 and 126), link
Vs 140 and 141. Further, link #200 is a proposed facility for the
future year and is expected to add capacity (and relieve
congestion) across screenline A-A.
All the necessary traffic data for the north-south corridor
and screenline A-A are shown in Table G-1. Note that traffic data
for link Vs 103 and 126 have been obtained from the traffic
estimation technique described in the preceding sections and Figure
E-15, whereas that for link #s 140, 141 and 200, and all capacity
data, are hypothetical numbers.
The redistribution technique is applied in the following
fashion. The manner in which screenline A-A is subdivided into
cutlines is as follows. Starting at one end of the screenline the
first cutline should normally extend across at least 3 facilities
(Figure G-1). The second cutline should do the same, and overlap
the first cutline such that the overlap extends across about half
of each individual cutline. Preferably, more than one facility
should be intercepted within the overlap. The third cutline should
be similarly laid out, and should start where the first cutline
terminates. Additional cutlines as needed should be similarly
established. Unless irregularities in the street system dictate
otherwise, the cutlines in parallel screenlines should be opposite
each other so as to intercept the same sets of highway facilities.
As an example, Figure G-1 shows the subdivision of screenline A-A
into three overlapping cutlines (i.e., p-p, q-q and r-r) to be used
in the redistribution of forecast year assignment volumes.
Screenline A-A will be analyzed using the hypothetical traffic data
exhibited in Table G-1.
Table G-2 shows the Worksheet used for the redistribution of
assigned volumes. Link description, plus traffic data for columns
a, c and e are filled in Table G-2 using the data given in Table G-
1. Such information is recorded for each of the three cutlines of
screenline A-A shown in Figure G-1. The cutlines are pro cessed
one at a time and the total assignment adjustment volumes (column
h, Table G-2) are input, when appropriate, into column e of the
subsequent cutline analysis. The order in which the cutlines are
processed is arbitrary, but such computations should proceed in an
orderly fashion from one end of the screenline to the other (say,
from left to right).
The calculations necessary for completing Table G-2 are as
follows (cutline p-p calculations are obvious from Table G-2, so
the following steps pertain to cutline q-q):
G-1
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G-2
TABLE G-1
TRAFFIC DATA FOR HIGHWAY LINKS
WITHIN THE NORTH-SOUTH CORRIDOR AND CROSSING SCREENLINE A-Aa
LINK BASE YEAR FUTURE YEAR
GROUND CAPACITY
# COUNTb ASSIGNMENTc
140 9,600 9,000 12,000
103 32,300 30,000 34,100
141 4,400 5,000 0
200d -- 8,000d 4,000d
126 5,300 6,000 5,900
TOTAL 51,600 58,000 56,000
FOOTNOTES:
a. All traffic data is 2-directional and measured as average
daily traffic (ADT).
b. Figure E-15, Column a for link #'s 103,, 126,*
c. Figure E-15, Column i for link #Is 103, 126.*
d. Link #200 is a new link contributing additional capacity
to the screenline capacity for the future year.
* All other data are hypothetical.
G-3
G-4
1. Sum the base year volumes, i.e, traffic counts (column a)
and determine the % volume contribution (column b) for
each link of cutline q-q. Note that since link #200 is a
new facility, base year traffic counts do not exist and
therefore columns a and b are left blank.
2. Since link #200 contributes additional capacity in the
forecast year, columns c and d are filled in a manner
similar to the preceding step.
3. Column e is now completed using the future year
assignment volumes (from the all-or-nothing assignment)
using data from Table G-1.
4. As a capacity change is expected to occur across cutline
q-q, column is completed for link #200. Thus, the
capicity assignment adjustment for link #200 is 18.6% x
40,558 = 7,544, i.e., this volume of traffic can be
expected for the new facility. The remaining forecast
year assignment volume in column f, i.e., 40,558 - 7,544
= 33,014, is distributed to the other links of cutline q-
q.
5. Hence the volume assignment adjustments (column g) for
link Vs 103 and 141 can be computed in the proportion
given in column b. Hence, for the former link, this
adjustment is 88.0% x 33,014 = 29,052, i.e., this volume
of traffic can be expected for link #103. A similar
computation is done for link #141.
6. Finally, the total assignment adjustment for each link
crossing cutline q-q is computed by adding the volumes in
columns f and g. Note that the totals for column e and h
are the same for cutline q-q; only the traffic within the
cutline has been redistributed among the three links.
The six steps are similarly undertaken for cutline r-r. For
r-r, the volumes for link Vs 141 and 200 in column e are the
assignment adjustments from column h of the previous calculations
for cutline q-q. Note that similar transformation was made for q-
q, (the volumes for link Ps 103 and 141 in column e are adjustments
from column h for cutline p-p). For p-p, however, no new
facilities cross the cutline. Therefore, the computations in
columns c, d and f are not necessary. The adjustments in column g
are arrived at by proportioning the sum of traffic in column e
using the percentages in column b. Thus, for link #140, the
proportioned traffic equals 20.7% x 46,100 = 9,542. The asterisks
in column h of Table G-2 indicate the final balanced volumes
resulting from the redistribution technique. To refine these
volumes, screenline A-A could be re-processed through the six steps
outlined above. The second iteration might result in a small gain
in accuracy of the balanced volumes. Iterations beyond the second
iteration are not recommended.
Figure G-2 illustrates the capacity, the base year volumes,
the future year assignment volumes and the balanced volumes for
links crossing screenline A-A. The user can observe the effect of
the redistribution of volumes among the facilities. The
redistribution technique can be similarly applied, if need be, to
other corridors in the study area shown in Figure E-3.
G-5
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G-6
APPENDIX H
DETAILS OF THE PARTIAL MATRIX TECHNIQUE (PMT)
Theory of the PMT
The PMT is based on a straightforward extension and
application of the theoretical work by Kirby 10/ . A brief
discussion of this theory and usage of the PMT is contained in
reference 10/. Two of the results of Kirby's theoretical work used
in the application of the PMT are as follows:
1. That the unknowns in the Gravity Model formulation can be
derived from a partial set of observed trips;
2. That the solution from the partial set is unique,
provided that the trip matrix cannot be partitioned such
that diametrically opposite quadrants are zero.
The implication of these results is that having calibrated a
Gravity Model to a partially observed matrix, one can use the
parameters that have been derived to estimate the values of the
unobserved trips of the matrix.
To demonstrate the capabilities of the PMT, consider a simple
example where a study area is bounded by an external cordon and
divided by a screenline running north-south (Figure H-1). Suppose
that the analysis areas in the study area can be grouped into
internal eastern zones (E) and internal western zones (W), and
external zones W. If the trip movements have been observed through
screenline and cordon interviews, then such observations would be
inserted in the "ticked" cells of the matrix. This partial set of
trip observations would, in effect, constitute the partial trip
matrix. The ultimate objective then is to estimate the trips in
the unobserved cells of this matrix, thus yielding a total trip
matrix. (In this particular example, the unobserved trips represent
the intraanalysis area trips.)
Now, the Gravity Model relationship in its most elementary
form is given by:
T = a P * b A * f(I ) * K . . . . . . . . . . . . . (1)
ij i i j j ij ij
where:
Tij = trips produced in analysis area i and attracted at
analysis area j
ai = a constant associated with the production of tripsat
i
Pi = total trip production at i
bi = a constant associated with the attraction of tripsat
j
Aj = total trip attraction at j
f(Iij) = a function of the generalized impedance between
interchange ij (usually the friction factor Fij)
Kij = socioeconomic adjustment factor (if necessary) for
interchange ij
H-1
Click HERE for graphic.
H-2
i = origin analysis area number, i=1,2,3 ... n
j = destination analysis area number, j=1,2,3...n
n = total number of analysis areas.
If Kij is assumed to equal 1 for all trip interchanges, and if
the total and total attractions for all the analysis areas are not
known (as productions would be the case if one were to obtain trip
interchange input from interviews only, as in the case of the PMT),
then the Gravity Model formulation given by Equation (1) reduces to
the following:
E
T = X * Y * f(I ) . . . . . . . . . . . . . . . . . (2)
ij i j ij
where:
E
Tij = the estimated number of partial trips produced in
analysis area i and attracted at analysis area j
Xi = a unique row factor associated with the production
of trips at i (i.e., Xi = aiPi ò 0)
Yj = a unique column factor associated with the
attraction of trips at j (i.e., Yj = bjAj ò 0)
o
If Tij is the observed number of total trips between i and j
(obtained from the screenline and cordon interviews), then the
calibration process entails the estimated partial trip interchanges
determination of f(Iij) such that the e "fit" the observed trip
interchanges (Toij).
Using the maximum likelihood function as the criterion for
fitting the Gravity Model given by Equation (2), Kirby has shown
that the values of Xi, Yj and f(Iij) are such that the following
conditions are satisfied:
1. The sum of the estimated partial trips must equal the sum
of the observed partial trips for each production
analysis area (row partial totals), i.e.,
E o
ä T = ä T . . . . . . . . . . . . . . . . . . . (3)
j ij j ij
2. The sum of the estimated partial trips must equal the sum
of the observed partial trips for each attraction
analysis area (Column partial totals), i.e.,
E o
ä T = ä T . . . . . . . . . . . . . . . . . . . (4)
i ij i ij
3. The total travel cost of the estimated partial trips must
equal the total travel cost of the observed partial
trips, i.e.,
E o
ä ä T * I = ä ä T * I . . . . . . . . . (3)
i j ij ij i j ij ij
The calibration process is thus one of establishing values of
Xi and Yj (in an iterative manner described below) and ensuring
that the estimated partial matrix row sums equal the observed
partial matrix row sums, and likewise :or columns, and ensuring
that the average trip lengths of the estimated and observed partial
matrices are the same.
H-3
Once the values of Xi and Yj and the calibrated impedance
function are established, these factors can then be applied to
determine the unobserved elements of the partial matrix, and thence
the total production and attractions for each analysis area.
It must be noted that the matrix cells which were previously
filled from the partial observations retain approximately the same
value in the total synthetic matrix and should therefore be
accurately observed. A very important assumption of the PMT is
that for those cells of the partial trip matrix for which trip data
is available (observed), this data represents all trips for that
particular ij pair. Note also that the trip data collected from
the interviews at the screenline and cordon stations could be for
HBW or HBNW or NHB trips, or for all purpose trips. In many cases
it would be most practical to record all trips without a purpose
stratification. Such an interview would be of particular relevance
for smaller urban areas where a distinction between the trip
purposes may not be worthwhile for quick-response planning. (See
subsection of Chapter Two entitled, One-Purpose Gravity Model.")
Computational Steps for Application of the PMT
In actual application of the PMT, the iterative manner in
which the Xi and Yj factors are established is by successively
balancing the row and column totals of the partial observed trip
matrix. These successive steps are algebraically described below.
This series of steps has been labelled Series B and Series C in
order to correspond with the steps described later in the section
entitled "An Example Application." Series A steps constitute those
preliminary steps that are accomplished "external" to the PMT and
precede the Series B steps. The Series B steps are as follows
(except where noted, these steps apply only to the observed cells
of the partial observed matrix):
STEP B1: Compute Row Balancing Factors 1 = 1Ri: For each row,
the row balancing factor is given by:
1
R = __________
1 i
ä A F
j j ij
STEP B2: Compute Trip Interchanges 1 for the Observed Cells of
the Partial Matrix = 1TEij: For each observed cell, the trip
interchanges are given by:
E
T = P A F * R
1 ij i j ij 1 i
Note that it has been assumed that Kij = 1 for all the
observed cells of the trip matrix in order to simplify the
computational steps. Where and when necessary the Kij factors can,
of course, be incorporated. For the unobserved cells, Kij is
constrained to be zero; this constraint is relaxed in Step C4 when
Ki, for these cells equals one (or the actual value if so desired
or necessary).
STEP B3: Compute Column (Attraction Areas) Totals I = äi
1TEij: For each column, the total (partial) attractions are given
by:
E
Column Total = ä T
i 1 ij
H-4
STEP B4: Compute Column Balancing Factors 2 = 2Cj: Since the
column totals derived from Step B3 will not agree with Ihe partial
attraction totals, the column balancing factor for each column
needs to be calculated as follows:
A
j
C = _________
2 j E
ä T
i 1 ij
STEP B5: Compute Trip Interchanges 2 for the Observed Cells of
the Partial Matrix = 2TEij: The trip interchanges computed from
Step B2 are now adjusted by using the Column balancing factor from
Step B4. Therefore, for each observed cell, the new trip
interchanges are given by:
E E
T = C * T
2 ij 2 j 1 ij
STEP 6: Compute Row (Production Areas) Totals 2 = äj 2TEij
For each row, the total (partial) productions are given by:
E
Row Total = ä T
j 2 ij
STEP B7: Factors 3 = 3Ri: Now since the row totals derived
from Step B6 will not be in agreement with the partial production
totals, the row balancing factor for each row needs to be
calculated as follows:
P
i
R = ____________
3 i E
ä T
j 2 ij
STEP B8: Compute Trip Interchanges 3 for the Observed Cells of
the Partial Matrix = 3TEij: The trip interchanges computed from
Step B5 are now adjusted by using the row balancing factor from
Step B7. Therefore, for each observed cell, the new trip
interchanges are given by:
E E
T = R * T
3 ij 3 i 2 ij
STEP B9: Compute Column (Attraction Area) totals 3 = äi 3TEij:
This step is similar to Step B3. Thus, for each column , the total
(partial) attractions are given by:
E
Column Total = ä T
i 3 ij
STEP B10: Compute Column Balancing Factors 4 = 4Cj: This
step is similar to Step B4. Since the column totals derived from
Step B9 will not agree with the partial attraction totals, the
column balancing factor for each column needs to be calculated as
follows:
A
j
C = ___________
E
ä T
i 3 ij
H-5
STEP B11: Compute Trip Interchanges 4 for the Observed Cells
of the Partial Matrix = 4TEij: This step is similar to Step B5.
The trip interchanges computed from Step B8 are now adjusted by
using the column balancing factor from Step BIO. Therefore, for
each observed cell, the new trip interchanges are given by:
E E
T = C * T
4 ij 4 j 3 ij
STEP B12: Compute Row (Production Area) Totals 4 = äj 4TEij:
This step is similar to step B6. Thus, for each row, the total
(partial) productions are given by:
E
Row Total = ä T
j 4 ij
STEP B13: Compute Row Balancing Factors 5 = 5Ri: This step is
similar to Step B7. Since the row totals derived from Step B12
will not be in agreement with the partial production totals, the
row balancing factor for each row needs to be calculated as
follows:
P
i
R = ____________
5 i E
ä T
j 4 ij
STEP B14: Compute Trip Interchanges 5 for the Observed Cells
of the Partial Matrix = 5TEij: This step is similar to Step B8.
The trip interchanges computed from Step B41 are now adjusted by
using the row balancing factor from Step B13. Therefore, for each
observed cell, the new trip interchanges are given by:
E E
T = R * T
5 ij 5 i 4 ij
It can be seen therefore, that except for the initial two
steps (i.e., Steps, B1 and B2), the subsequent steps represent the
successive adjustments of trip interchanges - a series of
adjustments by each column, and then a series of adjustments by
each row. (Note that in the normal application of the Gravity
Model, the production/row totals are constrained such that the
estimated row totals are equal to the observed productions; it is
the attraction/column totals that are iteratively "balanced.")
Hence, Steps B3-B5 and Steps B9-B11 (and Steps B15-B17, Steps B21-
B23, etc.) constitute a series of steps that perform adjustments by
each column, whereas Steps B6-B8 and Steps B12-B14 (and Steps B18-
B20, Steps B24-B26,etc.) constitute a series of steps that perform
adjustments by each row.
Ultimately, the successive adjustments will result in the
convergence of the trip interchanges, i.e., the estimated trip
interchanges (TEij) for the observed cells will equal the observed
trip interchanges (Toij). In other words, at some point, the
column and row balancing factors will equal unity. thus, if n is
the number of adjustments, then at the point of convergence:
C = 1 and R = 1
n j n+1 i
In practice and actual application of the PMT, near
convergence occurs when 8 ó n < 10, at which point the column and
row adjustment factors are approximately
H-6
equal to 1. At this juncture, the Series C Steps are entered in the
following manner:
STEP C1: Compute the Unique Row Factor Xi and the Unique
Column Factor Yj: These unique factors, used in Equation (2) above
are computed as follows:
X = P (ã/n R ) -- for each row
i i n i
Y = A (ã/n C ) -- for each column
j j n j
where ã represents the product, over n adjustments, of Ri and Cj
STEP C2: Compute Trip Interchanges for the observed Cells =
tEij : the trip interchanges are computed using Equation (2),
for the observed cells of the partial matrix. Thus:
E
T = X * Y * F
ij i j ij
STEP C3: Plot Trip Length Frequence Distribution of the
Estimated Partial Trips = TEij and Compare with the Observed
Partial Trips = Toij: The purpose of this comparison is to check
whether the estimated trip length frequency distribution agrees
with that for the observed trips. In actuality, this process is
the calibration of the friction factors. The calibration and the
adjustments of the F-factors can be carried out in the usual
manner. (See Reference 8 for example,) Then, using the calibrated
friction factors, the Series B steps must be reapplied, Step C3
reentered, and then the estimated and observed trip length
frequency distributions compared.
However, for sketch planning, this calibration can be
bypassed, in particular if a calibrated set of friction factors has
been used. Such calibrated friction factors can be obtained from
local study area data, or default values as presented in Appendix
A,may be used. In any case, when the friction factors are cali-
brated, i.e., when the trip length frequency distributions for the
estimated and observed trips match, Step C4 is entered.
STEP C4: Compute Trip Interchanges for the Observed and
Unobserved Cells = TEij : These trip interchanges are computed
using Equation (2) for the observed and unobserved cells of the
partial matrix. Thus, for every cell in the matrix:
E
T = X * Y * F
ij i j ij
As noted in the preceding discussion, the socioeconomic
factors (Kij), if used at all, had been assumed to be unity for the
observed cells of the pairtial matrix and constrained to be zero
for the unobserved cells. In Step C4, the constraint for the
unobserved cells is relaxed. Hence, Kij = 1, or if required, Kij
is set to some other value particular to that interchange.
STEP C5: Compute Total Trip Productions and Attractions for
All Analysis Areas: By using the now complete matrix, the total
trip ends are computed as follows:
E E
P = ä T and A = ä T
i j ij j ij
H-7
The PMT is now considered to be completely applied.
In order to illustrate the actual usage of the PMT, the
following example application is provided. This sample application
makes use of the Series A steps, and the Series B and C steps (the
latter two as described above).
An Example Application
Suppose that the average daily internal travel for five
districts in a hypothetical urban area of 60,000 population is to
be analyzed (The internal travel includes trips by all three trip
purposes, i.e., HBW + HBNW + NHB trips.) For this reason, a cordon
has been imposed around the CBD and a screenline running north-
south has also been sited.
The procedural steps required for the application of the PMT
are described below. As mentioned in the preceding sections, the
Series A steps constitute the preliminary set-up steps, whereas the
Series B and C steps represent the computational steps.
STEP A1: Map of Study Area: Lay out a map showing the five
districts, the distict centroid region boundaries (Figure H-2).
Also, the cordon line, the screenline and the interview stations
are located on the map.
STEP A2: Conduct Cordon and Screenline Roadside Interviews:
These interviews can be conducted as described in this illustrative
example, assume that these interviews resulted in the partial
matrix of trips shown in figure H-3.* Thus, for example, the
screenline interview station between districts #2 and #3 yielded
1,400 all purpose internal trips from district #2 to #3, and 2,700
trips from district #3 to #2. Figure H-3 also shows the row and
column summation of the partial-observed trips, i.e., the partial
production and attraction trip ends. Hence, for district #2, there
are 6,500 partial production trip ends and 7,000 partial attraction
trip ends. In all, the partial trip matrix yields 58,100 trip
interchanges between the 5 districts in the study area. The
partial P's and A's are recorded in the PMT Worksheet as shown in
Figure H-4. Normally the analyst would use factors from Appendix
A.
STEP A3-, Develop District-to-District Travel Times and
Distribution Factors = tij, Fij: This step is identical to Step 3
described in Appendix B. These travel times and distribution
factors are developed for all trip interchanges (actually, for one-
half of the 5x5 interchanges) and recorded in the appropriate
locations as exhibited in Figure H-4. It can be seen that it takes
8 minutes to travel (by highway) from district #2 to district #3,
and the corresponding all purpose distribution factor is 0.23.
(Note also that these same parameters hold for the district #3 to
#2 trip interchange.) The friction factors for this example are not
from Appendix A, but have been fabricated for this example.
___________________________
* Note that for purely illustrative purposes, the trips for the
partial-observed matrix have been made to correspond to those from
a full-scale GM. (See Figure B-5.)
H-8
Click HERE for graphic.
H-9
Click HERE for graphic.
H-10
Click HERE for graphic.
H-11
Having completed the preliminary Steps A1-A3, the planner is
now ready to embark on the Series B steps which enable the
computation of the trip interchanges for the partial trip matrix.
The Series B steps are applied in exactly the same manner as that
described above. The computations can be carried out using a desk
calculator with an accumulating memory.
STEP Bl: Compute Row Balancing Factors I = 1Ri: This factor is
best calculated by first computing the äj , AjFij for the partial-
observed cells: 1Rican then be obtained by taking the reciprocal of
äj , AjFij. For production district #2 then:
A F = (39,300 x 0.34) + (2,300 x 0.23) + (1,700 x 0.17) = 14,180
j 2j
.
. . R = 1/14,180 = 0.705 x 10-4
1 2
This step is similarly undertaken for all rows. The PFIT
Worksheet (Figure H-5) shows these computations.
STEP B2: Compute Trip Interchanges 1 for the Observed Cells of
the Partial Matrix 1TEij: For each observed cell, the trip
interchanges are given by:
E
T = P A F * R
1 ij i j ij 1 i
Hence, for the district #2 to #3 interchange:
E
T = 6,500 x 2,300 x 0.23 x 0.705 x 10-4 = 240 trips
1 23
All such computations for the observed cells are recorded in
Figure H-5. These computations can be performed most efficiently
for each row by inserting the (Pi - 1Ri) factor into the memory of
the desk calculator and then multiplying the appropriate Aj and Fij
factors for the observed cells.
STEP B3: Compute Column (Attraction Areas) Totals
1 = äi 1TEij: For each column, the total attractions are given by:
E
Column Total = ä T
i 1 ij
For attraction district #3, for example, the column total is given
by:
E
ä T = 310 + 240 = 550 trip ends
i i3
These summations are also shown in Figure H-5.
H-12
Click HERE for graphic.
H-13
STEP B4: Compute Column Balancing Factors 2 = 2Cj: The
balancing factor for each column is given by:
A
j
C = ______________
2 j E
ä T
i 1 ij
So, for attraction district #3:
2,300
C _____________ = 4.182
550
All the column balancing factors are recorded in Figure H-5.
STEP B5: Compute Trip Interchanges 2 for the Observed Cells of
the Partial Matrix = 2TEij : These interchanges can be computed
by using:
E E
T = C * T
2 ij 2 j 1 ij
For the district #2 to #3 interchange:
E
T = 4.182 x 240 = 1,000 trips
2 23
The PMT Worksheet in Figure H-5 exhibits all such computations. On
the desk calculator, Steps B3-B5 can be performed sequentially for
each column to achieve computational time savings.
STEP B6: Compute Row (Production Areas) Totals 2 = äj 2TEij :
For each row, the total productions are are given by:
E
Row Total = ä T
j 2 ij
For production district #2:
E
ä T = 5,260 + 1,000 + 400 = 6,660 trip ends
j 2 2j
All such computations are documented in Figure H-5.
H-14
STEP B7: Compute Row Balancing Factors 3 = 3Ri : The
balancing factor for each row can be computed as follows:
P
i
R = ________________
E
ä T
j 2 ij
Hence, for production district #2:
6,500
R = _____________ = 0.976
3 2
6,660
All the row balancing factors are shown in Figure H-5.
STEP B8: Compute Trip Interchanges 3 for the Observed Cells of
the Partial Matrix = 3TEij : For each observed cell, the trip
interchanges can be calculated using:
E E
T = R * T
3 ij 3 i 2 ij
Hence, the trip interchange from district #2 to #3 is:
3
T = 0.976 x 1,000 = 980 trips
3 23
These calculations are recorded in Figure H-6. Again, to
achieve computational time savings, Steps B6-B8 can be performed
sequentially for each row on the desk calculator.
From this point on, the PMT computational steps are identical
to those already accomplished. Thus, Steps B9 through B13
correspond to Steps B3 through B7, respectively. The computations
resulting from Steps B9 through B13 are recorded in Figure H-6
(along with all the computations conducted for the preceding
steps).
Figure H-7 exhibits the computations resulting from Steps B14
through B19 (corresponding to Steps B8 through B13, respectively)
and computations resulting from the preceding steps.
At the end of the Series B steps, the row and column balancing
factors (Ri and Cj) must approximate unity, otherwise an error must
have been made in the calculations. In fact, for each successive
calculation of the row or column balancing factor, the factor
should be rapidly converging to unity. In Figure H-7, the final
row balancing factor for production district #2 (7Ri = 7R2) is
0.992 and the final column balancing factor for attraction distirct
#3 ( 8Cj = 8C3) is 1.013. For the purposes of quick, manual
planning, these factors can be considered to be sufficiently close
to unity. At this juncture, the Series C steps are entered as
follows:
H-15
Click HERE for graphic.
H-16
Click HERE for graphic.
H-17
STEP C1: Compute the Unique Row Factor Xi and the Unique
Column jFactor Yj : For each row, the Xi factor is obtained from:
ã
X = P ( ____ R )
i i n i
n
Thus, for production district #2:
-4
X = 6,500 (0.705 x 10 x 0.976 x 0.992) = 0.434
2
For each column, the Yj factor is obtained from:
ã
Y = A ( ___ C )
n j
n
Thus, for attraction district #3:
Y = 2,300 (4.182 x 1.329 x 1.075 x 1.013) = 13,920
3
All computations resulting from this step are exhibited in Figure
H-8.
STEP C2: Compute Trip Interchanges for the Observed Cells =
TEij : For each observed cell of the partial trip matrix, the trip
interchanges calculated as follows:
E
T = X * Y * F
ij i j ij
Hence, for the district #2 to #3 interchange:
E
T = 0.434 x 13,920 x 0.23 = 1,390 trips
23
All such computations for the observed cells are recorded in Figure
H-8.
STEP C3: Plot Trip Length Frequency Distribution of the
Estimated Partial Trips = TEij - and Compare with the Observed
Partial Trips = Toij : For the purposes of small urban area
application, this step can be bypassed since it is assumed that
calibrated friction factors have been utilized in the preceding
steps. (See "STEP CV under section entitled, "Computational Steps
for Application of the PMT.") It is also assumed that the estimated
trip length frequency distribution matches the observed trip length
frequency distribution. Therefore, Step C4 can then be entered.
STEP C4: Compute Trip Interchanges for the Observed and
Unobserved Cells = TEij : Because Step C3 has been bypassed,
Step C4 is applicable for the unobserved
H-18
Click HERE for graphic.
H-19
only since the estimated trips in the observed cells will remain
unchanged. Thus, for the unobserved cells in the matrix, the trip
interchanges can be computed using (once again):
E
T = X * Y * F
ij i j ij
Hence, for the district #2 to #4 interchange:
E
T = 0.434 x 12,724 x 0.34 = 1,880 trips
24
All such computations for the unobserved cells are shown in Figure
H-8 also.
STEP C5: Compute Total Trip Productions and Attractions for
All Analysis Areas : The total trip ends can be computed as
follows:
E
P = ä T
i j ij
and
E
A = ä T
j i ij
For production district #2:
P = 4,690 + 2,070 + 1,390 + 1,880 + 430 = 10,460 trip ends
2
For attraction district #3:
A = 910 + 1,390 + 7,710 + 1,770 + 9,050 = 20,830 trip ends
3
The completed trip matrix (using the PMT) is displayed in
Figure H-9. This figure also shows the trip matrix obtained from a
full-scale GM. (See Figure H-9.) The superimposition of the PMT
trip interchanges with those obtained from the GM enables a
comparison to be made between these trips. It can be observed from
Figure H-9 that the PMT trip interchanges compare extremely well
with the GM trips, -in particular between those districts that have
relatively large numbers of both production and attraction trip
ends (e.g., districts #2, #3 and A). For these trip interchanges,
the percentage difference between the PMT trips and the GM trips
lies between -1.7% to +4.1%.
However, for district #1, which produces 6,000 trips (GM) this
percentage error ranges from +1.0% to +10.0% for trips from
district #1; for district #5, which attracts 8,200 trips (GM), the
percentage error ranges from +1.0% to +10.0%.
As a final step, the trips actually observed at the cordon and
screenline interview stations are inserted into the partial-
observed cells, whereas the PMT trips are retained for the
unobserved cells. The finalcompleted trip matrix is shown in
Figure H-10.
H-20
Click HERE for graphic.
H-21
Click HERE for graphic.
H-22
It can be seen that the use of the PMr enables not only the
completion of a partially observed trip matrix, but also a
synthesis of the production and attraction trip ends for the zones
in the study area. Further, if a cordon can be positioned at the
extremities of a study area, the PMT will also enable the
estimation of external trip ends and external trip interchanges.
H-23
REFERENCES
1. Smith, Wilbur and Associates, Future Highways and Urban
Growth, (New Haven Connecticut, 1966), Prepared under
Commission from Automobile Manufacturers Association.
2. Institute of Traffic Engineers, Transportation and Traffic
Engineering Handbook, (Englewood Cliffs, New Jersey; Prentice-
Hall, Inc., 1976).
3. Hansen, Walter G., "Traffic Approaching Cities," Public Roads,
Vol. 31, No. 7, (Washington, D.C., April.1961).
4. U.S. Department of Transportation, Nationwide Personal
Transportation Study: Report No. 1, (Washington, D.C., FHUA,
April 1972).
5. U.S. Department of Transportation, Nationwide Personal
Transportation Study: Report No. 8, (Washington, D.C., FHWA,
August 1973).
6. COMSIS Corporation, Quick-Response Urban Travel Estimation
Manual Techniques and Transferable Parameters: Users Guide,
National Cooperative Highway Research Program, Report 187,
(Washington, B.C., 1978).
7. U.S. Department of Transportation, (UTPS) Reference Manual,
(Washington, D.C., periodically released).
8. U.S. Department of Transportation, PLANPAC/BACKPAC - General
Information, (Washington, D.C., Federal Highway
Administration, April 1977).
9. National Committee on Urban Transportation (NCUT), Better
Transportation for Your City: A Guide to the Factual
Development of Urban Transportation Plans, (Brattleboro,
Vermont, Public Administration Service, 1958). Also 17
Technical "Procedural Manuals" on various activities.
10. Neffendorf, H. and Wooton, H.J., A Travel Estimation Model
Based on Screenline Interviews, PTRC Summer Annual Meeting
(1974).
U.S. GOVERNMENT PRINTING OFFICE : 1980 0-320-197/6271
