Calibrating & Testing a GRAVITY MODEL for Any Size Urban rea - Aug 1983
Click HERE for graphic.
Calibrating & Testing a GRAVITY MODEL
for Any Size Urban Area
U.S. DEPARTMENT OF TRANSPORTATION
Federal Highway Administration
Reprinted August 1983
PREFACE
Trip distribution is an important and complex phase of the transportation
planning process. It provides the planner with a systematic procedure
capable of estimating zonal trip interchanges for alternate plans of both
land use and transportation facilities. These zonal interchanges
constitute a basic part of the travel information necessary for
transportation planning.
This manual documents in detail the process of trip distribution utilizing
the gravity model as it is now defined. Since automated trip distribution
techniques have only become available in the last decade, the details
involved in the various steps are still being improved. However, every
attempt has been made to include in this manual the most up-to-date
information available.
A companion manual. the Traffic Assignment Manual (1)1 was published by
the Bureau of Public Roads in June 1964. Together, these manuals document
two of the basic steps necessary for transportation analysis and
forecasting.
The techniques described in these manuals have functioned satisfactorily
when used by the Bureau of Public Roads and several urban transportation
studies. The programs and procedures have proven to be quite efficient in
handling large as well as small urban systems.
The computer programs that are described in the text are, with the
exception of some peripheral IBM 1401/1410 programs, designed for use on
the high speed binary IBM 7090/7094 computer.
Actually, the analytical procedures could have been developed for use on
any of the several computer systems of the required capacity. In fact,
programs to accomplish these procedures have been developed for exclusive
use on the IBM 1401 (16K) and the IBM 1620 (60K) computers. They differ
principally in their focus on different sized urban areas. The latter two
systems have been documented in a form similar to this volume (2) (3) and
are available for distribution.
___________________________
1 The numbers in the parentheses identify references listed in the
bibliography.
i
In addition similar progras have been written for the Control Data
Corporation 3600 computer2 and for various Univac computers.3
The computer program descriptions, containing all of the information
necessary for program use, are described in the appendix of this manual.
The system described in this volume is designed to edit, sort, and link a
set of detailed trip records from basic travel inventories. It will build
complete tables of zonal trip interchanges from origin-destination survey
data for any combination of trip purposes or travel modes desired. The
system will compute the actual trip length frequency distribution for a
given set of data. It will completely develop multipurpose gravity models
to simulate existing or future trip distribution patterns. Finally, the
system will compare the base year zonal interchanges computed by the
gravity models with those obtained from the travel inventories.
It is possible by combining these programs with those concerned with
traffic assignment, to complete most of the analytical phases of a
comprehensive transportation planning study. In addition, it is possible
to examine interim computer results at almost any phase of the process.
This is a significant advantage, particularly in the developmental stages
of a study.
___________________________
2 Transportation Planning System for the Control Data 3600 Computer,
Data Centers Division, Control Data Corporation, May 1965.
3 Information is available from Univac Division of Sperry Rand
Corporation, New York 19, New York.
ii
TABLE OF CONTENTS
Page
PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .i
CHAPTER I. BACKGROUND
A. General Introduction . . . . . . . . . . . . . . . . . . I-1
B. Gravity Model Theory . . . . . . . . . . . . . . . . . . I-2
C. Gravity Model Application. . . . . . . . . . . . . . . . I-3
CHAPTER II. HISTORY OF THE GRAVITY MODEL
A. Early Uses of the Gravity Theory . . . . . . . . . . . .II-1
B. Adaptation of the Gravity Model Theory to Travel . . . .II-1
C. Analysis of Early Gravity Model Travel Studies . . . . .II-4
CHAPTER III. PRESENT USE OF THE GRAVITY MODEL
A. Definition of Parameters . . . . . . . . . . . . . . III-1
1. Trip production and attraction . . . . . . . . . . III-1
2. Spatial separation between zones . . . . . . . . . III-1
3. Traveltime factors . . . . . . . . . . . . . . . . III-2
4. Zone-to-zone adjustment factors. . . . . . . . . . III-3
B. Sample Problem . . . . . . . . . . . . . . . . . . . . III-3
C. Data Needed to Determine Parameters. . . . . . . . . . III-6
1. Origin-destination survey. . . . . . . . . . . . . III-6
2. Travel facilities inventory.,. . . . . . . . . . . III-7
3. Other inventories. . . . . . . . . . . . . . . . . III-8
D. Initial Decisions to be Made . . . . . . . . . . . . . III-8
1. Vehicle trip or person trip model. . . . . . . . . III-8
2. Trip purpose classification. . . . . . . . . . . . III-8
3. Treatment of external trips. . . . . . . . . . . . III-10
iii
Contents Page
CHAPTER IV. CALIBRATING THE GRAVITY MODEL
A. General . . . . . . . . . . . . . . . . . . . . . . . . IV-1
B. Phase One.--Preparing Basic Data. . . . . . . . . . . . IV-3
1. Editing trip records . . . . . . . . . . . . . . . IV-3
2. Sorting trip records.* . . . . . . . . . . . . . . IV-4
3. Linking trip records . . . . . . . . . . . . . . . IV-4
4. Selecting trip records . . . . . . . . . . . . . . IV-8
5. Determining spatial separation between zones . . . IV-8
a. Preparing the network. . . . . . . . . . . . . . IV-8
b. Determining interzonal driving time. . . . . . . IV-9
c. Determining the traveltimes. . . . . . . . . . .IV-12
d. Determining intrazonal driving times . . . . . .IV-15
C. Phase Two.--Analysis of Basic Data. . . . . . . . . . .IV-15
1. Building a table of zone-to-zone movements . . . . .IV-15
2. Obtaining a trip length frequency distribution . . .IV-19
D. Phase Three.--Developing Traveltime Factors . . . . . .IV-19
1. Selecting initial traveltime factors . . . . . . . .IV-19
2. Calibration procedures to obtain final
traveltime factors . . . . . . . . . . . . . . . . .IV-21
E. Phase Four -- Topographical Barriers . . . . . . . . . .IV-32
F. Developing Zone-to-Zone Adjustment Factors . . . . . . .IV-34
CHAPTER V. TESTING THE GRAVITY MODEL
A. General . . . . . . . . . . . . . . . . . . . . . . . . .V-1
B. Statistical Tests. . . . . . . . . . . . . . . . . . . . .V-1
CHAPTER VI. OTHER CONSIDERATIONS
A. Converting the Gravity Model Results to Directional
Movements. . . . . . . . . . . . . . . . . . . . . . VI-1
B. Forecasting Future Travel Patterns using the
Gravity Model. . . . . . . . . . . . . . . . . . . . VI-2
APPENDIX. TABLE OF CONTENTS. . . . . . . . . . . . . . . . . . .A-i
I. COMPUTATIONAL METHODS. . . . . . . . . . . . . . . . . . .A-1
A. Introduction . . . . . . . . . . . . . . . . . . . . . . .A-1
B. Equipment. . . . . . . . . . . . . . . . . . . . . . . . .A-1
C. Operating System . . . . . . . . . . . . . . . . . . . . .A-2
iv
Contents Page
II. PROGRAM DESCRIPTIONS . . . . . . . . . . . . . . . . . . .A-3
A. IBM 7090/7094 Programs . . . . . . . . . . . . . . . . . .A-4
1. PR-113, Trip table or skimmed tree format program. . .A-4
2. PR-116, Punch and sum trip ends program . . . . . . .A-7
3. PR-120, General purpose program . . . . . . . . . . A-12
4. PR-124, Comparison program. . . . . . . . . . . . . A-18
5. PR-126, Zone-district compressor program. . . . . . A-23
6. PR-127, Trip table conversion program . . . . . . . A-27
7. PR-130, Skim trees program* . . . . . . . . . . . . A-29
8. PR-133, Build trip tables program . . . . . . . . . A-35
9. PR-134, Trip length distribution program. . . . . . A-44
10. PR-135, Gravity model program . . . . . . . . . . . A-48
11. PR-151, Factor trip table program . . . . . . . . . A-58
12. PR-183, Interzonal volumes summary programs . . . . A-62
B. IBM 1401/1410 Programs . . . . . . . . . . . . . . . . . A-65
1. 501, Edit program. . . . . . . . . . . . . . . . . . A-65
2. 502, Edit program. . . . . . . . . . . . . . . . . . A-65
3. 401, Trip linking program. . . . . . . . . . . . . . A-85
III. STANDARD FORMATS . . . . . . . . . . . . . . . . . . . . A-93
A. BELMN Submonitor Control Cards . . . . . . . . . . . . . A-93
B. Program Control Cards. . . . . . . . . . . . . . . . . . A-94
C. Binary Tape Formats. . . . . . . . . . . . . . . . . . . A-96
D. Trip Record Formats. . . . . . . . . . . . . . . . . . . A-97
IV. DETAILS OF BELMN OPERATION . . . . . . . . . . . . . . . A-99
V. REFERENCES . . . . . . . . . . . . . . . . . . . . . . .A-103
v
Chapter I
BACKGROUND
A. General Introduction
Federal, State, and municipal agencies concerned with making decisions
on when and where to construct new urban roads and streets, or to
improve existing ones, must consider many factors in reaching sound
decisions. Consequently, considerable time, money, and effort are
usually expended in the planning and design of such improvements. For
the most part, the planning work is carried on within the framework of
an urban transportation study.
Since the end of World War II urban transportation studies have been
conducted in an increasingly comprehensive manner. Significant
improvements in both basic study philosophy and analysis methodology
have greatly contributed to a better understanding of the urban
transportation problem. Urban traffic patterns now, and in the future,
are a function of:
1. The type and extent of the transportation facilities available in
an area;
2. The pattern of land use in an area, including the location and
intensity of use; and
3. The various social and economic characteristics of the population
of an urban area.
The transportation planning process utilizes these interrelationships to
provide quantitative information on the travel demands generated by
alternate land use patterns and transportation systems. Such
information can then be used to make decisions on when and where
improvements should be made in transportation networks, thus satisfying
the present and future travel demands and promoting desirable land
development patterns.
Analysis of many travel habit studies, particularly the home interview
origin-destination surveys, in relation to the use of land and the
various social and economic characteristics of trip makers, indicates
that zonal trip interchanges can be estimated, within reasonable limits
of accuracy, by mathematical formulas called "trip distribution models."
When these same characteristics for the future urban area can be
predicted, it is possible to compute a forecast of that area's trip
distribution patterns through mathematical model techniques.
I-1
The use of trip distribution models in transportation planning offers
certain advantages over other trip distribution forecasting techniques.
Earlier it was suggested that a basic aim of the transportation planning
process was to provide decision makers with quantitative information
about the consequences of their decisions concerning the type, location,
size, and timing of transportation improvements. Mathematical trip
distribution models provide a common base for simulating the travel
patterns expected to result from a variety of different highway or mass
transit systems. This allows public officials to estimate and judge, in
advance, the probable consequences in terms of travel patterns of a
variety of different transportation systems.
Although several different types of traffic models are now in existence
and currently being utilized in transportation studies around the
country, this volume is concerned solely with the gravity model. A
discussion of the theory and practical application of this traffic model
will be presented on subsequent pages. This discussion, however, should
not be interpreted to imply that the Bureau of Public Roads favors the
gravity model over other traffic models. In fact, the Urban Planning
Division of the Bureau of Public Roads is planning to prepare similar
volumes for other traffic models as well. A project conducted by the
Urban Planning Division to test, evaluate, and compare four major trip
distribution techniques has recently been completed (4).
B. Gravity Model Theory
To date, the most widely used trip distribution model has been the so-
called "gravity model." As the name implies, this model adapts the
gravitational concept, as advanced by Newton in 1686, to the problem of
distributing traffic throughout an urban area (5). The gravity model
has been the most widely used formula mainly because it is simple in
concept and because it has been well documented.
In essence, the gravity model says that trip interchange between zones
is directly proportional to the relative attraction of each of the zones
and inversely proportional to some function of the spatial separation
between zones. This function of spatial separation adjusts the relative
attraction of each zone for the ability, desire, or necessity of the
trip maker to overcome the spatial separation involved. Mathematically,
the gravity model is stated as follows:
Aj
-------
b
dij
Tij = Pi ___________________________________
A1 A2 An
----- + ----- +........... ------
b b b
di1 di2 din
I-2
Where: Tij = trips produced in zone i and attracted to zone j
Pi = trips produced by zone i
Aj = trips attracted by zone j
dij = spatial separation between zones i and j. This is
generally expressed as total traveltime (tij)
between zones i and j.
b = an empirically determined exponent which expresses the
average areawide effect of spatial separation between
zones on trip interchange.
C. Gravity Model Application
In applying a gravity model trip distribution formula to urban studies,
it is necessary to develop the parameters in the gravity model formula
for each urban area under study. Furthermore, these parameters are
developed for each of several different categories of trips. These
categories take into account the basic purpose for making trips and are
generally referred to as trip purpose categories. Past experience has
demonstrated that the exponent of traveltime is not constant for all
intervals of time. Thus it is necessary to work with a gravity model
formula which differs from that shown previously. This revised formula
is expressed as follows:
Pi Aj Fij Kij
Tij = -------------------
n
ä Aj Fij Kij
j=1
Where: Fij = empirically derived traveltime factor which
expresses the average areawide effect of spatial
separation on trip interchange between zones
which are tij apart. This factor approximates
1/tn where n would vary according to the
value of t, and where t is the traveltime
between zones.
Kij = a specific zone-to-zone adjustment factor to
allow for the incorporation of the effect on
travel patterns of defined social or economic
linkages not otherwise accounted for in the
gravity model formulation.
And where: Tij, Pi, and Aj are the same as previously described.
The use of a set of traveltine factors to express-the effect of spatial
separation on zonal trip interchange, rather than the traditional
inverse exponential function of time, simplifies the computational
requirements of the model. It also takes account of the fact that the
effect of the spatial separation on trip making generally increases in a
more complex manner than can be represented by the single exponent.
I-3
Chapter 11
HISTORY OF THE GRAVITY MODEL
A. Early Uses of the Gravity Theory
The theory of gravity was introduced by Issac Newton in 1686. New-ton
postulated that the gravitational force which acts between two bodies in
space was in direct proportion to the mass of the two bodies and in
inverse proportion to the square of the distance between the bodies.
It was not until the first half of the 19th Century that the theory of
gravity was applied to human interaction. At that time, H. C. Carey (6)
theorized "Gravitation is here, as everywhere, in the direct ratio of
the mass and the inverse of distance." Work by E. G. Ravenstein (7) in
1885 and later by E. C. Young (8) confirmed the belief that
gravitational function does apply to the migration of people from one
area to another.
A key effort in this field is associated with W. J. Reilly (9) in his
study of the retail trade areas of moderately sized American towns.
Reilly came to the conclusion that:
"Under normal conditions two cities draw retail trade from a
smaller intermediate city or town in direct proportion to some
power of the population of these two large cities and in an
inverse proportion to some power of the distance of each of the
cities from the smaller intermediate city."
This is an analogue of Newton's Law of Gravity. Further examples of the
use of the gravity function are available in the works of Zipf (10),
Cavanaugh (11), and Dodd (12).
B. Adaptation of the Gravity Model Theory to Travel
The early users of the gravity model in transportation planning applied
it to studies of intercity travel. In the 1920's for example, the
Swedish investigator Pallin used the gravity model with a distance
exponent of 2 to determine intercity traffic flaws. In 1954, J. D.
Carroll (13) used the gravity formula to help determine the area over
which urban centers have influence. Using intercity telephone messages
and intercity travel for some 21 cities in Michigan, Carroll concluded
that the exponent of distance should be about 2.8 instead of Pallin's
2.0.
II-1
Since that time, the distance factor in the gravity model formula has
been the subject of much debate. The work by both Pallin and Carroll
suggested that the effect of distance is not really uniform and its
relationship is not a simple inverse one, but one in which distance is
raised to some power other than unity. One of the underlying problems
in determining values for the exponent is the variation in the measure
used to express distance. If airline distance is used, one exponent
will result; if over-the-road distance or time is used, others will
result; and so on.
At about the same time, research by Alan Voorhees (5) (14) endeavored to
further quantify this exponential value. Based on origin-destination
survey data collected in Fort Wayne, Indiana, Voorhees found that the
exponential value of spatial separation varied by trip purpose.
Comparing the exponent for total travel between cities (about 2.5) with
that for intracity travel (about 1.5) reflects, to some extent, the
effect of using different measures to express the spatial separation
between the areas under consideration. Airline distance has generally
been used for intercity travels while over-the-road driving time has
been used for intracity travel. The variation between these two
exponents, however, may be explained in part by the fact that neither of
the traveltimes used took into account terminal time.1 In intercity
travel where most of the trips are relatively long, the effect of
omitting 5 or 6 minutes of terminal time is probably negligible. In
intracity travel, however, when the median traveltime is generally less
than 20 minutes, a 5- to 6-minute terminal time will have a considerable
effect.
In order to determine the effect of terminal time on the exponent of
distance, Hansen (15) studied the results of an analysis of travel
patterns in Baltimore, Maryland. His study showed that by adding 5 to 6
minutes of terminal time to interzonal driving time the exponent for
total trips came to about 2.5, the same as for intercity travel.
Further analysis of the Baltimore data by Hansen (15) also substantiated
the previous research concerning the variation of exponents by trip
purpose.
Hansen (16), in research using Washington, D.C., data, has also shown
that the exponent is not constant for all time increments. Figure 1
shows the variation he found. If the exponents had been constant, all
the curves would have been linear.
Besides these and other empirical studies (17 (18) (19) which have shown
the need for a variable exponent in the gravity model, there is also a
theoretical rationale behind this notion. This was demonstrated mathe-
matically by Tanner (20) in Great Britain. He showed that a constant
exponent cannot yield reasonable results for both short trips and long
trips unless the range between the longest and the shortest trip in the
area is small.
___________________________
1 Teminal time is the time which is added to the driving time to
account for the congestion in the zone at each end of a trip.
II-2
Click HERE for graphic.
Figure 1.--Traveltime factors for Washington, D. C., 1955.
II-3
Whitmore (21),in a rather detailed study of traveltime.factors, indica-
ted that variation in traveltime exponents between cities is due to
factors other than the measure of spatial separation. He found that
city size, population and car ownership help to explain the variation.
C. Analysis of Early Gravity Model Travel Studies
The work of the above researchers in applying the gravity model theory
to travel, particularly urban travel, has been substantial. This is not
to say that all the problems have been solved, nor that there exists a
perfect tool for estimating trip distribution patterns. This certainly
is not the case. However, this work was an excellent beginning of an
analytical approach that has become an invaluable tool for the
transportation planner.
An analysis of the results of this early research work indicates four
significant findings.
1. Spatial separation between zones appears to be best measured by
"over-the-road" driving time between zones, plus some measure of
terminal times in the zones at each end of the trip.
2. The exponent of traveltime differs by trip purpose. It appears to
vary roughly with the importance of the trip, generally decreasing as
the trip becomes more important. For example, work trips which appear
to be the most important, have a lower exponent than social-recreation
trips.
3. The exponent of traveltime is not constant for all intervals of
time within each trip purpose. This variation is most pronounced for
work trips. For most trip purposes the exponent generally increases as
the time interval increases.
4. The exponent of traveltime alone does not, when considered in
relationship to the use of land, completely explain the propensity for
travel between two points. Travel patterns can also be affected by
various social and economic linkages which to date have not been
completely identified or quantified. Hence, factors other than
traveltime factors must be taken into account. These secondary
adjustments are called "K" factors and will be discussed in detail in
chapter III.
II-4
Chapter III
PRESENT USE OF THE GRAVITY MODEL
A. Definition of Parameters
1. Trip production and trip attraction.--From the gravity model
formulation shown in chapter I, it can be seen that four separate
parameters are required before the trip interchanges (Tij) can be
computed. Two of the basic parameters, the number of trips "produced"
(Pi) and the number of trips "attracted" (Aj) by each traffic zone in
the study area$ are related to the use of j the land and to the
socioeconomic characteristics of the people who make trips.
The gravity model distributes trips from production zone to
attraction zone, while the other travel models in use distribute trips
from origin zone to destination zone. To demonstrate the production and
attraction definition, it is first necessary to class all trips as home
based or nonhome based. Home based trips always have one end at the
residence of the trip maker. Nonhome based trips have neither end at
the residence of the trip maker.
Home based trips are always produced by the zone of residence of the
trip maker whether the trip begins or ends in that zone. Home
based trips are always attracted at the nonresidential end of the trip.
Nonhome based trips are always produced by the zone of origin and
attracted by the zone of destination.
2. Spatial separation between zones -- As previously discussed, the
spatial separation between zones can be measured by one of several
parameters. To date, the most effective measure seems to be traveltime.
The total traveltime between zones is the sum of the minimum path
driving time between zones plus the terminal times at both ends of the
trip. Terminal times are added in order to allow for differences in
parking and walking times in these zones, as caused by differences in
congestion and parking facilities. This provides a more realistic
measure of the actual spatial separation (in time) between zones as it
is likely to influence automobile drivers in their decisions as to
places to work, shop, etc.
III-1
The minimum path driving time between each pair of zones is obtained
by the traffic assignment process. The traffic assignment process works
with data showing the distance and travel speed over major routes of the
transportation system. These data ire used in preference to the trip
times reported in the O-D home interview survey because people tend to
report traveltime to the nearest 15 minutes even when asked to specify
time to the nearest minute.
Terminal times on the other hand, can be obtained from data on
average walking distances, which are generally available from parking
surveys. They can also be estimated by personal judgment. A reasonable
estimate of the terminal time is better than omitting it completely.
Intrazonal driving times, the average driving times of those trips
that start and end within-the same zone, must also be estimated.
Terminal times are added to intrazonal driving tine to arrive at
intrazonal traveltime.
3. Traveltime factors -- Traveltime factor 1 (Fij) express the
effect that spatial separation exerts on trip interchange. They
indicate the impedance to interzonal travel due to spatial separation
between zones. In effect, these factors measure the probability of
tripmaking at each one-minute increment of traveltime.
To obtain traveltime factors for the present period, it is currently
necessary to go through a process of trial and adjustment. Today's
traveltime factors are usually assumed to remain the same into the
future. The validity of this assumption has never been definitely
proven, but evidence from studies of work trip travel patterns in
Baltimore (14) for the time period between 1926, 1946, and 1958,
indicates that there is some basis for making this assumption. In
addition Pyers and Bouchard (22) have shown that the traveltime factors
for Washington, D.C., remained constant from 1948 to 1955.
Whitmore (21), however, in his analysis of traveltime factors from
many cities suggests that traveltime factors may vary over time. This
research only utilized data for single points in time and this premise
must be verified. Whitmore suggests that the introduction of an
expressway system could have an effect on traveltime factors.
The Puget Sound Transportation Study has varied their base year
traveltime factors when making forecasts.2 This application had certain
unique aspects. For example, the level of service offered by the
transportation
___________________________
1 Traveltime factors are sometimes referred to as "Friction Factors"
or as "propensity factors." Figure 1 illustrates a set of traveltime
factors for six trip purposes utilized in Washington, D.C. (22).
2 A report is being prepared by the Puget Sound Transportation Study
staff to document the conditions and assumptions regarding their
forecast of traveltime factors.
III-2
system varied significantly from the base year to the forecast
conditions. CBD speeds reflecting heavy congestion on the arterial
streets in the base year plan were drastically improved with the
addition of a freeway with an assumed minimum speed of 45 miles per
hour. This large increase in system speeds allows trips to go much
farther in a fixed time. For example, at a speed of 15 miles per hour a
10-minute trip is a 2- 5-mile trip. At 45 miles per hour a 10-minute
trip is a 7.5-mile trip. In such situations it may be desirable to
develop travel cost factors (i.e., weigh in distance on the minimum time
path) rather than traveltime factors.
4. Zone-to-zone adjustment factors -- The remaining input to the
gravity model formula. reflects the effect on travel patterns of social
and economic characteristics of particular zones or portions of the
study area. These are represented by the zone-to-zone adjustment factor
(Kij ). These factors reflect the effects on travel patterns of social
and economic characteristics which are not otherwise accounted for in
the use of the model. If found to be necessary, they must be
quantitatively related to socio-economic characteristics of the
particular zones to which they apply. It is necessary to relate the
adjustment factors to characteristics of the zones so that they may be
forecast as a function of the socioeconomic conditions estimated for the
future land use plan. Although the gravity model provides for these
adjustments very few cities have found it necessary to use them.
B. Sample Problem
The application of the gravity model formula can be illustrated by the
following example. Work trips produced by the residents of one zone are
distributed within a simple four-zone study area. The problem can be
stated as follows:
One thousand work trips are produced by the residents of zone 1 each
day. It is desired to distribute these trips to zones 1, 2, 3, and 4.
The four possible attraction zones have the following characteristics;
Zone 1 has an intrazonal time of 1 minute and has 1,000 work trips
attracted to it from all zones in the study area.
Zone 2 is 14 minutes from zone 1 and has a total of 700 work trips
attracted to it from all zones in the study area.
Zone 3 is 16 minutes from zone 1 and has a total of 6,000 work trips
attracted to it from all zones in the study area.
Zone 4 is 20 minutes from zone 1 and has a total of 500 work trips
attracted to it from all zones in the study area.
Figure 2 illustrates this problem graphically.
III-3
Click HERE for graphic.
Figure 2 -- Hypothetical four-zone problem.
III-4
Using the gravity model formula and the traveltime factors from table 2,
the work trip distribution pattern for zone 1 is determined as shown in
table 1.
Table 1 shows that the 1,000 work trips produced by the residents of
zone 1 would be distributed as follows: 186 trips remaining in zone 1,
88 trips to zone 2,680 trips to zone 3, and 46 trips to zone 4.
Table 1 -- Tabulation for sample problem.
Friction factor
Zone Aj Terminal time Driving time tij Fij AjFij Tij
1 1,000 2 3 7 100 1,000 186
2 700 2 10 14 68 476 88
3 6,000 4 10 16 61 3,660 680
4 500 3 15 20 49 245 46
Note: Adjustment factors (Kij ) were not used in this sample
problem.
4
ä Ai Fij = 5,381
i=1
Table 2 -- Traveltime factors for sample problem
Traveltime Traveltime factor
minutes Fij
1.0 200
7.0 100
11.0 80
14.0 68
16.0 61
17.0 58
20.0 49
21.0 47
25.0 39
Click HERE for graphic.
Figure 3 -- Plot of traveltime factors for sample problem
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C. Data Needed to Determine Parameters
1. Origin-destination survey -- There should be available factual
data in sufficient detail and of the proper statistical stability to
provide reliable estimates of the gravity model parameters. In this
respect, the home interview survey yields the most complete and accurate
data for computing these parameters for use in the gravity model.
The desired data can best be collected through a comprehensive home-
interview survey using direct person-to-person interviews. Under
certain circumstances, however, satisfactory data might be obtained
through telephone interviews, pick up cards, or mailed questionnaires.
In all cases, sufficient controls must be exercised to assure that the
resulting travel data are complete and statistically unbiased. It is
also important that information pertaining to the following items be
obtained from each dwelling unit contacted:
a. Address of dwelling unit
b. Number of persons residing in dwelling unit
c. Number of cars owned by residents of dwelling unit
d. Occupation of household head
e. For each trip taken by each resident of the dwelling unit:
(1) Identification of person making trip
(2) Identification of trip
(3) Address of origin of trip
(4) Address of destination of trip
(5) Start time
(6) End time
(7) Purpose at origin end
(8) Purpose at destination end
(9) Mode of travel
Small O-D sample sizes ranging from 0.1 to 1 percent have been used
in several transportation studies. Those using such small samples for
calibrating the gravity model feel that they are adequate to develop a
total study area universe of trips. Others question such claims and
argue that this procedure should be used only to update the original
survey. Research has shown, however that a small sample yields very
little information on trip making by zone (23). Trip production and
trip attraction rates cannot be obtained on a zonal basis from this type
of survey. Consequently, some assumption has to be made as to how the
total universe of trip productions and attractions will distribute
themselves on a zonal basis. Procedures and assumptions which have been
used in various studies to synthesize zonal production and attraction
rates without a comprehensive O-D home interview survey have been
documented. However, at the present time, the small random sample
technique is considered useful only for broad and general studies or for
updates of comprehensive studies.
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Another type of home interview survey sometimes recommended is a form
of "clustered" survey where a rather small percentage of the total
dwelling units are interviewed. The dwelling units to be interviewed
are "clustered" into a few pre-selected zones which reflect ranges in
the factors which affect travel. Several zones are selected to reflect
ranges in such factors as residential density, car ownership rates,
income, family size, distance from the central business district, and
distance from the nearest large employment or commercial center.
Subsequently, a standard size sample (based on population) is
interviewed in the selected zones.
One of the principal reasons for conducting a "clustered" type sample
is to obtain data on trip generation rates at the home. Since the
selected zones exhibit a range in the factors which affect travel,
relating these characteristics to the trips generated by the residents
of each zone is claimed to yield relationships useful for estimating
future trip generation rates from the home. Research conducted using a
special "clustered" sample collection in Pittsburgh, Pennsylvania, found
that a significant drawback of conducting a "clustered" type home
interview survey was that zonal trip attraction rates in each zone could
not be established since a total universe of trips was not obtained
(24). So. from the standpoint of developing a gravity model even for
broad planning purposes, this type of survey has disadvantages.
Consequently, a home interview of a sample size as recommended in the
Bureau of Public Roads Manual of Procedures for Home Interview Traffic
Studies (25) is preferable.
In addition to a home interview survey of internal travels, an
external cordon survey (26) and a truck and taxi survey (27) should also
be included to complete the picture of travel in the urban area under
study.
2. Travel facilities inventory -- Besides sufficient reliable data on
travel patterns, information must also be available on the major travel
facilities in the area. The following data are usually tabulated for
major sections of the highway and transit facilities in the area:
a. Location
b. Physical dimensions
(1) Length
(2) Width
(3) Number of lanes
c. Average speed of travel in both peak and off-peak hours
d. Signalizations, parking requirements direction of travel and
other data for capacity calculations
e. Existing traffic volumes
The information is used in calculating the driving tine between zones.
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3. Other inventories -- Since this manual is concerned mainly with
the trip distribution aspects of the gravity model, data concerning
travel patterns and spatial separation between zones are all that are
generally required. However, since it is possible that zone-to-zone
adjustment factors may be required, information relative to
socioeconomic indicators may also be necessary. Data sufficient for the
trip generation analysis will generally be adequate for developing
socioeconomic adjustment factors.
In the remaining discussions it will be assumed that all the required
inventories have been taken and the data are available for use.
D. Initial Decisions to be Made
1. Vehicle trip or person trip model -- Once a transportation study
has decided on the basic type of trip distribution model to be used, in
this case the gravity model, there remain a great many choices as to the
manner in which this model is to be utilized to provide reasonable
estimates of travel patterns.
Perhaps the first question is whether the model should distribute
vehicle trips or total person trips. The answer is directly related to
both the objectives and needs of the study and to the size of the area
involved. The type of modal split analysis is usually the prime
determinant. In most studies a vehicle trip model is utilized. The
modal split is determined at the trip generation phase of the analysis
and the auto driver and transit passenger trips are distributed
separately via each mode.
In other studies, where a more extensive modal split analysis is
being made, total person trip distributions are necessary. The modal
split is then made separately for each zone-to-zone person trip
movement.
The complexity of the latter analysis can be demonstrated by
considering that the number of modal split determinations necessary is
equal to the square of the number of zones. In the former type of nodal
split analysis, only one modal split determination is made for each
zone.
2. Trip purpose classification -- A decision must also be made as to
how many and what trip purpose categories will be used in the study.
Gravity model trip distribution formulas have been developed using as
few as one trip purpose and as many as nine or more. There is no clear
agreement on this point and it is at least partially a function of the
scope and objectives of the study, as well as the size of the urban area
involved. As a general rule, it is desirable to take into consideration
the number of trips in each category, and the trip length
characteristics for each of the trip purpose categories and the ability
to forecast the categories separately. The amount of data preparation
tine, computer tine, and analysis time must also be considered.
Several studies in large urban areas have used the following trip
purpose categories in their gravity model with satisfactory results:
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a. Home based work -- those trips between a person's place of
residence and his place of employment for the purpose of work.
b. Home based shop -- those trips between a person's place of
residence and a commercial establishment for the purpose of shopping.
c. Home based social-recreation,those trips between a-person's
place of residence and places of cultural, social, and recreational
purposes.
d. Home based school -- those trips by students between the place
of residence and school for the purpose of attending classes.
e. Home based miscellaneous -- all other trips between a person's
place of residence and some form of land use for any other trip purpose.
f. Nonhome based -- any trip which has neither origin nor
destination at home regardless of its purpose.
g. Truck trips
h. Taxi trips
In some large areas where these eight purposes have been used, it has
been observed that the results could have been improved with further
stratification without causing additional difficulty in forecasting.
For example, in a study of travel patterns in Washington, D.C., it was
observed that the gravity model results could probably have been
improved if work trips had been further stratified to distinguish
between government and nongovernment workers. Some studies also
reported the need for further stratification of shopping trips to
distinguish between convenience shopping trips (trips to grocery stores,
etc.) and other shopping trips.
Most of the recent gravity model studies in small urban areas have
been using three trip purpose categories, home based work, home based
nonwork and nonhome based trips. Home based work trips are those
defined previously in category "a." Other home based trips are those
defined in categories 'lb" through "ell above. Categories defined as
'If" through "h" composed the nonhome based trip group. A study of
travel patterns in Sioux Falls, South Dakota (23), showed that the
differences in the accuracy obtained when using eight trip purposes as
compared with three purposes are insignificant in small areas.
Consequently, it appears that in large urban areas an eight purpose
model is desirable but in small urban areas (less than 100,000
population), a three purpose model may be sufficient.
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3. Treatment of external trips -- The treatment accorded to external
trips, that is, trips with one or both ends outside the cordon line,
presents the transportation planner with a choice. In some studies, the
external cordon stations have been considered as fictitious zones and
have been assumed to produce and attract trips in a manner similar to
the internal zones. Generally, it is undesirable to do this for the
following reasons:
a. Trips made by those persons living inside the cordon may
exhibit different trip length characteristics than those made by persons
who live outside the area.
b. External-to-external trips are associated with the study area
in question for only a small portion of their total journey and, there-
fore, exhibit distribution characteristics which have nothing at all to
do with the study area.
Consequently, it is generally desirable to treat the total universe
of trips as three distinct types:
a. Internal trips, those with both ends of trip within the cordon
area.
b. External trips, those with one end inside the cordon and one
external end.
c. Through trips, those with both ends outside the cordon.
For the first group of trips the gravity model can be used directly.
For the second group of trips the gravity model can also be used.
However, since the trip length characteristics of these trips are
generally different from those in the first group, a separate gravity
model analysis should be made. The external trips are normally
considered as being produced at the external stations and attracted at
the internal zones. For the third group of trips (through trips) a
growth factor technique such as the Fratar (28) procedure is
recommended.
III-10
Chapter IV
CALIBRATING THE GRAVITY MODEL
A. General
After all of the basic decisions have been made about the specific form
which the gravity model will take, it is necessary to develop each of
the parameters of the gravity model formula and to calculate the
estimated trip interchanges. The phases involved in calibrating a
gravity model trip distribution formula for an urban area, as well as
those concerned with testing the calibrated model, are shown in figure 4
on the next page.
Very briefly, these steps can be described as follows:
1. Phase one, depicted by the unshaded blocks, is concerned with
processing basic data on the area's travel patterns and transportation
facilities into a more usable form for analysis purposes.
a. For the travel pattern inventory, this involves editing,
sorting, and linking of the basic trip records. This can be done on an
IBM 1401 (16K) electronic computer.
b. For the transportation facility inventory this involves
building a network description on the IBM 7090 from records containing
information on the location and characteristics of major segments of the
network. Next, the minimum time paths between all zone pairs are
calculated.
2. Phase two, which is shown in the lightly shaded blocks, utilizes
the previously processed survey trip records to obtain complete tables
of trip movements for any desired combinations of trip purpose and
travel mode. From this, a record is also made of the number of trips
produced (P.) and attracted (Ai) by each zone. The resulting trip
tables are then i related to the minimum path traveltimes for all zones
(obtained in phase one) to obtain trip length frequency distributions.
3. Phase three is shown in the heavily shaded blocks. This phase is
concerned with the development of traveltime factors for each of the
gravity models to be calibrated. Trip productions (Pi) and attractions
(Aj) by zone, together with the minimum path traveltimes between zones
and j an assumed set of traveltime factors (Fij ) are inserted into the
gravity model formula
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Click HERE for graphic.
Figure 4 -- Gravity model calibration and testing process.
IV-2
and the trip interchanges (Tij) are calculated. The estimated trip
length frequency distributions are then manually compared with the
appropriate frequency distributions from the surveyed trips, and the
assumed traveltime factors are revised accordingly. A new set of trip
interchanges is calculated and the process of trial and adjustment is
continued until the two trip length distributions are in approximate
agreement.
4. Phase four, shown by the crosshatched blocks) is concerned with
the development of adjustment factors which may be required to properly
calibrate the models to accurately simulate existing travel patterns.
Estimated interchanges are compared with surveyed interchanges, and
revisions are made, if required, as follows:
a. Geographical bias, as caused by topographical barriers such as
rivers, is eliminated by adjustments to the minimum path traveltimes.
b. Geographical bias, as caused by defined social or economic
linkages, is eliminated by zone-to-zone adjustment factors (Kij).
5. Phase five, which is indicated by the dotted blocks, is concerned
with the testing of the calibrated gravity models to be certain that
they accurately simulate existing travel patterns.
B. Phase One--Preparing Basic Data
1. Editing trip records -- In any analysis that uses the survey data,
it is always necessary to edit the information to insure that the items
of data have been correctly coded and punched. This is particularly
important where a great deal of time and money is to be expended in the
processing and analysis of these data. If the source data are not
rigidly controlled and edited, it is possible that much useless analysis
will result. This is particularly true when using the system of
programs described in this volume as some of the IBM 7090 programs have
internal controls which reject trip records when they contain certain
unacceptable information. To avoid these costly problems and to permit
smooth processing in later phases of model development) all trip records
should be edited using an appropriate edit program. An IBM 1401 edit
program is described in detail in the appendix. This program will edit
up to 50 data fields for characters which may be unacceptable to the
program user. It can also transfer these fields into any format desired
for use in later programs. (The program which "links" trip records
requires these records to be in a specified format.)
Input to the IBM 1401 edit routine consists of the home interview
trip records (cards) in any format. Output consists of the edited and
reformatted records on tape, an on-line printout of records which
contain unacceptable characters with an error message indicating the
position of the unacceptable characters. Each of the trip records that
contained unacceptable characters is punched on a new card. These
unacceptable records are then corrected manually and resubmitted to the
edit routine. When the corrected
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cards have successfully passed the edit routine, they go directly on
tape and may be merged with the previously edited and reformatted
records. These records are now acceptable and are in the proper format
for the subsequent computer programs discussed below.
2. Sorting trip records -- It is necessary for the linking program to
have the trip records in a sample number, person number, and trip number
sort. The sample number is the primary sort, person number is the
secondary sort, and trip number the tertiary sort. This sort is
necessary to sequence the trip pattern of each trip maker in the order
in which the trips were made on a particular day. This is required to
"link" trip records if linking is necessary. Sort programs are
available in most program libraries. Output from the sort program
consists of the edited trip records on tape and in low to high sort by
sample number, person number, and trip number.
3. Linking trip records -- Figure 4 shows that the next step is to
"link" the internal survey trip records. Because of the standard
origindestination survey definition of a trip many journeys made by a
trip maker have to be represented by two or more trip records even
though only one journey is involved. In an origin-destination survey,
one trip ends and another begins every time a person changes his mode of
travel, or an autodriver stops to serve a passenger, or when the trip
maker reaches his ultimate destination. There are two types of trips
which require linking, change mode and serve passenger trips. If each
of these trips are analyzed separately the relationships between the
actual starting point, the ultimate destination, and the purpose of trip
would be lost. It also would be difficult to relate the type and
intensity of trip making to the type and intensity of the land use.
Consequently, it is usually desirable to combine or "link" those trips
with a "purpose to" or "purpose from" of either "change mode of travel"
or "serve passenger" so that the relationship between the purpose and
the ultimate destination of the trip is preserved.
Some examples of those trips which might be combined or "linked" are
shown in figures 5 and 6.
Figure 5 illustrates an auto driver driving his car from home to a
fringe area parking lot, where he boards a bus and rides to work. In an
origin-destination survey this journey would be recorded as two separate
trips. The first trip would be recorded as an "auto driver" trip from
"home" to "change mode of travel." The second trip would be recorded as
a "transit passenger" trip from "change mode of travel" to "Work."
Since the ultimate purpose of this journey was to get from home to
work, it is desirable, for analytical purposes, to "link" these two trip
records into one which covers the entire journey. In this particular
case the "linked" trip would become a home-to-work trip since this was
the ultimate purpose of the trip. The mode of travel would be bus, the
assumption being that if satisfactory bus service had been available at
the trip makers home, he would have used it. Mode of travel is assigned
according to a priority listing which normally ranks transit over the
automobile. Regardless of the phase of the journey, that mode used
which is of highest priority on the list is assigned to the "linked"
trip.
IV-4
Click HERE for graphic.
IV-5
Figure 6 illustrates a similar situation. A person drives his car
from home to the home of a co-worker and they both proceed to work. In
this case, the auto driver's journey would be recorded as two separate
autodriver trips, the first one from "home" to "serve passenger" and the
second one from "serve passenger" to "work." Since the auto driver's
ultimate purpose was to get to work, it is again desirable for analysis
purposes to "link" these two trip records into one which covers the
entire journey. In this case, the auto driver's "linked" trip would
become a home-to-work trip by automobile based on the same reasoning as
for the previous example.
There are two additional cases in the recording of trips which are
handled by utilizing the program options. The first of these types
occurs when a wife drives her husband to work and then returns home.
These two trips would be coded as home to serve passenger and serve
passenger to home. The "linked" card for these trips would show an
invalid home-to-home trip for the wife, provided the normal logic was
followed. Instead, the serve passenger code for each trip is changed to
personal business. This procedure is outlined in the program
description. The normal process is then followed.
The second type concerns those trips which have only one trip record
in the journey. For example, a trip by a person who changes mode of
travel at an airport or railroad station and leaves the city and does
not return that day, would be recorded in an origin-destination survey
as only one trip with a purpose to of "change mode of travel." The one
trip record is used as the "linked" trip record after changing "change
mode of travel" code to "personal business" code.
Trip linking is not necessary in all studies. For example, in urban
areas where "change model' trips may be small in number because of the
lack of transit facilities and where "serve passenger" trips may also be
small in number because of the absence of car pooling, trip linking may
not be necessary. For analysis purposes trips of this type can often be
combined with the other trip purposes with no significant loss in
accuracy. However, in larger urban areas, it is generally desirable to
link trips.
The trip linking process may be accomplished on the IBM 1401 computer
using the trip linking program described in the appendix. Some typical
information taken from each record to be linked is shown in table 3. The
final "linked" trip record is written on tape with those records that
did not require linking.
The trip linking process causes a decrease in both the absolute
number of "trips" taking place and in the total vehicle (or person)
miles of travel in the urban area. The loss in vehicle miles results
from the more direct routing of some linked trips. The exact amount of
the decrease in the number of trips can be determined by simple
subtraction of the number of trips in the "linked" records from those in
the "unlinked" records. The slight decrease in vehicle-miles of travel
can be obtained by assigning both the "linked" and the "unlinked" trip
records to a comprehensive highway network and subtracting the two
resulting vehicle-miles of travel. From analysis of past studies, it
appears that the decrease in trips and in vehicle-miles of travel is of
little consequence.
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Table 3--Location of information for linked trip record
Column Information Instructions
1 Card number (1/)
2 County (1/)
3- 4 Tract (1/)
5- 7 Sample number (1/)
8-11 Subzone of residence (1/)
12-14 Blank (1/)
15 Ring (1/)
16-17 Month (1/)
18 Week in the month (1/)
19 Day in the week (1/)
20 Length of residence (1/)
21 Previous address (1/)
22 Reason for move (1/)
23-24 Occupation and industry (1/)
25 Interviewed (1/)
26-27 Person number (1/)
28-29 Trip number Last card
30 Race and sex (1/)
31-34 Origin subzone First card
35 Blank (1/)
36-39 Destination subzone Last card
40 Mode of travel Mode prior
3-1-2-4-5(2/)
41-43 Starting tine First card
44-46 Arrival time Last card
47 Purpose "From" First card
48 Purpose "To" Last card
49 Persons in car If mode 1 in col. 40,
use last card, if not
leave blank.
50 Parking If mode 1 in col.40,
use last card, if
not leave blank.
52-62 Route of travel Leave blank
63 Cars owned (1/)
64-65 Total persons (1/)
66-67 Total trips (1/)
68-77 Blank (1/)
78-80 Factor (tenths) (1/)
___________________________
(1/) Information is the same in both cards, and can be taken from
either first or last card.
(2/) Use the highest priority mode code appearing in any of the
trips in linking sequence.
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4. Selecting trip records -- As shown in figure 4, the next step in
the calibration of the gravity model is to select the basic trip records
for model calibration.
All the information collected in the travel pattern inventory is
assumed to have been processed through the editing and, in the case of
the internal survey, the linking phase.
The information in the detail trip cards, from each of the
inventories (i.e., home interview, external cordon, and truck and taxi),
should be compatible. Depending on the decisions reached on the items
discussed in the previous chapter, certain of these detail trip records
must now be selected for further processing, as it is these records
which will be used in calibrating the gravity models.
For example, if it has been decided to calibrate a gravity model for
vehicle trips during the average 24-hour day, then the following trip
types would be used:
a. Internal vehicle trips, those with both ends of trip within the
cordon area;
b. External vehicle trips, those with one end inside the cordon and
one end external;
c. Through trips, those with both ends outside the cordon.
The type (a) trips would be selected from the home interview survey
and truck and taxi survey detail trip cards. The type (b) trips would
be selected from the external survey records. The remaining external
survey trips would constitute the type (c) trips.
The type (a) and (b) trips are normally utilized to calibrate
internal and external gravity models. A single purpose external model
should be sufficient for most urban areas; however, if there is one type
of dominant external movement such as travel to a military installation
just outside the cordon, it may be desirable to isolate these trips into
a separate trip category and to calibrate a separate model.
The type (c) trips are typically expanded using the Fratar growth
factor technique. An IBM 7090 program is available for this purpose in
the Bureau of Public Roads computer program battery.
5. Determining spatial separation between zones -- This subject,
which will be discussed only briefly in this volume, is treated fully in
the Traffic Assignment Manual (1).
a. Preparing the network -- A map is prepared which describes the
components of the transportation system. The beginning and ending of
each of the significant elements of the system is defined, along with
the type of facility, its length, and its operating characteristics.
IV-8
To uniquely define each section of the transportation system, a
numbering system is used that also designates type of facility.
Figure 7 shows a small urban area which can be used to illustrate the
mechanics of this process. The study area has been zoned and the street
classification is shown. The numbering system to be used to code the
network for assignment must be within the size limitations imposed by
the computer programs. For purposes of this discussion the limitations
imposed by the traffic assignment programs (1), currently being used by
the Bureau of Public Roads, will be followed. These programs will
handle a maximum of 3,999 nodes and centroids, and approximately 750 of
these can be zone centroids when using the gravity model. More
centroids can be accommodated if fewer than six trip purposes are
specified for a given computer run.
Figure 8 shows a more schematic illustration of the area involved
including the allocation of node numbers. The following numbering
system has been used:
(1) Zone centroids and external stations 001 to 50
(2) Arterial street nodes 70 to 400
This numbering system allows for the incorporation of additional nodes
which may be needed in defining the future transportation system for the
area.
In the traffic assignment programs the zone centroids and external
stations must be numbered in an unbroken sequence beginning with 001.
In most cases the numbers used during the field surveys are not in
sequence and must be converted. External stations must be placed at the
end of the sequence. Since the urban area under consideration has 50
zones and stations, only the numbers between 1 and 50 have been used.
These have been indicated in figure 8 by dots.
With the zone centroids and external stations identified, it is
necessary to number each highway intersection to identify the sections
between them. The numbers used in this identification should be within
the indicated ranges, depending on whether freeways or arterial streets
are involved.
Once all intersections in the urban area that are on the coded system
have been identified, it is necessary to code the distance and speed of
each section. The distances and the travel speeds are determined from
an analysis of data collected in the travel facility inventory to
provide the operating characteristics of each section. All the data
necessary for the computer to calculate zone-to-zone driving times are
now available.
b. Determining interzonal driving time -- The build and update
network description program examines the transport ation network data
for several standard errors 1. In addition, this program processes the
transportation network data for use in later programs. The print link
data program prints out a description of the network for use by the
analyst in correcting any errors in the network.
___________________________
1 See Traffic Assignment Manual (1) for detailed descriptions of
these programs.
IV-9
Click HERE for graphic.
Figure 7 -- Sample street classification and base map.
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Click HERE for graphic.
Figure 8 -- Sample network map.
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After the network has been corrected, minimum time paths (driving
times) from selected centroids to all other nodes are determined. The
build trees and format trees programs compute and print trees as aids to
checking the reasonableness of the network description. The "trees"
show minimum time paths and times of travel from a given zone to all
nodes in the highway network. The results can be plotted directly on a
map, as illustrated in figure-9, for checking.
Once the network is verified as adequately simulating the existing
system, all minimum path driving times are computed using the build
trees program. For use with the gravity model the trees are reduced,
("skimmed") to show only the driving times between zone centroids.
Table 4 is a printout from a formatted skim tree.
c. Determining the traveltimes -- Spatial separation between zones
appears to be more realistically approximated by traveltimes than by
driving times. The zone-to-zone traveltime is the sum of the over-the-
road driving time between zones and the terminal times within the origin
and destination zones. Consequently, it is necessary to develop a
measure of terminal time for each zone in the study area to be combined
with the information on driving time in determining spatial separation
between zones.
Terminal times may result from the following conditions:
(1) The time spent in looking for a parking place at the
nonhome end of a trip.
(2) The time spent in walking from a parking place to the
actual destination of a trip, be it an office, store, recreation
facility, or home.
(3) The time spent in walking from a trip origin, be it
the home, an office or other such origin, to the parking place.
(4) The time spent in getting from the parking place to
the street system at the origin end of the trip.
There are no absolute rules for estimating terminal times. Several
methods have been employed in various transportation studies, including
(1) the subjective allocation of a terminal time to each zone based on a
knowledge of the study area or upon data derived from studies such as a
parking survey, (2) relating the values of terminal time to the distance
from the CBD, (3) the use of an index that is a relative measure of
congestion conditions in a zone.
One recent study employed a so-called subjective method in allocating
terminal times to each zone for a small urban area (23). From the
results of a central business district parking survey, it was observed
that in the downtown area, an average of two minutes was spent in
walking from
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Click HERE for graphic.
Figure 9. Minimum path tree with isochronal contours.
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Table 4 -- Output of IBM 7090 Skim Trees Format Program
Sample output Sioux Falls, South Dakota System 56-1
Zone-to-Zone Driving time -- In minutes
Zone 1 to all other zones
Zone 0 1 2 3 4 5 6 7 8 9
00 3 1 3 2 1 2 1 4
10 4 5 8 7 6 7 9 10 9 4
20 5 5 7 8 8 11 9 11 12 4
30 5 7 7 8 9 8 9 9 12 3
40 2 3 4 5 6 7 8 8 6 4
50 4 4 7 7 8 4 5 6 9 7
60 9 11 5 6 8 9 3 5 7 5
70 7 8 9 7 8 8 8 9 9 11
80 7 6 6 8 9
IV-14
parking space to the store or office of ultimate destination.
Furthermore, it was estimated that an average of three minutes was spent
in cruising for a parking space. Consequently, for all zones in the
central business district, a terminal time of five minutes was used; for
residential zones, a terminal time of one minute was used; for zones
with moderate amounts of commercial activity, intermediate values of
terminal time were used.
It is next necessary to incorporate the calculated terminal times
into the trees to change the driving time to traveltime. This is accom-
plished by using the skim and update trees program (see the program
description in the appendix). The terminal times are specified through
the use of terminal time cards. This program adds the terminal time for
the respective zones to the skim trees, thereby producing a series of
binary records containing the traveltimes between each pair of zone
centroids. Table 4 illustrates the type of output which is obtained by
formatting the skim trees (PR-113).
Another method that has been utilized to incorporate the terminal
times into the analysis is to modify the coded highway network. Using
this procedure terminal times are added to "dummy" links which connect
the centroid to the highway network. (See page III-27 of the Traffic
Assignment Manual.)(1)
d. Determining intrazonal driving times -- It is noted by the
lightly shaded block in table 4 that the procedures do not yield any
measure of time for trips that do not leave a particular zone. This
time is called intrazonal driving time and must be derived separately.
One method of arriving at an estimate of intrazonal driving time is to
analyze the driving times to adjacent zones. Figure 10 illustrates this
procedure. The average of the driving times from the centroid of zone
15 to the adjoining zone centroids is 3.6 minutes.
The intrazonal driving time is taken as one-half of this average
driving time, or 1.8 minutes. The rounded values would then be
incorporated into the skim trees by using the update skim trees program
described in the
appendix.
C. Phase Two -- Analysis of Basic Data
1. Building a table of zone-to-zone movements -- Figure 4 shows that
a key step in the analysis of the basic trip data is the determination
of zone-to-zone movements for each of the several trip purposes. The
trip table builder program performs this function through the following
four operations:
a. Converts survey zone numbers to zone centroid numbers.
b. Determination of the zone of production and the zone of
attraction for each trip record.
c. Classification of each trip record into one of several trip
purposes.
IV-15
Click HERE for graphic.
Figure 10 -- Determination of intrazonal driving time.
IV-16
d. Determination of the number of trips between each zone of
production and every zone of attraction for the several trip purposes.
e. Accumulation of the number of trips produced and attracted by
each zone in the study area for each trip purpose.
The first two operations process and identify data for further
analysis in the remaining operations. The second two operations provide
the necessary information for many of the subsequent analyses in the
gravity model calibration and testing process. The trip interchanges,
for example, will eventually be combined with the minimum path
traveltimes to obtain a oneminute frequency distribution of trip
occurrence for each trip category as. shown in figure 11.
Click HERE for graphic.
Figure 11 -- Trip length frequency distribution for total trips, Sioux
Falls, S.D.
The number of trips produced and the number of trips attracted by
each zone in the study area are two of the necessary inputs to the
gravity model formula. These values are used throughout the entire
calibration process. In addition, these data are used with land use and
socioeconomic data to develop a basis for determining future zonal trip
production and trip attraction values.
IV-17
Regression analysis can be employed to determine a mathematical
equation which expresses the relationship between a dependent variable
(zonal trip production or trip attraction by any desired trip purpose or
travel model category) and one or more independent variables such as car
ownership, residential density, employment, or the type and intensity of
specific kinds of land uses.
The trip table builder examines each trip record to determine the
zone of production and a zone of attraction for each trip. All urban
trips can be divided into two broad basic categories, home based and
nonhome based. Home based trips must have either their origin or their
destination at the residence. All those trips which have neither their
origin nor their destination at the home are designated as nonhome based
trips.
For home based trips, the zone of production is always the zone of
residence. Since either the origin or the destination of the trip can
be at the home, each record is examined to determine whether the zone of
residence is the same as the zone of origin or the zone of destination.
Whichever one of these two zones is the same as the zone of residence,
it becomes the zone of production. The remaining zone is designated as
the zone of attraction.
All nonhome based trips are considered as being -produced by the
zone of origin of the trip. Consequently, for nonhome based trips the
zone of production is always the zone-of origin and zone of attraction
is always the zone of destination.
At the same time the trip table builder program determines the
zone of production and the zone of attraction, it also classifies each
trip record into specified categories of trip purpose or travel model
classifications. A general trip purpose code is assigned to each trip
record. Essentially, the program examines each trip record for the
"purpose to" and the "purpose from" and assigns the appropriate general
purpose code. Home based trips are assigned a purpose on the basis of
the purpose at the nonhome end. Trips with neither a "purpose to" nor
11purpo se from" of "home" are assigned the general purpose nonhome
based. For example, a trip record with the code for home in the
"purpose to" column and work in the purpose from" column would be
assigned the general purpose code for home based work trips. If a trip
record has the code for work in the "purpose from" column and the code
for shop in the "purpose to" column, it would be assigned the general
purpose code for nonhome based trips because neither end of the trip was
at home. In a similar manner, trip records can be classified by travel
mode or other desired categories.
When these two preliminary steps have been completed, the program
accumulates the movements between each zone of production and every zone
of attraction according to the desired trip purpose. This program also
accumulates all the trips produced and trips attracted by each traffic
zone according to these same purposes.
IV-18
Input to the trip table builder program consists of the edited and
linked trip records. Specified details of input sorts for home based
and nonhome based trips are contained in the program writeup.
The output from the trip table builder is in two parts. First, a
printed summary of zonal trip production and trip attraction values for
each desired trip purpose and travel model category is obtained. An
illustration of this output is shown in table 5. Trip productions in
each zone can be obtained by adding the "OUTS" to the "INTRAS." Trip
attractions in each zone can be obtained by adding the "INS" to the
"INTRAS." This information will then be used as an input to gravity
model calculations.
Second, a binary table of zonal trip interchange (production and
attraction) is obtained for each trip purpose. If desired, a printed
format (similar to table 4) of these binary trip interchanges can be
printed out for visual inspection. This operation is accomplished by
the format trip tables or skim trees program.
A new program (punch and sum trip ends) has recently been written
to eliminate the computations required in using the BCD output of the
trip table builder program. This new program prepares printed tables of
trip productions and trip attractions and also zonal parameter cards for
input to the gravity model program.
2. Obtaining a trip length frequency distribution -- The next step in
the gravity model calibration process is to obtain a trip length
frequency distribution by one-minute traveltime increments, for each
trip purpose being analyzed. The table of zone-to-zone movements for
each trip purpose and the updated skim trees are used as input to the
trip length frequency distribution program.
This program works as follows: By accumulating the number of trips
between each pair of zones according to the traveltime between the
zones, and repeating this process for all possible zone pairs, the
number and percentage of total trips in each traveltime increment is
obtained.
The input data for each run of the program are the updated skim trees
and the trip table for the desired trip purpose or travel mode category.
The output is a listing of the number and percent of trips for each trip
purpose occurring at each one minute increment of traveltime. The use
of this program is described in the appendix.
D. Phase Three -- Developing Traveltime Factors
1. Selecting initial traveltime factors -- At the present time, a
specific mathematical equation or function which can adequately express
the effect of spatial separation on zonal trip interchange is not
available. A single exponential function of traveltime is known (see
chapter II) to be inadequate. Consequently, it is necessary to go
through a trial and adjustment (calibration) procedure, to fit the model
to a particular urban travel situation. The traveltime factors
developed in this manner are an empirical measure of the relationship of
spatial separation and travel.
IV-19
Table 5 -- Summary of trip ends, sample printout from the trip table
builder program
TRIP END SUMMARY G M WORK TRIPS - SUMMARY OF TRIP ENDS - PAGE
(1) (2) (3) (4) (5) (6) (7)
TOTAL TOTAL TOTAL
ZONE INS CUTS INTRAS INS & OUTS TRIPS TRIP ENDS
(2) & (3) (4) & (5) (4) & (6)
1 2,033 17 2 2,050 2,052 29054
2 680 0 c 680 680 680
3 1,792 c c 1,792 1,792 1,792
4 916 113 7 1,029 1,036 1,043
5 19124 85 6 1,209 1,215 1,221
6 1,097 19 1 1,116 1,117 1,118
7 882 18 1 900 901 902
8 16 1 c 16 16 16
9 290 303 7 593 600 607
10 61 666 3 727 730 733
11 486 438 22 924 946 968
12 262 707 22 969 991 1,013
13 3C7 370 12 677 689 701
14 156 576 9 732 741 750
15 45 717 4 762 766 770
16 47 353 2 400 402 404
17 47 0 c 47 47 47
18 76 2C9 2 285 287 289
19 138 407 4 545 549 553
20 64 659 3 723 726 729
" " " " " " "
81 0 0 0 0 0 0
82 0 0 0 0 0 0
83 0 0 0 0 0 0
84 0 0 0 0 0 0
----- ----- ------- ------ ----- ----- -----
TOTAL 24,631 24,631 530 49,262 49,792 50,322
IV-20
The initial set of traveltime factors for each trip purpose can be
determined in at least two ways. First, one can assume that each
traveltime factor has a value of one, or, in other words, that
traveltime has no effect on trip interchange. It is known that this is
not the case, but this method allows you to initiate the calibration
procedures. The second and most expedient method of beginning the
calibration process is to use a set of traveltime factors taken from a
city of comparable size and use these to calculate a gravity model
distribution of trip interchanges.
The most preferable method for determining traveltime factors is the
second method as it usually requires fewer calibrations.
See tables 6 and 7 for examples of traveltime factors used in actual
gravity model calibrations.
2. Calibration procedures to obtain final traveltime factors -- With
the initial set of traveltime factors developed for each trip purpose,
it is now possible to calculate trip interchanges using the gravity
model program. Input to the gravity model program consists of the
following items:
a. Zonal trip production and trip attraction values by purpose as
obtained from the trip table builder program,
b. Minimum path traveltimes for all zones (including intrazonal
traveltimes) as obtained from the skim trees program. These data
generally remain the same for all trip purposes but may change for
different travel models.
c. Initial traveltime factors for each one-minute increment of
traveltime.
The output from this program consists of the following items for each
trip purpose:
a. A table of zone-to-zone movements as estimated by the gravity
model formula. This table is in binary form in a format that is
identical to the binary trip table obtained from the survey data using
the trip table builder program.
b. A trip length frequency distribution, by one-minute traveltime
increments of trip interchanges estimated by the gravity model formula.
These distributions contain intrazonal trips. A sample of this output
is shown in table 8.
c. A table of accessibility indexes (which is the denominator of
the gravity model formula) for each zone. This accessibility value, a
byproduct of the calibration, is often used in connection with land use
forecasting techniques and in certain modal split procedures. This
output is a program option and may be suppressed if desired.
IV-21
Table 6 -- Sioux Falls traveltime factors
Traveltime Home based Work Home based Nonwork Nonhome based
1 275 335 390
2 255 325 380
3 240 305 350
4 220 280 310
5 205 245 250
6 180 205 205
7 160 170 165
8 138 140 130
9 120 115 105
10 102 94 84
11 88 76 69
12 75 62 57
13 64 50 47
14 55 40 38
15 45 32 31
16 36 26 25
17 28 22 20
18 18 18 13
19 9 15 8
20 2 13 3
IV-22
Table 7-Traveltime factors used for New Orleans, Louisiana
Minutes Purposes
Home to Home to Home to Home to Home to
Traveltime Work Shop Soc.-Rec. School Other NHB
1 1,450 7,200 7,800 4,300 6,800 5,100
2 1,150 7,000 1,150 5,600 5,100 3,400
3 740 4,600 2,500 1,500 3,400 1,700
4 540 2,800 1,390 840 1,700 950
5 430 1,300 840 550 880 530
6 345 700 650 390 530 330
7 285 420 400 290 340 220
8 240 250 305 230 237 150
9 198 170 240 190 168 110
10 170 120 190 155 123 81
11 149 82 159 130 92 63
12 126 61 130 110 72 51
13 110 46 110 94 58 40
14 97 36 91 80 48 33
15 86 27 80 74 38 27
16 77 23 70 64 32 23
17 69 18 60 57 27 20
18 62 15 54 50 23 17
19 56 12 48 46 20 15
20 50 10 42 43 18 13
21 45 9 39 39 15 11
22 42 8 35 35 13 10
23 38 7 32 33 12 9
24 35 6 29 30 10 8
25 32 5 26 28 9 7
26 29 4 24 25 8 6
27 27 4 23 24 7 6
28 25 3 21 22 7 6
29 23 3 20 21 6 5
30 21 3 18 20 6 5
31 19 3 17 19 5 4
32 18 2 16 17 5 4
33 17 1 15 17 4 4
34 16 14 16 4 3
35 15 13 15 4 3
36 14 13 14 4 3
37 13 12 13 3 3
38 12 12 12 3 2
39 11 11 11 3 2
40 10 10 10 3 2
42 9 9 9 2 2
43 8 8 7 2 1
45 7 8 5 1 1
47 6 7 3
50 5 6 2
52 4 6 1
56 3 5
62 2 4
71 1 3
73 2
78 1
IV-23
Table 8. -- Output of gravity model program, trip length
distribution, work trips
SIOUX FALLS NO 2 CARD INT-INT TRIP LENGTH FREQUENCY W/INTRA AND TERMS 1
TRIP LENGTH DISTRIBUTION PURPOSE NO. 1 PAGE 1
TRIP LENGTH PERCENT ACCUMULATED
MINUTES TRIPS OF TOTAL PERCENTAGE
0 0 0.000 0.000
1 0 0.000 0.000
2 0 0.000 0.000
3 380 1.508 1.508
4 372 1.477 2.985
5 889 3.529 6.514
6 19752 6.954 13.468
7 2,295 9.110 22.578
a 39728 14.798 37.376
9 39371 13.381 50.757
10 39334 13.234 63.991
11 3,225 12.801 76.792
12 19944 7.716 84.508
13 11,771 7.030 91.538
14 19022 4.057 95.595
15 412 1.635 97.230
16 256 1.016 98.246
17 442 1.754 100.000
TOTAL TRIPS FOR THIS PURPOSE 25,193
TOTAL PERSON HOURS OF TRAVEL 4,017
AVERAGE TRIP LENGTH, THIS PURPOSE 9.569 MINUTES
IV-24
d. A table of comparisons between the trips attracted
n
(ä T )
i=1 ij
to each zone by the gravity model and the trips
attracted (Aj) to each zone as input on the zonal parameter cards.
This table shows the numerical differences and the percentage
differences between the two values for each zone, a sample of this
format is shown in table 9.
The operation of the gravity model program is as follows: Zonal trip
interchanges are first calculated using the previously described input
data. Trips attracted to each zone in the study area are then compared
with those trips attracted to each zone as given by the trip table
builder program. After making this comparison, the program, at the
option of the user, will automatically adjust (iterate) each zonal trip
attraction factor by the ratio of the O-D trip attraction factor to the
gravity model results. (A review of the gravity model formula will show
that there is no assurance inherent in the formula that these two
attraction figures will be equal on a zonal basis.) The program will
then calculate an entirely new set of trip interchanges based on the
adjusted attractions.
During the initial calibration runs or until the trip length
frequency curves are in fairly close agreement it is not necessary to
specify more than one iteration. Some analysts prefer to specify two
iterations throughout the calibration process so that the effect, if
any, of the adjusted attractions on the trip length frequency can be
ascertained. In either instance, the traveltime factor calibration
should utilize the trip length frequency from the first iteration.
The gravity model program also has an option which allows the binary
output (trip tables) to be suppressed. This reduces the running time on
the computer by about 30 percent. It is recommended that this option be
employed until the gravity model trip distributions approach the O-D
trip distributions.
The trip length frequency distributions are the outputs most directly
used at this point. Table 8 illustrates the format of this output. In
addition to these data, the person hours of travel are also calculated.
The percentages of total trips, for each trip purpose are plotted on
rectangular coordinate paper along with the O-D trip length frequency
for each trip purpose. Figure 12 shows the estimated and the survey
trip length frequency curves for one purpose. Also shown in figure 12
are the person hours of travel and the average trip length. This
information is sufficient to begin the trial and adjustment procedure to
determine the "best" set of traveltime factors for each trip purpose.
Since the gravity model uses data directly from the field surveys to
express all parameters except the traveltime factors, any difference
between the two trip length frequency curves are due principally to the
initial values of the traveltime factors. Comparisons between the
actual and the-estimated trip length frequency curves indicate the
degree to which the traveltime factors were correctly chosen.
IV-25
Table 9 -- Output of gravity model program, comparison of trips
attracted to each zone by the gravity model with trip
attraction values used in calculation
SIOUX FALLS INTERNAL TRIP GRAVITY MODEL DISTRIBUTION
CALIB. NO. 1 ITERATION NO. 2
COMPARISON OF TRIP ATTRACTION TO TRIPS ATTRACTED - PURPOSE NO. 1
PAGE 1 OF 03
TRIP TRIPS PERCENT
DISTRICT ATTRACTION ATTRACTED DIFFERENCE DIFFERENCE RATIO
1 29031 29033 2 .09 .999
2 687 683 -4 -.58 1.006
3 1,784 19785 1 .05 .999
4 919 923 4 .43 .996
5 1,118 1,119 1 .08 .999
6 1,111 1,108 -3 -.27 1.003
7 881 880 -1 -.11 1.001
8 19 20 1 5.26 .950
9 292 287 -5 -1.71 1.017
10 67 75 8 11.94 .893
11 504 502 -2 -.39 1.004
12 282 285 3 1.06 .989
13 322 326 4 1.24 .988
14 156 145 -11 -7.05 1.076
15 48 59 11 22.91 .814
16 57 52 -5 -8.77 1.096
17 38 39 1 2.63 .974
18 78 81 3 3.84 .963
19 145 145 0 .00 1.000
20 67 63 -4 -5.97 1.063
81 0 0 0 ---
82 0 0 0 ---
83 0 0 0 ---
84 0 0 0 ---
--------- --------- --------
TOTALS 25,150 25,161 11
Click HERE for graphic.
Figure 12.--Trip length frequency for nonhome based trips,
Washington, D. C., 1955.
The comparison is made between the O-D and the gravity model curves
based on the following criteria:
a. Both curves should be relatively close to one another when
compared visually.
b. The difference between average trip lengths should be within +3
percent.
If the comparisons do not meet these criteria, then the adjustments
should be made to the initial set of traveltime factors.
The traveltime factors are adjusted by an iterative procedure. To
make this adjustment, the standard form shown in table 10 is used for
recording the information. The actual adjustment is made for each
traveltime increment by multiplying the traveltime factor used by the
ratio of the percentage of surveyed trips to the percentage of gravity
model trips.
Mathematically for each time increment:
F = F x OD% / GM%
adj. used
where: F = Traveltime factor to be used in next calibration
adj.
F = Traveltime factor used in the gravity model run
used being analyzed
OD% = Percentage of origin-destination survey trips
GM% = Percentage of gravity model trips from the run being
analyzed
This calculation results in the adjusted traveltime factor for each
one-minute increment of traveltime.
The adjusted traveltime factors are then plotted against their
respective traveltime increments on log-log graph paper as shown in
figure 13. This is done for each trip purpose, An analysis of those
plots will generally indicate that for certain points the adjusted
traveltime factors do not reflect the gravity model theory. In essence
this theory says that the greater the spatial separation between two
zones, the less the probability for trip making. Examining table 10 for
trips which are 7 minutes long the traveltime factor is 119, while the
traveltime factor for zones which are 8 minutes long is 126, which is
somewhat greater and consequently is contrary to the gravity model
theory. To adjust for this illogical situation, a "line of best fit" is
fitted to the distribution of points. This fitted line should be as
smooth and as straight as possible, keeping in mind that it should also
approximate the distribution of points. The line shown in figure 13
meets these criteria satisfactorily.
IV-28
Table 10.--Traveltime factor adjustment
(2) x (3)(From figure 13)
---- x 3
(4)
(1) (2) (3) (4) (5) (6)
Adjusted
Traveltime % Trips Traveltime % Trips traveltime Traveltime
(Actual) factor (Est. #1) factor factor #2
0 0 0 0 0
2 0 0 0 0 0
3 1.508 172 1.165 223 300
4 1.477 162 0.970 247 247
5 3.529 152 2.607 206 206
6 6.954 142 5.616 176 176
7 9.110 132 10.135 119 145
8 14.798 122 14.379 126 126
9 13.381 112 14.725 102 110
10 13.234 102 13.410 101 101
11 12.801 92 13.032 go go
12 7.716 82 8.342 76 76
13 7.030 72 7.496 68 65
14 4.057 62 4.479 56 56
15 1.635 52 1.840 446 446
16 1.016 42 0.934 46 40
17 1.754 32 0.791 71 32
18 0 0 0.060 0 0
19 0 0 0.020 0 0
20 0 0 0 0 0
Note: This table represents a ficticious problem
IV-29
Click HERE for graphic.
Figure 13.--Traveltime factor vs. traveltime.
IV-30
It is important to keep the "line of best fit" smooth and as straight
as possible for the following reasons:
a. Smooth curves can be approximately defined in a mathematical
expression; possibly, one that is not complex.
b. If these curves can be approximated by a mathematical
expression, meaningful comparisons can be made between these expressions
for different urban areas with various population and density
characteristics.
c. These comparisons would eventually help quantify, with a
mathematical function, the effect of spatial separation between zones on
trip interchange.
Once the line of best fit has been drawn, a new set of traveltime
factors is selected from it. For example, the new traveltime factor for
7 minutes would be 145; for 8 minutes it would be 126; for 15 minutes it
would be 46 and so forth.
The new sets of traveltime factors are then used in the next
calibration of the gravity model program. Zonal trip production (Pi)
and trip attraction (A values and the minimum path traveltimes (tij)
between all zones remain as previously described for use in the first
calibration. This second calibration results in another estimate of
trip interchanges, and a new trip length frequency distribution. As in
the previous calibration, the gravity model trips attracted to each zone
in the study area n
(ä Tij) are automatically compared.
i=1
The trip length frequency curves for the second calibration are
then plotted and compared with those resulting from the origin-
destination survey. If this comparison does not meet the criteria
outlined previously, another new set of traveltime factors is developed.
The gravity model program is then rerun and the calibration process
repeated until these criteria are met. Operationally, this trial and
adjustment procedure for determining traveltime factors should take
approximately three calibrations, assuming that reasonable first
approximations of the traveltime factors were used.
When the traveltime factors are reasonably close,the optional
second iteration to balance attractions should be specified. The
gravity model program will then automatically calculate a second set of
trip interchanges using the same input data except that in place of the
original trips attracted (Aj), the adjusted trips attracted (adjusted
Aj) are used.
The entire process may be repeated for a third iteration if
necessary. Actually this third iteration is usually only on the final
calibration, if at all. Experience has shown that the second iteration
gravity model attractions
n
(ä Tij )
i=1
are approximately equal to the trip attraction
factors (Aj) for each zone. On this last iteration, second or third,
whichever the case may bet all four items of output data are obtained
for analyzing the model results.
IV-31
E. Phase Four -- Topographical Barriers
Many of the gravity model studies conducted to date have shown that
topographical barriers, such as mountains, rivers, and large open
spaces, may cause some bias in the gravity model trip interchange
estimates. For example, a recent study in Washington, D.C., (29)
indicated that the Potomac River had some influence on trip distribution
patterns. A study in New Orleans, Louisiana, (30) indicated similar
findings. A study in Hartford, Connecticut, (31), indicated that the
toll bridges crossing the Connecticut River also affected travel
patterns.
The nature of the influence of such topographical barriers is not known.
All of the above-mentioned studies have analyzed the apparent reasons
why these barriers have influenced travel patterns in their own unique
situation. In Washington, D.C., (29) it was attributed to the fact that
off-peak hour traveltimes did not correctly indicate the amount of
congestion which was present on bridges crossing the Potomac River. An
analysis of congestion patterns in the region showed that there was
greater congestion in the area of the Potomac River than elsewhere in
the region. From this analysis, it was reasoned that a more realistic
measure of the traveltime on these bridges was required. In the
Hartford study (31), it was attributed to the fact that tolls are
collected on several bridges crossing the Connecticut River. Since
travel costs can also influence travel patterns, it was concluded that
this cost barrier should be reflected by increased traveltimes on those
bridges where tolls were collected. In New Orleans (30), the
Mississippi River separates portions of the study area. Many persons
cross this river by ferry boat, as well as over the bridge. It was
concluded that traveltimes on these bridges should be increased to allow
for the effect of the long traveltimes necessary in crossing the river
by ferry boat.
In each of the above cases, the effects of topographical barriers were
accounted for in the gravity model by inserting time penalties on
portions of the transportation network. The need for these penalties is
a result of the present lack of knowledge of a precise measure of
spatial separation between zones.
The examination of the traveltime patterns for bias caused by topography
involves an analysis of the differences between the estimated and the
surveyed trips crossing the various topographical barriers in the study
area. Essentially, it is a screenline analysis. The trip interchanges
developed from the travel pattern survey are compared directly with
those of the final gravity model calibration. These comparisons are
made by using the results of the accumulate selected interzonal volumes
program (PR-183). This program will accumulate trip movements between
any desired portions of the urban area. The results are compared and,
if a bias exists in the gravity model estimates, the necessary steps can
be taken to correct the situation in subsequent gravity model
calibrations.
IV-32
This analysis should generally be made for the principal trip purpose.
It can be made either on the zonal interchanges or it could also be made
using district-to-district movements. In either case, the binary tables
of both actual and estimated interchanges are supplied to program (PR-
183) and any desired movements can be obtained for analysis.
This program has been used in connection with research work by the
Bureau of Public Roads using data for Washington, D.C. Using both the
actual and the estimated trip interchanges, for each of five major trip
purposes, the trips crossing the Potomac River, from each direction were
extracted and tabulated as shown in table 11.
Inspection of the volumes in table 11 shows that the gravity model
overestimated trips crossing the Potomac River in both directions and
for all trip purposes. This indicates that the river definitely acts as
an impedance to travel. The largest over-estimate, in terms of volumes
of trips, is for work trips. This indicated that the over-estimate had
some connection with peak period congestion. As was indicated earlier,
this was found to be the case.
To correct for the effect of such barriers in subsequent gravity model
calibrations, traveltime impedances are inserted in these portions of
the transportation network which traverse the barrier being analyzed.
This is done directly on the affected links (usually bridges) by
updating the network description or in certain instances by using the
skim and update trees program.
The amount of time barrier to impose is determined by a trial and error
procedure. In New Orleans, La., for example, a time barrier of 7
minutes was first imposed on all those portions of the transportation
network crossing the Mississippi River. Subsequent analysis of the
revised gravity model estimate of trips crossing this river showed that
the time barrier was too high. By adjusting it, the correct time
barrier was finally set at 6 minutes. A similar procedure was used in
Hartford, Connecticut, and Washington, D.C.
An investigation of traffic using the Potomac River crossings (22)
substantiated the fact that these barriers depend on the relative
congestion on the bridges. The congestion was found to be directly
related to a "volume to capacity" ratio of the traffic on the bridges.
This ratio is then used to forecast the barriers for the future year.
It is important to point out that when time penalties are imposed on
portions of the transportation network, these penalties must be brought
to bear on the trip length frequency distribution of the survey trips.
This can be done by updating the network description and rebuilding the
trees. The trip interchanges for each trip purpose are then rerun
through the trip length frequency program.
The revised trip length frequency distributions are then used as a base
against which any subsequent gravity model estimates are compared.
IV-33
Table 11 -- Comparison of trips, by trip purpose, crossing the
Potomac River - Gravity model versus 1955 O-D interview
survey
Person trips by residents of
Trip purpose Maryland and D. C.Virginia
Model Survey % Diff. Model Survey % Diff.
Home based work 83,000 72,000 +15% 120,000 97,000 +23%
Home based shop 3,500 2,000 +75% 7,000 6,500 + 7%
Home based social-
Recreation 13,000 12,500 + 4% 21,500 19,000 +13%
Home based school-
miscellaneous 9,000 9,000 - 15,500 12,000 +29%
Nonhome based 14,000 13,500 + 3% 13,500 12,000 +12%
TOTAL 122,500 109,000 +12% 177,500 146,500 +20%
F. Developing Zone-to-Zone Adjustment Factors
There may be factors, other than those related to traveltime, which
could affect patterns of urban travel. Travel patterns may also be
influenced by various social and economic conditions. The effect of
these factors can be accounted for in the gravity model formula by the
use of zone-to-zone adjustment factors (Kij).
Due to the limited research on this particular point, the underlying
reasons behind the need for Kij factors are not well understood.
However, several studies (29) (30) (31) have indicated that the
following may influence our ability to identify the real causes for the
need to incorporate zone-to-zone adjustment factors into the gravity
model formula.
1. The trip purpose stratifications used today may not be precise
enough to account for all of the basic differences in travel patterns.
For example, it is possible that all the work trips produced by a
particular zone are those trips made by industrial workers. When
distributing these trips by the gravity model, or any other traffic
model for that matter, the largest proportion of these trips would be
sent to the closest zones with large employment centers, regardless of
the type of employment which is available. This means that many of
these industrial workers may be sent to large offices and
IV-34
commercial establishments, mainly because of their proximity to the
residences of these workers. However, if total work trips were to be
further stratified according to white collar and blue collar workers,
for example, this deficiency might be corrected. However, such a
stratification may create problems in forecasting trips, since it would
be more difficult to forecast the place of residence and the employment
opportunities for blue collar and white collar workers than it would be
for all workers.
2. It is customary to develop a set of traveltime factors for each
trip purpose category. Since trips between all zones are used in
developing these factors, they represent the average areawide effect of
traveltime on trip interchange. However, there is some evidence which
tends to show that traveltime factors vary by zone depending on the
characteristics of the people who live in each zone. These factors may
also depend upon the distribution of land uses immediately adjacent to
these zones.
3. There is some evidence that factors such as income and residential
density may influence the need for zone-to-zone adjustment. It is not
yet clear whether these two factors may actually be a reflection of
items I and 2 or whether they are independent factors in themselves. In
Washington, D.C., for example, it was observed that law income families
were not as likely to work in the central business district as were
higher income families. This observation was made by direct comparison
of zonal interchanges estimated by the gravity model formula and those
from the origin-destination survey. However, since average areawide
traveltime factors and only a six-purpose trip stratification were used,
this conclusion may be somewhat weak.
Regardless of the reason for zone-to-zone adjustment factors, the need
may exist for incorporating them into the gravity model formula. In
some cases these adjustments (Kij) may be significant and in others
they may not be necessary at all. Generally, in the large urban areas
where there are many types of employment, shopping, and recreation,
these adjustments may be necessary. However, in the smaller urban
areas, the need for Kij factors is small and in most cases the factors
are not necessary at all.
Even with many limitations on the understanding of the Kij factor,
tests to determine the extent of required adjustments and
procedures for incorporating them into the model have been devised and
used in several studies. The procedures require an analysis of the
differences between the trip interchanges calculated in the final
calibration of the gravity model and those measured in the O-D survey.
This analysis is performed on data for the trip purposes where problems
are suspected using procedures described below.
Limited experience has shown that it is the large traffic generators for
which the gravity model trip interchanges must be adjusted. Trips
between all zones and the central business district of an urban area,
for example, may require adjustment. Occasionally, trips between one
city of an urban complex and another city within the same complex must
be adjusted. The procedure used in developing adjustment factors is to
compare the trip interchanges between large traffic generators as
estimated by the gravity model with those developed from the origin-
destination survey. These comparisons are usually done graphically.
IV-35
The first step is to combine the trip purpose categories into major
groups. For example, if trips between all zones and the central
business district were to be examined, it would be desirable to look at
home based work trips and home based shopping trips separately, while
the remainder of the trips may be combined into one major group. Work
trips and shopping trips should be analyzed separately because of the
importance of the central business district as a generator of these two
types of trips. All remaining trip purpose categories could then be
combined by using the general purpose program. This combining is done
for both the gravity model interchanges and those from the origin-
destination survey.
The specific movements to be examined in the "K" factor analysis may be
isolated through the use of the interzonal volumes summary program.
Figure 14 illustrates this analysis for the central business district
trips.
A district map is used in this examination, one for each major trip
purpose category examined. Sector lines are drawn to denote major
traffic drainage corridors. One fictitious radial transportation route
is assumed to be centered in each of these sectors. The movements
between each district and the central business district are then
manually "assigned" to the fictitious facility within the sector in
which the district is located. These volumes are then accumulated as
the fictitious route approaches the central business district.
Generally, three values are shown for each corridor-- the total origin-
destination survey movements, the total gravity model movements, and the
difference between the two. Using this procedure, any systematic errors
which reflect the need for zone-to-zone adjustment factors can be easily
located.
The same procedure could be repeated for any desired traffic movement.
Once the analyses are completed, the need for adjustments must be
determined. Generally the amount of adjustment would be dependent on
the ratio of the origin-destination survey results to the gravity model
results for a particular movement. But, it is also dependent to a more
limited extent on the proportion of trips produced in any zone which are
to be adjusted. A recent study in Washington, D.C., (29), concluded
that the following formula expressed the relationship between the
adjustment factor required for any zonal movement and these two factors:
1 - Xi
Kij = Rij ------------------
1 - Xi Rij
where: Kij = adjustment factor to be applied to movements
between Zone i and zone j (or district i and
district j)
Rij = ratio of origin-destination survey results to the
gravity model results for the movement between zone
i and zone j
Xi = ratio of OD trips from zone i to zone j to total
OD trips leaving zone i
IV-36
Click HERE for graphic.
Figure 14 - Graphical analysis to determine the need for zone-to-
zone adjustment.
IV-37
This formula modifies the initial adjustment factor (Rij ) to account
for the fact that the final factor (Kij) appears in both the numerator
and the denominator of the gravity model equation, and thus its effect
in the numerator is buffered. This buffering is critical if from 10-40
percent of the trips out of a zone have factors applied all in the same
direction (i.e., all positive or all factional). In this situation it
is necessary to apply this formula to maintain the proper adjustments.
If over 40 or under 10 percent of the trips leaving a zone are to be
adjusted, Rij should be used as the Kij factor.
The distribution utilizing the adjustment factor should be checked to
determine if the proper adjustment has been attained. In some instances
it may be necessary to modify certain of the initial Kij factors and to
calculate a new trip distribution in order to attain the desired
accuracy.
The following example will illustrate the use of this formula. It has
been determined that work trips between all districts and the central
business district must be adjusted. District 100 produces 5,000 total
work trips daily. The origin-destination survey reported that 1,000 of
these trips went to the central business district. The gravity model
however, estimated that only 500 of these trips went to the central
business district. The adjustment factor to correct the gravity model
results for this condition would be calculated as follows:
1,000 1 - (1,000/5,000)
K = ----------- * --------------------------- = 2.67
100-CBD 500 1 - ((1,000/5,000)(1,000/500))
This factor would then be inserted into the gravity model formula with
other calculated adjustment factors and a revised trip distribution
pattern obtained.
The trip length frequency of this revised trip distribution pattern must
be checked against the origin-destination survey distribution to verify
its correctness.
IV-38
Chapter V
TESTING THE GRAVITY MODEL
A. General
The gravity model program produces a synthetic trip distribution pattern
which is an approximation of existing conditions. It must be realized
that variations between the existing and the estimated conditions are
inherent in any approximation process. Tests can be made to determine
the accuracy of the procedure used in forecasting future travel
patterns. Several types of tests are available to aid the
transportation analyst in evaluating the procedure.
The analytical tests which were described in chapter IV, are designed to
assist in analyzing and adjusting the model for bias in movements
crossing topographical features or for bias associated with income or
other socioeconomic characteristics. Upon completion of the analytical
tests.% statistical tests may be undertaken to provide an overall
measure of quality of the final calibrated model.
B. Statistical Tests
The statistical tests are generally applied only to a calibrated gravity
model. The total trips from the calibrated gravity model are compared
to the origin-destination survey trip interchanges after both are
assigned to the same spider network. Urban areas with a population less
than 100,000 may find it feasible to assign their trips to the actual
network rather than to a spider network. The trip comparison program is
used in making the comparisons and the details concerning this program
are found in the appendix.
This comparison program accepts as input two binary loaded networks, one
containing the surveyed information and the other the corresponding
gravity model estimates.
The program operates as follows: It first produces a table of
differences between the gravity model and origin-destination survey
movements as illustrated in table 12. Next, the program separates the
link volumes into 16 groups depending on the survey volume. For each of
these 16 volume groups the differences between the origin-destination
survey and the gravity model movements are tabulated according to
magnitude into 32 difference groups.
V-1
Table 12 -- Output of trip comparison program link volumes
A Node B Node O-D Volume G-M Volume Difference
1 9 38,680 43,412 4,732
1 500 16,452 16,428 -24
1 509 36,412 36,180 -232
2 3 5,812 5,692 -120
2 7 3,552 3,704 152
2 500 1,704 2,040 336
2 509 10,796 11,460 664
3 2 11,428 129440 19012
3 4 2,820 2,180 -640
3 6 5,944 6,724 780
3 280 3,492 4,036 544
4 3 10,404 11,900 19496
4 5 31,940 30,340 -1,600
4 284 119664 10,556 -19108
4 285 4,872 39676 -1,196
5 4 8,832 7,736 -l,096
5 6 18,600 23,628 5,028
5 19 16,708 12,392 -4,316
6 3 5,352 6,012 660
6 5 3,704 4,628 924
6 7 9,128 l0,416 1,288
6 22 9,944 10,756 812
7 2 2,932 2,748 -184
7 6 2,936 1,920 -1,016
7 8 8,476 8,348 -128
V-2
Table 13 shows the frequency of occurrence of various differences
between the gravity model and the origin-destination survey movements
within the 8000-9999 volume group. It also shows the sum of these
differences, the sum of their squares, the mean difference, the standard
deviation, the root-mean-square error, the percent root-mean-square
error, and the total trips from both sources, within this volume group.
It can be seen that a total of 102 movements fall into this category.
The same procedure is used on all volume groups. If the relative error
for each group is within the limits of accuracy the transportation
planner is willing to accept, then the model is deemed statistically
satisfactory. If it is not within acceptable limits, the source of the
error must be located using the analytical tests outlined in chapter IV
and the model revised.
The trip comparison program may also be used to compare compressed
binary trip tables. This test is somewhat more stringent than the
spider network comparison as there is no chance for geographic or
socioeconomic bias to be averaged out in the assignment.
When evaluating the accuracy of travel models the accuracy of the
origindestination survey data should also be considered. Figure 15
developed by A. Sosslau and G. Brokke can be used to estimate the
accuracy of survey volumes given the home interview sampling rate. For
example, given a sampling rate of 5 percent, a volume of 10,000 trips
estimated from the home interview survey can be expected to be accurate
within +8 percent at the two-thirds level of confidence.
It follows that if a model demonstrates an accuracy at each volume level
equivalent to the accuracy of the survey data, the calibration can be
considered complete. To achieve any further accuracy other sources of
data would have to be used.
V-3
Table 13 -- OutPut of trip comparison program frequency distribution
and analysis of differences, volume group - 8,000 to 9,999
Sum of
Difference Frequency Differences
-99,999 AND OVER 0 0
-75,000 TO -99,998 0 0
-50,000 TO -74,999 0 0
-25,000 TO -49,999 0 0
-20,000 TO -24,999 0 0
-15,000 TO -19,999 0 0
-10,000 TO -14,999 0 0
-8,000 TO -9,999 0 0
-6,000 TO -7,999 0 0
-5,000 TO -5,999 0 0
-4,000 TO -4,999 0 0
-3,000 TO -3,999 0 0
-2,000 TO -2,999 5 -12,612
-1,000 TO -1,999 18 -27,616
-500 TO -999 11 -8,332
0 TO -499 16 -3,26o
0 TO 499 15 4,020
500 TO 999 14 11,024
1,000 TO 1,999 15 21,428
2,000 TO 2,999 5 11,824
3,000 TO 3,999 3 10,908
4,000 To 4,999 0 0
5,000 TO 5,999 0 0
6,000 TO 7,999 0 0
8,000 TO 9,999 0 0
10,000 TO 14,999 0 0
15,000 TO 19,999 0 0
20,000 TO 24,999 0 0
25,000 TO 49,999 0 0
50,000 TO 74,999 0 0
75,000 TO 99,998 0 0
99,999 AND OVER
TOTALS 102 7,384
SUM OF SQUARES = 192,891,392
MEAN DIFFERENCE = 72
RMS ERROR = 1,375
STANDARD DEVIATION = 1,373
TOTAL O-D TRIPS = 909,180
TOTAL G.M. TRIPS = 916,564
PERCENT RMS ERROR = 15.43
V-4
Click HERE for graphic.
Figure 15 -- Relation of percent root-mean-square error and volume for
various dwelling unit sample rates.'
V-5
Chapter VI
OTHER CONSIDERATIONS
A. Converting the Gravity Model Results to Directional Movements
Once the gravity model trip interchanges have been shown to reproduce
the travel patterns surveyed by the field inventories, it is desirable
to convert the gravity model results to directional movements between
origin and destination zones. The gravity model results yield movements
from zones of production to zones of attraction. The converted
movements may be used for directional assignment to the transportation
network. Provision has been made to convert the gravity model results
using the trip conversion program.
Consider the following examples of the conversion to directional
volumes. Zone 1 produces 100 work trips which are attracted to zone 2.
This is shown schematically in figure 16. Each of these trips is
produced in the home zone and attracted by the zone at the nonhome end
of the trip.
Click HERE for graphic.
Figure 16 -- Case I - Schematic gravity model trip interchange.
These gravity model trip interchanges converted to directional origin-
destination movements are illustrated in figure 17.
VI-1
Click HERE for graphic.
Figure 17--Case I - Schematic origin to destination interchange.
In current practice a 50-50 split is usually assumed for all home based
trips. Since for nonhome based trips, the zones of production and
attraction remain the same as the zones of origin and destination,
respectively, no splitting of these trips is required. The output from
this program is a binary trip table of directional movements between all
origin and destination zones. This output can then be assigned to the
transportation network to obtain directional volumes.
In certain areas unique situations may exist where it might be desirable
to convert on other than a 50-50 basis. The trip conversion program
provides the user with this option. This same option may also be used
to factor an ADT trip table (by purpose) to a directional peak hour trip
table.
Specific details on the trip conversion program can be found in the
appendix.
B. Forecasting Future Travel Patterns Using the Gravity Model
The calibrated gravity models developed from present data are used to
estimate future travel patterns for any desired year or land use
pattern. Many of the phases related to the process of estimating future
travel patterns are outside the scope of this manual. Figure 18
illustrates the complete urban travel forecasting process. Inspection
of this figure shows that future trip distribution is influenced by many
other elements in the forecasting process. The primary elements are the
traveltime factors developed in the calibration of the model, the future
network, and the future land use. Each of these elements is in turn
conditioned by the basic travel characteristics, the existing network,
the forecast of economic activity and population, and the community
goals and policies.
VI-2
Click HERE for graphic.
Figure 18 -- Urban travel forecasting process.
VI-3
Briefly the process may be described as follows:
The entire forecast is based upon the estimate of future economic
activity and population. Once this estimate is available, the economic
activity and population must be translated into land requirements and
distributed among the various zones. The trip generation is then a
direct function of land use.
Trip generation relationships are developed using the base year data.
These mathematical expressions, which relate trip production and
attraction to various land use and socioeconomic indicators, are applied
to the future land use to arrive at future generation.
A proposed transportation system is determined for the future time
period. The location and extent of this system can be influenced by
present points of congestion and probable changes in land development
patterns. The proposed system is then coded and described to the
computer in the same manner as described in chapter IV for the present
system. The minimum path traveltimes between all zone pairs for the
proposed system are then calculated.
Traveltime factors, as developed from present data, are used for the
future time period. Very limited evidence leads to the conclusion that
this is a reasonable assumption to make.1 However, much research work
is required on this point before the assumption can be accepted without
reservation.
In addition, if zone-to-zone adjustment factors (Kij ) were found
necessary for the present time period, they may also be necessary in the
future. These are developed for the future based on their relationship
to the same specific socioeconomic characteristics. For example, a
recent study in Washington, D.C., (22) developed zone-to-zone adjustment
factors for all home based work trips to the central business district.
The factors were then related to the income level of the persons living
in each zone. The socioeconomic adjustment factors for the forecast
period were determined by analyzing the forecast estimates of zonal
income.
The essential techniques have thus been described for the calibration of
a gravity model for base year data and for the application of this
technique to a forecast year.
The gravity model provides the transportation planner with an effective
tool to relate the characteristics of land use (as represented by
generated trip ends) to the characteristics of the transportation system
in order to simulate the distribution of trips. The feedback from the
transportation system to the land use and vice versa is the key to the
transportation system analysis.
The transportation planner has many alternate approaches to systems
analysis available to him. Alternate land use configurations can be
studied with respect to a single transportation plan or more likely
alternate transportation systems can be studied with respect to a given
land use plan. The number of combinations of land use and
transportation systems requires a systematic approach to the problem.
___________________________
1 For further discussion see page III-2.
VI-4
It is generally agreed that a first step in the process should be the
assignment of future trips to the present plus committed system. The
specific additional steps in the systems analysis will be conditioned by
the land use and transportation systems to be evaluated. The reader is
referred to the Traffic Assignment Manual (1) for a more detailed
discussion of the programs and procedures to be used in systems
analysis.
VI-5
APPENDIXES
Table of Contents
Page
I. COMPUTATIONAL METHODS. . . . . . . . . . . . . . . . . . . . . A-1
A. Introduction . . . . . . . . . . . . . . . . . . . . . . . A-1
B. Equipment. . . . . . . . . . . . . . . . . . . . . . . . . A-1
C. Operating System . . . . . . . . . . . . . . . . . . . . . A-2
II. PROGRAM DESCRIPTIONS. . . . . . . . . . . . . . . . . . . . . A-3
1. PR-113, Trip table or skimmed tree format program . A-4
2. PR-116, Punch and sum trip ends program . . . . . . A-7
3. PR-120, General purpose program . . . . . . . . . . A-12
4. PR-124, Comparison program. . . . . . . . . . . . . A-18
5. PR-126, Zone district compressor program. . . . . . A-23
6. PR-127, Trip table conversion program . . . . . . . A-27
7. PR-130, Skim trees program. . . . . . . . . . . . . A-29
8. PR-133, Build trip tables program . . . . . . . . . A-35
9. PR-134, Trip length distribution program. . . . . . A-44
10. PR-135, Gravity model program . . . . . . . . . . . A-48
11. PR-151, Factor trip table program . . . . . . . . . A-58
12. PR-183, Interzonal volumes summary program. . . . . A-62
13. 501, Edit program (IBM 1401/1410) . . . . . . . . . A-65
14. 502, Edit program (IBM 1401/1410) . . . . . . . . . A-65
15. 401, Trip linking program (IBM 1401/1410) . . . . . A-85
III. STANDARD FORMATS. . . . . . . . . . . . . . . . . . . . . . A-93
A. BELMN Submonitor Control Cards.. . . . . . . . . . . . . A-93
B. Program Control Cards. . . . . . . . . . . . . . . . . . A-94
C. Binary Tape Formats. . . . . . . . . . . . . . . . . . . A-96
D. Trip Record Formats. . . . . . . . . . . . . . . . . . . A-97
IV. DETAILS OF BELMN OPERATION. . . . . . . . . . . . . . . . . . A-99
V. REFERENCES. . . . . . . . . . . . . . . . . . . . . . . . . . A-103
A-i
Appendix I
COMPUTATIONAL METHODS
A. Introduction
This appendix presents a detailed description of a battery of computer
programs to automate the operations described in the text. These
programs are designed for production-oriented batch processing. Most of
the programs operate on the IBM 7090 computer. Data for-mats for the
7090 computer are entirely compatible between programs and all operate
under the supervision of the BELMN submonitor. Data reduction and
editing are performed using programs written for the smaller IBM 1401
computer. There is no monitor system for this smaller computer.
The remainder of information on computer operation includes: (1) A
description of the operating system; (2) the program descriptions; and
(3) a description of standard data formats.
The operating system hardware and software will be described in only as
much detail as is necessary to operate the programs in production. A
more extensive discussion, including the information necessary to
program for the system, is available in an earlier publication, Traffic
Assignment Manual (1), published by the Bureau of Public Roads. To
alleviate repetitive items in the program descriptions, common items
will be discussed in a-separate section and referenced in the program
descriptions as required. The descriptions will be in an abbreviated
format, suitable for production operation of the programs. There is a
description for each program discussed in the text, with the exception
of a sort program. The sorting operations may be performed using any
standard library sort program available at most computer installations.
There are some differences in the operation of the submonitor (BELMN) as
described in the Traffic Assignment Manual (1) and as described here.
The information contained in this volume is the most current and refers
to the latest version of BELMN as available from the Urban Planning
Division, Bureau of Public Roads. It should be noted that any
previously described operations may still be performed and have not been
eliminated.
B. Equipment
Two different types of computing equipment are used in the application
of the following programs: (1) A BCD IBM 1401/1410 and (2) a binary IBM
7090/7094. The programs for the latter machine operate on a 32K IBM
7090/7094
A-1
computer with an on-line printer, two data channels, and an optional on-
line card reader. The editing programs require a 16K IBM 1401 With two
tape units. The linking program requires an 8K IBM 1401 with two tape
units.
All the IBM 1401 programs require three index registers, sense switches,
high-low-equal compare, the advanced programing package, a 1402 card-
readpunch, and a 1403 printer.
C. Operating System
The IBM 7090 programs operate under the supervision of the BELMN
submonitor. The submonitor is designed to be initiated by a senior
monitor, which is the integral part of a computer installation's
operating system. The senior monitor will not be described here. It is
intended that the user will adapt the BELMN submonitor to operate under
the control of his particular senior monitor. The primary function of
the senior monitor is to schedule the processing for many different
types of jobs and to reduce the idle time between jobs. A series of
BELMN programs is operated as a unit job under a senior monitor, or if
desired the series may be run independently.
Thus, BELMN allows the user the flexibility of either remote operation
of these programs under his installation's particular batch-processing
monitor, or direct processing without any monitor system. In either
case, the BELMN submonitor has complete control of operations during the
processing of the gravity model programs, and at completion either halts
(with no senior monitor) or returns to the senior monitor.
Each of the BELMN programs that are to be used is "stacked" on a
magnetic tape which will be referred to as the "program library tape."
The BELMN submonitor controls the initialization of a specific program
from this tape by means of various control cards. It also handles the
transition from program to program, the various housekeeping operations,
and the return to the senior monitor system in use.
In order to initialize the BELMN submonitor, a small program, referred
to as the "BELMN loader," is loaded into storage by the senior monitor
and executed. These instructions must also be available in storage to
refresh the BELMN monitor and to allow return to the installation's
senior monitor. It is also possible to start operations by mounting the
library tape on tape unit Al and pressing "LOAD TAPE" on the console.
This is possible because the BELMN submonitor programs contain the BELL
(BESYS3, distributed by the Bell Telephone Laboratories) senior monitor.
In the latter case, more tape units will be available to the user,
though the computer will halt at the completion of operations and must
be restarted.
Thus the BELMN submonitor allows ready reference to, and use of, a
senior monitor as desired, but it can also operate independently of it.
A-2
Appendix II
PROGRAM DESCRIPTIONS
This appendix presents, in an abbreviated form, descriptions of the
programs required to calibrate and test a gravity model trip
distribution These descriptions will reference material in appendices
III and IV. This is done to prevent the repetition of items which will
remain the same in each program description. The user should refer to
appendix III for the standard formats of BELMN control cards, subject
program control cards, and for standard input data and output data
formats. Appendix IV contains the details of the operation of the BELMN
submonitor. The user should refer to appendix IV for the information
necessary to operate BELMN with his specific senior monitor system.
This appendix also describes the uses and results of the various BELMN
control cards. It is preferable that someone with computer programing
experience read appendix IV and develop the method to initiate the BELMN
submonitor.
A-3
1. PR-113, TRIP TABLE OR SKIMMED TREE FORMAT PROGRAM
IBM 7090/7094
A. Identification
Deck No.: BS0113
Written by: P. Jennings, G.E. Computer Division, February 1960 for
IBM 704. Revisions for IBM 7090 by W. Hansen, Vogt-Ivers
and Associates, and L. Seiders, BPR.
Assembly Date: July 27, 1964.
B. Purpose
PR-113 converts binary trip tables or skim trees into a BCD format
suitable for off-line printing.
C. Data Requirements1
1. Tape inputs
a. Binary trip table or skimmed trees
2. Card inputs (in order required)
a. Call card
b. Identification card
c. Parameter card
(1) Options
Card columns Contents Result
1 "1" Skimmed tree input
1 blank Trip table input
___________________________
1 See section "E" of the appendix for standard data formats.
A-4
PR-113
(2) Parameters
Card columns Contents
37-39 Number of zones
d. Selected zones card
e. Tape assignment card (Optional)
Field Tape Normal tape assignments
1 Trip table or B5
skimmed trees
D. Program Operation
The program reads the cards in the above order, checks them for
correctness, stores them in memory, and prints them on the system output
tape.
The first record specified on the control card is selected and read by
the program. It then is processed and written in BCD form on the off-
line print tape. The program proceeds to the next designated record and
repeats the operation. This continues until all selected records have
been processed. At the end of the job, the input tape is rewound and
control is returned to BELMN.
This program has been designed to print the trip tables on 72 column
paper with from one to four tables to a page depending upon the maximum
size of the table.
Number of zones Tables per page
210 or more 1
140-209 2
70-139 3
69 or less 4
At the end of each table, the total trips for that table are printed.
E. Timing
Processing requires 2-10 seconds for each record (origin zone) depending
upon the number of zones in the trip table, and the number of nonzero
trip transfers.
A-5
PR- 113
F. Error Conditions
1. "NO ONE PUNCH IN COL. 72"
2. "NO TWO PUNCH IN COL. 72"
3. "NO THREE PUNCH IN COL. 72"
All of the above are printed under the card in error and are caused by
improper identification.
4. "LAST ZONE NO. OMITTED"
Number of zones missing from parameter card.
5. "A3 END OF TAPE. DIAL NEW A3" (On-line)
Self explanatory.
6. "TOO MANY TAPES---"
More tapes on assignment card than are required.
7. "BAD CHANNEL ASSIGNMENT."
Improper channel, must be "A' or "B"
8. "BAD TAPE NUMBER"
Improper unit number, must be zero or one to nine.
NOTE: All of the above conditions, except "5," result in a
return of control to the senior monitor system.
A-6
2. PR-116, PUNCH AND SUM TRIP ENDS PROGRAM
IBM 7090/7094
A. Identification
Deck No.: BS0116
Written by: L. Seiders, BPR, February 1965.
Assembly Date: March 26, 1965
B. Purpose
PR-116 prepares printed tables of summary of trip ends and/or prepares
zonal parameter cards for input to the travel model programs.
C. Data Requirements1
1. Tape inputs
a. Binary trip tables
2. Card inputs (in order required)
a. Call card
b. Identification card
c. Parameter card
(1) Options
Card columns Contents Results
1 "1" Card images will be
written on punch tape
1 blank Do not punch cards
2 "1" Set districts equal to
zones on punch cards
___________________________
1 See section "E" of the appendix for standard data formats.
A-7
PR- 116
Card columns Contents Results
2 blank Zones on the punch cards
will be either the ones
read from the "3" cards
or blank.
3 "1" Special. Only cols. 7-66
on the punch cards can
be used. Cols. 67-72
will be labeled with
cols. 49-54 of the
parameter card, cols.
73-80 will be blank and
cols. 1-6 will contain
the zone number.
3 blank No effect
4 pilot Do not print the trip end
summaries
4 blank No effect
(2) Parameters
Card columns Contents
37-39 Number of zones
42 Number of tapes
49-54 Label for option 3
d. Zone district equivalent ("3") cards
These cards are utilized by options I and 2 only. The program
will place the district in cols. 4-6 of the punch card output. If no "3"
card is read for a zone the district is left blank.
Card columns Contents
4- 6 District
10-12 First zone of district
16-18 Last zone of district;
this field may be
left blank if there is only a
single zone in this district.
72 "3" (necessary for identification)
A-8
PR-116
e. Punch field selection ("4") card
This card can be used to designate the format of the punch
cards. If this card is not used the following card is simulated:
12,48,l8,54524,60,30,66,369?2,42,78.......4
Card columns Contents
1- 2 Column on punch card in which total
trips sent for tape 1 are placed
3 Comma
4- 5 Column on punch card in which total
trips received for tape 1 are placed
6 Comma
7-12 Same as cols. 1-6, but for tape 2
13-18 Ditto, tape 3
19-24 Ditto, tape 4
25-30 Ditto, tape 5
31-35 Ditto, tape 6
72 "4" (necessary for identification)
The punch card location of trips sent and received for each tape must
compose 6 card columns. The right most column must be a multiple of 6;
greater than 11 and less than 79. The same columns may be specified for
different tapes, in which case an accumulation is obtained. Null fields
are allowed; i.e., if n commas appear in a row, n-1 tape fields are
skipped, keeping the normal fields in effect. Example: everything is
normal except it is desired to also include the trips sent from tape 3 in
column 12 with tape 1, and the trips received from tape 4 in column 54
with tape 2. The card would be punched as:
Card columns Contents
1-11 ,,,,12,,,54
The first blank terminates the redesignations; zero also acts as a blank
field.
A-9
PR- 116
f. Tape assignment (110") card
This card must be present, and must be the last card in the
input data deck. If normal tape assignments are to be used, the card may
be left blank, with the exception of column 72.
Field Contents
1 Binary trip table, purpose 1
2 " " " " 2
3 " " " " 3
4 " " " " 4
Etc.
Only those fields that are needed should be used.
D. Program Operation
The input cards are read in any order so long as the "0" card is last.
After 6 "1" cards are read, additional "1" cards are merely listed off-
line to document the run; therefore, as many 111" cards as desired may be
used, but only the first P1 will be used with the trip end summaries.
"1" "3," and "4" cards are all optional. The tapes are placed on any
units, so long as the "0" card specifies the units, if they are not on the
expected ones. Tape units should be alternated in pairs; tapes 1 and 2
should be on opposite channels, etc. The program always exits to BELMN.
Data cards are not edited.
E. Timing
If both trip end summaries and punch cards are specified, the program will
run at P times tape speed, with the time closely divided between read tape
time and output print time. Three tapes of 419 zones each, with all
output specified have been run in 1.1 minutes. If option 4 is specified,
ran time would be less than half.
F. Error Conditions
1. INVALID CARD
Col. 72 is mispunched on preceding data card. Two such are
overlooked.
___________________________
1 "P" refers to number of trip tables employed.
A-10
PR- 1 16
2. NO PARAMETER CARD
Self-explanatory; run ended.
3. TAPE ON UNIT HAS (Octal) FOR ID WORD FOR ZONE ____________
IT SHOULD HAVE (Octal)
Self-explanatory, program proceeds to message 6.
4. (Unit) - UNREADABLE RECORD (on-line)
Self-explanatory, program proceeds to message 5.
5. TAPE ERROR-SEE ONLINE COMMENTS
ZONE ____________________________
Self-explanatory, program proceeds to message 6.
6. DUE TO TAPE ERROR, THE FOLLOWING TAPES ARE NOT USED
(Tape Unit), (Tape Unit)
Note: All of the above return control to the senior monitor
system.
A-11
3. PR-120, GENERAL PURPOSE PROGRAM
IBM 7090/7094
A. Identification
Deck No.: BSO120
Written by: L. Seiders, BPR
Assembly date: April 21, 1965
B. Purpose
1. To accept a varied number of binary trip tables (or skim trees)
and perform one of the following operations on them and produce a new
binary trip table.
a. Add up to 12 tables at a tine
b. Interpolate between two tapes
c. Sort a table to produce a table of special format
d. Determine vehicle-minute deficiency
e. Determine vehicle-minute deficiency delay
f. Subtract one table from another
g. Multiply one tape by another
h. Save trips of selected times
i. Divide tape 1 by tape 2
2. Factor the output of (1) if desired.
3. Obtain a summary of trip ends on the output tables.
C. Data Requirements1
1. Tape inputs
a. Binary trip tables or skim trees
___________________________
1 See section "El' of the Appendix for standard data formats.
A-12
PR- 120
2. Card inputs (in order required)
a. Call card
b. Tape assignment card
Field Tape Normal Assignments
1 Output tape A5
2 Input tape 1 B5
3 Input tape 2 A6
4 Input tape 3 B6
5 Input tape 4 A7
6 Input tape 5 B7
7 Input tape 6 A4
8 Input tape 7 B8
9 Input tape 8 A9
10 Input tape 9 B9
11 Input tape 10 AO
12 Input tape 11 B1
13 Input tape 12 B2
c. Identification cards
Any number of "1" cards may be read and printed off-line at
the beginning of the run. If option 36 (for purpose 3) is specified the
first "1" card read will head each page of trip end summaries.
d. Selected times ("3") card
This card is needed with Option 8 only. Desired whole
minute times, or ranges of times may be specified on this card. Single
times are separated by commas; ranges of times are designated by placing
a dash between the specified limits. For example: it is desired to
specify times 3,17-19, 21-24,39,40,60,90-95. The card would be punched as
follows:
3,17-19,21-24,39,40,60,90-95.....3
A-13
PR- 120
The first number may begin anywhere on the card and the
first blank to appear thereafter terminates the selections. Any number
exceeding 6 characters (most unlikely) will be limited to the right-most
6 characters.
e. Parameter card
This card must be present and is the last card read by the
program. Whena "2" card is read, the program begins processing the tapes.
(1) Options
Card columnsContents Results
1 "1" Add trip tables.
2 "1" Interpolate on a straight line basis
between the years specified for tapes
1 and 2 on the "2" card.
Interpolation may extend beyond or
before the years of the two tapes, or
it may fall between. Assume input
tape 1 is for 1960 and input tape 2 is
for 1985. Output tape may be for year
2000, 1953, or 1974.
3 "1" Sort and sequence askim tree. Input is
a normal skim tree; output is a skim
tree in sortby time sequence with the
corresponding zone number located in
the decrement portion of the word.
4 "1" Vehicle-minute deficiency is obtained
by subtracting airline skim trees
(tape 1) from minimum groundpath skim
trees (tape 2) and multiplying the
difference by interzonal trips (tape
3).
A-14
PR-120
Card columnsContents Results
5 "1" Vehicle-minute deficiency delay is
obtained the same as Option 4, but the
answer is divided by interzonal
distance (tape 4).
6 "1" Subtract tape 2 from tape 1.
7 "1" Multiply tape 2 by tape 1.
8 "1" Save trips of selected times is
accomplished by scanning the skim tree
(tape 1) and zeroing out the trips on
(tape 2) whose interzonal trip time
does not fall within one of the
specified ranges.
32 "1" Print trip end summaries.
33 "1" Negative difference in-options,
2,4,5,6, are NOT set to zero, but are
left as minus numbers.
34 "1" List negative entries.
35 "1" If this option is specified, any
messages after tape processing is
begun are printed on-line only. This
is useful if tape drives are limited,
particularly if Option 1 is specified.
Warning: not recommended for use with
Option 32.
If any negative answers occur in Option 2 or 4-6, they are set to zero.
Option 33 can be used to bypass the zero portion.
A-15
PR-120
(2) Parameters
Card columns Contents
37-39 Number of zones (N)
422 Number of tapes (P)
45-48 Year of output tape (EG. 1975)
51-543 Year of input tape I (EG. 1964)
57-60-3 Year of input tape 2 (EG. 1983)
61-66 Multiplication constant (XXX.XXX). All
entries in all output tables are
multiplied by this constant. Each
table is then prorated to assure that
the new total for the table is equal
to the old total before factoring. It
is possible that the total could be in
error by 1; the total is rounded to
the nearest number. The decimal point
is assumed between columns 63 and 64.
If no factoring is desired leave these
columns blank.
D. Program Operation
PR-120 reads, writes off-line, and edits the data cards. When the 2 card
is reached, it unpacks the options and parameters, checks for a factor and
then makes any tape reassignments altering any so designated on the
previously read "0" card (if used). If any tape reassignments are
improper, a message is written and the job ended. If everything is in
proper order, all tapes are rewound and processing begins. The "0," "1,"
and "3" cards are all optional.
If any tape transmission errors occur during the run, an explanatory
message is written, all tapes are unloaded, and the job ended.
___________________________
2 Needed for option 1 only.
3 Needed for option 2 only.
A-16
PR-120
E. Timing
PR-120 for all practical purposes, runs at tape speed. Six tapes of 419
zones have been added in less than 2 minutes, and 10 tapes of 650 zones
have been added in 5 minutes. Timing normally depends on the number of
input tapes.
F. Error Messages
1. IMPROPER TAPE ASSIGNMENT CHECK ("0") CARD
Written on and off-line
2. IMPROPER IDWORD ON TAPE (Unit), HAS (Octal), SHOULD BE (Octal)
ZONE ____________________.
3. INVALID CARD TYPE
Column 72 of the previously listed card is mispunched.
4. TOO MANY TAPES
Error in col. 41-42 of "2" card.
5. (Unit) - UNREADABLE RECORD (On-line)
TAPE ERROR-SEE ON-LINE COMMENTS
Note: All the above return control to the senior monitor.
A-17
4. PR-124, COMPARISON PROGRAM
IBM 7090/7094
A. Identification
Deck No.: BS0124
Written by: Original IBM 704 program by G. Brown (WMATS) and J.
Manning (BPR) in 1961. Converted to BELMN by Vogt-
Ivers and Associates in 1964. Modifications by L.
Seiders (BPR) in 1964.
Assembly Date:May 16, 1965
B. Purpose
1. To compare binary trip tables: (1) Model versus origin-
destination survey or (2) model versus model.
2. To compare binary loaded networks: (1) Model versus origin-
destination survey or (2) model versus model.
3. To compare slightly dissimilar binary loaded networks: (1) Model
versus origin-destination survey or (2) model versus model.
4. To prepare BCD tabular results of these comparisons showing:
a. Volume differences by zone or link
b. The frequency distribution of volume differences by
specified volume groups
c. Certain statistics for each volume group
C. Data Requirements1
1. Tape inputs
a. Binary trip tables or loaded networks
2. Card inputs (in order required)
a. Call card
b. Identification card
c. Parameter card
___________________________
1 See section "E" of the Appendix for standard data formats.
A-18
PR- 124
(1) Options
Card columnsContents Results
1 blank Compare binary trip tables
1 "1" Compare binary loaded
networks
2 blank The loaded networks are
compatible
2 "1" The loaded networks are not
compatible, compare only
equivalent links
3 blank Do not include differences
in frequency tables when
tape "1" volumes are zero
3 "1" Include differences in
frequency tables when
tape "1" volumes are zero
4 blank Print tables of link-by-link
or zone-by-zone compar
isons ("table 1")
4 blank Do not print "table 1"
5 "1" Do not read any volume group
("3") cards. The program
will supply group limits3
6 "1" Do not read any difference
group ("4") cards. The'
program will supply
group limits4
___________________________
3 Lower limits of volume groups as supplied by program are: 500,
1000, 2000, 3000, 4000, 5000, 6000, 8000, 10,000, 15,000, 20,000, 25,000,
50,000, 75,000 and 99,999.
4 Lower limits of difference groups as supplied by program are: 50,
100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, 1,250, 2,000, and
2,500.
A-19
PR- 124
(2) Parameters
Card columns Contents
37-39 Number of zones
41-44 Last node number
d. Volume group "3" cards
The program requires that 15 volume groups be specified, 11
on the first card and 4 on the second card. The numbers specified on the
card are expected to be the lower limit of the volume group and these
numbers must be increasing across the card. Each number occupies one 6
column field. The lower limit of the first group is assumed to be zero
and this should not be entered. For example, the following 4 volume
groups:
0 to 499
500 to 999
1,000 to 2,499
2,500 and over
would be coded as follows:
Card columns Contents
1- 6 "500"
7-12 "1000"
13-18 "2500"
72 "3" (necessary)
e. Difference group ("4") cards
The program requires that 15 groups be specified, 11 on the first card
and 4 on the second card. The format is entirely similar to that for the
volume group cards, except that the lower limit of a difference group is
coded in each 6 column field. Again the program assumes the lower limit
of difference group one to be zero. A positive group and an equivalent
negative group will be automatically created for each coded difference
group. Negative groups should not be coded into the cards. Thus, 16
difference groups above zero and 16 difference groups below zero will be
created. For example, the following 8 difference groups:
-2,500 and less
-1,000 to -2,499
-500 to -999
0 to -499
0 to 499
500 to 999
1,000 to 2,4999
2,500 and over
A-20
PR- 124
would be coded as follows:
Card columns Contents
1- 6 "500"
7-12 "1000"
13-18 "2500"
72 "4" (necessary)
f. Tape assignment card2
Field Contents Normal tape assignments
1 Tape "1" B5
2 Tape "2" A7
D. Program Operation
BS0124 is called from the library tape by means of the program call card,
and control is transferred to it. A sign-on message is written off-line
indicating the date of the program assembly. The program then reads and
prints off-line the first card, assuming that it is the identification
card and saving it for use in the printed page headings. The parameter
card is then read, printed off-line, checked, and unpacked to determine
the options and program parameters. Volume and difference group cards are
then read, printed off-line, checked, and stored for future reference. If
a tape assignment card is present, reassignments are made as required.
If loaded networks are to be compared, 8,000 links are read in from tape
"1," followed by 8,000 links from tape "2." When the network system has
less than 8,000 links, the entire loaded network is read into storage. A
node by node comparison is performed and the differences computed. The
volumes and differences, by link, are written (optionally) as "table 1" on
the BCD print tape. If the options indicate that the networks are
dissimilar, only those links which are compatible are compared and all
others are ignored. If this option is not expressed, the networks are
assumed equivalent and incompatible links are listed out. If more links
remain to be processed, these are read in and the above operations are
repeated.
As each link is processed it is placed in one of 16 volume groups, based
on the link volume from tape "1." Each link is further sorted by
difference, again using tape "1" as a base, into 32 difference groups per
volume group. If option 3 is not specified, differences with zero tape
"1" volumes are not entered in the frequency table.
___________________________
2 The reader should note that throughout this description, the inputs
shall be referenced as tape "1" and tape "2," where "1" will be used as
the base for comparison and statistical calculation.
A-21
PR-124
For each volume group the program calculates: sum of the squares of the
differences, the mean difference, the standard deviation about the mean,
the "root-mean-square error" and the percent RMS error, and the total
trips for tapes "1" and "2."
Alternatively, if trip tables are to be compared, the procedure is the
same except that trips between zone pairs are compared rather than link
loads. A table of differences is again calculated with tape "1" as the
base and the above mentioned statistics are calculated. There is no
provision to compare dissimilar trip tables.
E. Timing
Trip tables can be compared at nearly tape speed. If option 4 is not
specified considerable time can be spent printing "table 1." Two 500 node
binary loaded networks can be compared (printing both table 1 and table 2)
in approximately 1 minute on the IBM 7094.
F. Error Messages
1. "IMPROPER CARD"
Written after a card which is improperly identified in column
72.
2. "AN EOF HAS BEEN ENCOUNTERED"
An unexpected tape mark has been encountered during tape
transmission. Check input tapes.
3. "REDUNDANCY - SEE ON-LINE COMMENTS"
A redundancy error has occurred during tape transmission. Check
tape indicated by on-line comments.
4. "SCALE PARAMETERS OVERLAP, CHECK CARD NO. ________________"
There is an overlap in the limit specifications for the volume
or difference groups. Check the card indicated.
5. "ZONE __________________ IMPROPER ID WORD (Tape Unit)"
The first word of the record for this zone is not in the proper
format.
6. "MISMATCHED LINKS, A NODE ______________________ B NODE,
NO. 1 ___________________ B NODE, NO. 2 _____________"
Self-explanatory. The input files should be checked.
Note: All errors return control to the senior monitor.
A-22
5. PR-126, ZONE-DISTRICT COMPRESSOR PROGRAM
IBM 7090/7094
A. Identification
Deck No.: BS0126
Written by: R. Bunyan, Alan Voorhees and Associates, September 1963
Assembly Date: September 28, 1964
B. Purpose
1. To prepare a binary tape of district-to-district trip volumes
from a binary tape of zone-to-zone trip volumes, according to certain
districtzone equivalents.
2. BS0126 can also be used to expand a trip volume tape by filling
with zeros.
C. Data Requirements
1. Tape inputs
a. Binary trip tables
2. Card inputs
a. Call card
b. Identification card
c. Parameter card
(1) Parameters
Card columns Contents
37-39 Number of zones on input tape
___________________________
1 See section "E" of the Appendix for standard data formats.
A-23
PR-126
3. Control card (District equivalents card)
There must be only one card per district and all districts must
be present in sequential order. All zones of input must also be accounted
for, though a zone may be placed in more than one district. If the user
wishes to change the zone numbering, each district may be set equal to a
single zone, with districts required in sequential order while zones can
be in any order. The zones in a district are specified in columns 1 to
66, in a format of 6 column fields. In preparing the card, place the
first zone right-justified in column 6. If it is to be a single zone
follow with a comma (, in column 7. If it is to be the first zone of a
consecutive series, punch the last zone of the series in column 12 (right-
justified) followed by a comma, if more zones are to follow. Additional
series or single zones may be selected by using the successive 6-column
fields through card column 66. Any combination of grouped and single zone
selections may be made as long as column 66 is not exceeded. The district
number to correspond to the selected zones is punched right-justified in
columns 68-70. A "3" punch in column 72 is required to identify the
district equivalents card.
For example, assume zones 6, 9-15, 18-20, and 27 to be compressed into
district 5. The control card would be punched as follows:
Card columns Contents
6 6
7 "," (comma necessary)
12 "9"
17-18 "15"
19 "," (comma optional)
23-24 "18"
29-30 "20"
31 "," (comma optional)
35-36 "27"
70 "5"
72 "3" (necessary)
A-24
PR- 126
4. Tape assignment card
Field Contents Normal tape assignments
1 Input (zonal) tape B5
2 Output (district) tape B6
3 First intermediate
storage tape A5
4 Second intermediate
storage tape B2
D. Program Operation
BS0126 is called from the binary tape by means of the program call card,
and control is transferred to it. The program reads the "1" and "2"
cards, prints them off-line, and stores the information. The "3" cards
are read into the equivalents table and checked. When the tape assignment
card is read the program performs the necessary tape assignments and
begins processing.
It then searches the input zonal volume tape for the zones specified for
the first district and accumulates them. This results in a table of
district to zone interchanges. The destination zones for this accumulated
district are them combined to give district-to-district trip interchanges.
This table is then written as a single binary record of the output tape
and this procedure continues with the next sequential district.
Processing continues until all the districts are completed in this manner.
The user should note that BS0126 can also be used to expand or square the
table of a binary trip volume tape:
The program will write a record of n (number of districts) with zeros
(with the exception of the identification word) for a district with no
specified zonal equivalency.
E. Timing
Timing will vary greatly depending on the grouping of zones into districts
and the sequence of zones within the district sequence.
F. Error Conditions
1. "ERROR IN PARAMETER CARD, JOB TERMINATED"
The parameter card does not have a "2" punch in column 72 or
columns 37-39 do not contain the number of zones on the input
tape.
A-25
PR-126
2. "ERROR IN CONTROL CARD, JOB TERMINATED"
The district equivalents cards are not in an ascending order by
district number, or a zone selection series is improperly
specified.
3. "NO EQUIVALENT FOR ZONE _________________ RUN TERMINATED"
The zone number indicated has not been placed within a district.
4. "ZONE ______________________ NOT ON INPUT OR PARAMETER ERROR"
The zone number indicated is not on the input tape. Check the
input tape or the number of zones specified on the parameter
card.
5. "END OF FILE, BCD INPUT. JOB TERMINATED."
Necessary input cards are not all present.
6. "READ ERROR ON INPUT. RUN TERMINATED."
7. "OUTPUT WRITE ERROR. RUN TERMINATED."
Both of these messages are self-explanatory I/O errors. These
tapes should be checked.
8. "BAD CHANNEL ASSIGNMENT"
9. "BAD TAPE NUMBER"
Tape assignment card has an improper tape number.
10. "TOO MANY TAPES---"
More tapes are assigned than are specified on the parameter
card.
Note: All above conditions return control to the senior
monitor.
G. Other Messages
1. "____________________ DISTRICTS"
Number of districts on output tape.
2. "JOB COMPLETED"
Execution has been completed and control is returned to the
BELMN control program.
A-26
6. PR-127, TRIP TABLE CONVERSION PROGRAM
IBM 7090/7094
A. Identification
Deck No.: BS0127
Written by: Brown, WMATS, June 1961 for IBM 704; revised for IBM
7090 BELMN by F. Hood, WMATS, and Manning, BPR, May
1962.
Assembly date: October 7, 1963
B. Purpose
PR-127 takes a file of trip volumes in which values represent trips
produced at the origin zone, and converts it into a file of origin-
destination movements. At the same time, these volumes may be factored so
that the output values represent a specific percentage of input values.
The percentage (factors) may be varied in order to build tables for a.m.
peak and p.m. peak travel, etc.
C. Data Requirements1
1. Tape inputs
a. Binary trip tables
2. Card inputs
a. Call card
b. Identification card
c. Parameter card
(1) Parameters
Card columns Contents
37-39 Number of zones
___________________________
1 See section "El' of the Appendix for standard data formats.
A-27
PR-127
Card columns Contents
47-48 Percent origins (percent of trips
produced by a zone to be converted
into "trips originated by" that zone)
e.g., "39" for 39% origin factor.
65-66 Percent destinations, e.g., "69" for
69% destination factor.
d. Tape assignment card
Field Contents Normal tape
assignments
1 Input-binary trip table B9
2 Intermediate storage tape B2
3 Output-binary trip table A5
D. Program Operation
The trip volume tape is read one record at a tine. As each of these
records is placed in memory, its duplicate is written out on the
intermediate tape. On completion of this phase, both tapes are rewound
and the first group of converted trip records is written on the output
tape. The intermediate tape is then read completely, rewound, and the
second group of trip records written on tape A5. The original input tape
is then read completely, rewound, and the third group of trip records is
written. This process continues until the output tape is completed. An
end of file is written on the output and the tapes are then rewound.
E. Timing is related to the square of the number of zones.
For 419 zones, processing required 5 minutes of IBM 7094 time.
F. Error Conditions
"NO ONE PUNCH IN COLUMN 72 - Card which has error"
Identification card error.
"NUMBER OF ZONES NOT GIVEN"
Parameter card does not have last zone number.
"NO PERCENTAGE GIVEN"
Neither origin nor destination factor has been punched in the
parameter card.
"NO TWO PUNCH IN COLUMN 72 - Card which has error"
Parameter card error.
Note: All of the above conditions result in control returning to
the senior monitor.
A-28
7. PR-130, SKIM TREES PROGRAM
IBM 7090/7094
A. Identification
Deck No.: BS0130
Written by: Original IBM 704 Program by A. Sosslau, BPR in 1961.
Revised for IBM 7090 by Brown, Voorhees in 1962.
Converted to BELMN by Bunyan, Voorhees, in 1963.
Assembly Date: February 17, 1964
B. Purpose
1. To prepare an interzonal traveltime binary file, for input to the
gravity model distribution program, from a file of binary trees produced
by the build trees program.
2. To update a file of interzonal traveltimes or trip volumes.
C. Data Requirements1
1. Tape inputs
a. Binary trip tables or trees
2. Card inputs
a. Call card
b. Identification card
c. Parameter card
(1) Options
Card columns Contents Results
1 blank All BCD input cards will
be written on A3
1 "1" Only the "1" and "2" cards
will be written on A3
___________________________
1 See section "E" of the Appendix for standard data formats.
A-29
PR-130
Card columns Contents Results
3 blank Tree times scaled according
to the longest link time
(assumes binary trees as
input)
3 "1" No scaling will be done
(assumes binary skimmed
trees as input)
4 blank Input on B5, output on A4
4 "1" Input on B2, output on B6
5 blank Updating will be done
5 "1" No update cards will be read
(2) Parameters
Card columns Contents
37-39 Last zone number
46-48 Scale factor (longest link time) if
option 3 not specified. Same units
(X.XX minutes) as used when the trees
were built.
d. Tape assignment card (must be present)
Field Contents Normal tape assignments
1 Input tape B5
2 Output tape A4
e. TERM card (used only if terminal times are to be added)
Card columns Contents
1- 4 "TERM"
f. Terminal time ("T") cards
Terminal times for consecutive zones are punched, right-
justified, in successive three column fields, with the beginning zone
number in cols. 4-6.
A-30
PR-130
Card columns Contents
4- 6 First zone of the group on this card
(Zi)
7- 9 Terminal time for Z
10-12 " " " Zi + 1
13-15 " " " Zi + 2
....
64-66 " " " Zi + 19
72 "T" (optional)
A "T" card need not have times for 20 zones. There may be
any number of "T" cards.
g. UPDT card (must be used if option 5 not specified)
Card columns Contents
1- 4 "UPDT"
h. Update ("U") cards
Card columns Contents
4- 6 Origin zone (OZ)
10-12 First destination zone of range (D1)
16-18 Last destination zone of range begun
by D1. May be blank if D2 = D1.
19 Blank, if UT (cols. 20-24) is to
replace the amount in the input
record; "+," if UT is to be added to
the record; or "-," if UT is to be
subtracted from the record.
20-24 Amount of update in whole minutes or
trips (UT)
72 "U" (optional)
A"U" card is required for each range of zones.
A-31
PR- 130
i. Last card (must be used if option 5 not specified)
Card columns Contents
1- 4 "LAST"
D. Program Operation
BS0130 is called from the library tape by means of the program call card,
and control is transferred to it. It first reads and prints off-line the
"1" and "2" cards, and then unpacks the parameter ("2") card and
determines the options and parameters. The tape assignment card is then
read and any necessary changes made.
If the user has specified that updating will be done a card is read from
the BCD input. If it is a TERM card, the terminal time cards are read
until a UPDT card is encountered. When no updating is to be done, these
operations will not be performed.
The program then reads N+1 words from the binary input (N = number of
zones). The identification word is converted so that it contains the
origin zone in the decrement and the number of zones in the address. The
remaining N words are converted to whole minutes in accordance with the
scale factor and the sign and backnode are set to zero. If scaling is not
specified the program assumes a skimmed tree input and the above
operations are not performed.
If no updating is to be done, the skimmed tree is written on the binary
output tape. If updating is to be done, the skimmed tree is retained in
storage and update cards are read and entered (added, subtracted, or
inserted) until all updates are completed for this origin zone. The
program then adds the terminal times into the record. The skimmed and
updated tree is then written on the binary output tape. The program
repeats the above operations for each record until all zones have been
processed. If a LAST card is encountered in reading cards, no further
update cards are read and the records are processed without entering
further updates.
Upon reaching the last zone, the binary output is end filed and it and the
binary input tape are rewound.
The cards must be used in the order as shown in card inputs. Cards e
through i are optional. If card e is used, cards f, g, and i must be used
also. If "U" cards (h) are used, cards g and i must also be used. A
complete run (skim, add terminal times and apply updates) would involve
all the cards a-i.
E. Timing
A 300 zone tree can be skimmed and updated in about 1-2 minutes.
A-32
PR-130
F. Error Messages
1. "READ ERROR, BCD INPUT"
Ten unsuccessful attempts have been made to read the BCD input.
2. "ERROR IN ID CARD"
The first card read did not have a "1" in column 72. It was
accepted as the "I" card anyway. Run continues-.
3. "ERROR IN PARAMETER CARD. JOB TERMINATED"
The second card read does not have a "2" in col. 72, the number
of zones (cols. 37-39) is missing, or the longest time factor
(cols. 46-48) is missing.
4. "END OF FILE, BCD INPUT. JOB TERMINATED."
An end of file has been encountered on A2 (or the card reader)
before all the input cards have been read.
5. "WRONG IDENT. ON UPDATE FILE"
The card following the "2" card was neither a TERM nor a UPDT
card. (Option 5 not specified.) Run continues as though option
5 were specified.
6. "NO ZONE IN TERMINAL TIME CARD."
A card(s) between the TERM card and the UPDT card had nothing in
cols. 1-6. The offending card is printed following the message,
and is not used. The next card is read. When 5 such cards are
found, the run is terminated.
7. "2ND DEST. ZONE IS LESS THAN FIRST."
8. "NO ORIGIN ZONE IN UPDATE CARD."
9. "NO DEST. ZONE IN UPDATE CARD."
10. "UPDATE CARD OUT OF SORT."
The above 3 messages are self-explanatory and all refer to the
cards read between the UPDT and the LAST cards. The offending
card is printed after the message and is not used. Five bad
update cards are allowed before the run is terminated.
11. "READ ERROR, BINARY INPUT. JOB TERMINATED."
Ten unsuccessful attempts have been made to read the binary
input tape.
12. "PREMATURE END OF FILE ON BINARY INPUT, RUN TERMINATED."
An end of file has been encountered before the specified number
of zones has been read.
A-33
PR- 130
13. "UNABLE TO WRITE BINARY OUTPUT. JOB TERMINATED."
Several unsuccessful attempts have been made to write the output
tape.
Unless noted, all the above errors return control to the senior
monitor.
G. Other Messages
1. "END OF BCD OUTPUT TAPE."
2. "END OF BINARY OUTPUT TAPE."
Above messages written on-line and the program halts to allow
the operator to mount new tapes. Pressing start continues run.
3. "END OF JOB."
Written when program has completed successfully. Control
returns to BELMN control program.
A-34
8. PR-133, BUILD TRIP TABLES PROGRAM
IBM 7090/7094
A. Identification
Deck No.: BS0133
Written by: Brown, May 1962, revised for BELMN by Bunyan
Assembly date: February 28, 1964
B. Purpose
PR-133 prepares binary files of trip volumes from O-D survey cards. For
home-based trips, the zone of residence (production zone) is regarded as
the "origin" zone and the zone of attraction as the "destination" zone.
Nonhome based trips, which must be processed separately, are built-in true
origin-destination form. Up to six files of trips may be built during a
single run of the program (except that home based and nonhome based must
be built in separate runs). Files may be built for specified purposes of
travel, modes of travel, land uses, occupations, etc., or for any combi-
nation of these.
C. Data Requirements
1. Tape inputs Tape unit
a. O-D survey cards A4 (or A2)
2. Tape outputs Tape unit
a. Trip table 1 B2
b. " " 2 B3
c. " " 3 B4
d. " " 4 B5
e. " " 5 B6
f. " " 6 B7
___________________________
1 See section "El' of the Appendix for standard data formats.
A-35
PR- 133
3. Card inputs (in order required)
a. Call card
b. Identification card
c. Parameter card
(1) Options
Card columns Contents Results
27 "1" No header or trailer cards
28 "1" Second reel of trip cards
on A5 following end of
tape one.
29 "1" Trip cards are on A4
rather than A2
30 "1" No equivalent cards
(2) Parameters
Card columns Contents
6 Number of purposes - also number of
output tapes (1 to 6)
9-12 Blank if trip purpose is reported by
means of purpose "from" and purpose
"to." "Ill if trips are home based and
a blank or zero if trips are nonhome
based.
13-18 Maximum number of error cards allowed
19-24 Trip scale factor. This number is
usually either 1 or 10 depending on
whether trips are reported in whole
numbers or in tenths respectively.
Immediately prior to writing,
accumulated trip volumes are divided
by the number punched in this field.
34-35 Contains the blocking factor for the
trip cards, maximum of 50 cards per
physical record.
A-36
PR- 133
Card columns Contents
37-39 last centroid number
47-48 Number of words per card. Each card
must contain a number of columns equal
to some multiple of six. Example:
When 80 column cards are put on tape
they must be expanded to 84 columns,
commonly referred to as card to tape
80/84. In this example the word count
would be 14, i.e., 84 divided by 6
(number of characters per word equals
14. If the card records are blocked,
a card record must not exceed 14
words.
d. Format specification card
This card specifies the fields in the survey card from which
certain items of data are to be extracted. For each item of data the last
column of the field and the number of columns in the field must be
provided.
Data item Last column No. of columns
1. Zone of residence Cols. 2-3 col. 6
2. Origin zone 8-9 12
3. Destination zone 14-15 18
4. Purpose (from)1 20-21 24
5. Purpose (to)1 26-27 30
6. General purpose1 32-33 36
7. Purpose flag1 38-39 42
8. Trip factor 44-45 48
9. Land use (origin) 50-51 54
10. Land use (destination) 56-57 60
11. Mode of travel 62-63, 66
___________________________
1 Depending on which method of reporting trip purpose is used, the
first or second pair of these fields may be blank.
A-37
PR- 13 3
A "3" punch in column 72 is required to identify the
format specification card.
If, for example, the survey card had the zone of
residence punched in cols. 14-17, then the specification card would have
"17" Punched in cols. 2-3 and "4" punched in col. 6.
If mode or land use are not present in the survey cards,
or if they are not required as criteria for building trip tables, the
appropriate field in the specification card may be left blank. This
does not apply to the purpose or zone fields. Data items not listed
above (e.g., day of the week, occupation, etc.) may be specified in
place of mode or land use.
PR-133 is written to accept a basic trip survey card in
which at least items 1, 2, and 3 and either 4 and 5, or 6 and 7 are
present. Hence these items must be accounted for in the specification
card. If zone of residence is not reported in the survey card or if, as
in the case of nonhome based trips, it is not to be used, then item 1
should have the same specification as the zone of origin. If trip
purpose is not reported, or not used, cols. 9-12 of the parameter card
should be left blank and "81" and "1" should be punched as the last
column and number of columns for both items 4 and 5 in the specification
card.
e. Trip criteria cards
These cards provide the program with sets of criteria
according to which trips are accumulated in specified tables. By means
of this device, the user has complete freedom of selection over the
input data (survey cards). For example, the following binary tables are
typical of those which might be obtained during a single run of the
program.
(1) Home-to-work auto driver trips with residential land
use at the origin and industrial land use at the destination,
combined with work-to-home auto driver trips having industrial
land use at the origin and residential land use at the
destination.
(2) Home-to-shop transit, auto-driver, and auto
passenger trips having residential land use at the origin and
commercial land use at the destination, combined with the
reverse of this.
In general, purpose, mode, and land use are specified.
Provision is made for 18 purpose codes, 10 mode codes, and 10 land use
codes. Zero is recognized as a legitimate code.
Criteria cards are prepared by punching a "1" in the
appropriate column. The format for these cards is as follows:
A-38
PR-133
Card columns Designation Possible codes
1-18 From purpose 0-17
19-36 To purpose 0-17
37-46 Mode 0-9
47-56 Land use (origin) 0-9
57-66 Land use (destination) 0-9
67-72 Table (tape) number 1-6
For purposes of illustration, the following survey card codes will
be assumed.
Trip purpose code Mode code Land use code
00 - Home 1 - Auto driver 1 - Residential
01 - Work 2 - Auto passenger 2 - Industrial
02 - Shop 3 - Transit 3 - Commercial
In order to build the trip tables described in (1) and (2) above,
the following criteria cards would be required.
a. "1" punch in cols. 1, 20, 38, 48, 59, and 67.
b. "1" punch in cols. 2, 19, 38, 49, 58, and 67.
c. "1" punch in cols. 1, 21, 38-40, 48, 60, and 68.
d. "1" punch in cols. 3, 19, 38-40, 50, 58, and 68.
Trip criteria cards are used by the program in the following way:
First, a table is compiled containing two words for each criteria card.
Then, as each survey card is read in, the appropriate data items are
encoded into two words. The pair of words thus formed is then tested
against each pair of criteria words. When a pair of criteria words is
found which includes (in the logical sense) the survey card pair, the
trips from this card are entered in the appropriate table.
It is important to note that the program does not seek an
exact match between the word pairs. Hence it is not necessary for each
criteria card to contain a unique set of criteria. As seen in the
example above, criteria cards c. and d. each contain mode codes 1
through 3.
When trip purpose is reported in the survey cards by means of a
general purpose code and a flag it is unnecessary to punch a home
purpose code in the criteria cards. In this case, when the program
encodes the survey card data, either the "from" or "to" purpose fields
of the code word will be ignored, depending on the direction indicated
by the flag.
A-39
PR- 133
f. End of data card
A card with a "9" punch in column 72 will signal the program
that the last criteria card has been read.
g. Zone equivalent cards These are punched one to each
survey zone (or subzone) as follows:
Card columns Contents
1- 6 Survey zone number
7-12 Assignment zone equivalent
(centroid)
These cards are written on tape in 14-word format. The
first card in the file is a label card having EQUIV punched in columns
1-5. The last card in the file is a trailer card having ENDEQ punched
in columns 1-5.
Note: Assignment zone numbers must be allocated to
survey zones in such a way that when the survey zone
numbers are ordered in an increasing sequence the
associated assignment zone numbers form a monotonically
increasing sequence.
h. Survey cards
Since there is complete variability of card format (and
data content) between one survey and another, PR-133 has been written to
accept cards in any format. Format specifications are provided by the
user for a particular run of the program. (See above.)
Survey cards are written on tape in full 14-word (84-
column) format. Cards may be optionally blocked by any number up to 50
cards per physical record. Any records of padding added during blocking
will be rejected as cards in error.
If the user chooses to use header and trailer labels the
following format must be followed: The first card on a reel is a label
card having TRIPS -punched in columns 1-5 and the reel number (1, 2....)
punched in columnThe last card on a reel is a trailer card having ENDS
punched in columns 1-4. The last card on the final reel has LAST punched
in columns 1-4.
Home based trip cards must be sorted by zone of residence
prior to use in program BS0133; nonhome based trips, which must be
processed separately. should be sorted by origin zone. If the nonhome
based trip cards are included with the home based trip cards, each of
the former will be rejected as errors during the building of the home
based tables. In the converse situation, all home based cards will be
rejected as errors. This will prohibitively increase computer running
times.
A-40
PR-133
D. Program Operation
During the first phase of operation the program reads, interprets, and
stores the program control cards up through the zonal equivalent cards.
During the second phase, the survey cards are read in, decoded, and
checked for errors record by record. Cards in error are written on an
error tape for off-line printing.
The trip tables are built for each origin zone in increasing sequential
order. Each card is matched against the criteria set by the user to
determine which, if any, trip table it is to be entered in. A count is
kept of all cards failing to meet any criteria. This is printed out at
the end of the run. When all the trip cards for a particular origin
zone are processed, the trip tables for that zone are written on the
binary output tapes. Processing then continues as above for the next
sequential origin zone.
As the trip tables are being accumulated, a summary of trip ends for
each of the outputs is also accumulated. During the final phase of the
program, the trip end tables are written on tape for off-line printing.
Due to differences in rounding techniques the trip end summaries from
BS0133 will vary slightly from those produced by BS0116 or BS0120.
E. Timing
Significant increases in running speed may be made by blocking the input
trip cards. For 50,000 survey cards, blocked 10 cards per record,
processing 160 zones requires approximately four minutes per output
tape.
F. Error Conditions
1. "NO HEADER ON TRIP CARD TAPE, IGNORED."
2. "THE FOLLOWING DATA CARDS ARE IN ERROR."
Followed directly by one or more of the following. Processing
continues until the allowed number of error cards is reached.
a. "HFLAG _______________(Card in error)_____________ "
Not a valid home based trip.
b. "ALPHA _______________(Card in error)_____________ "
An alphabeticcharacter is coded in a numeric field.
c. "IDZONE _______________(Card in error)_____________ "
Error in destination zone.
d. "OZONE _______________(Card in error)_____________ "
Error in origin zone.
e. "OSORT _______________(Card in error)_____________ "
Card out of originzone sort.
f. "RZONE _______________(Card in error)_____________ "
Error in residence zone.
A-41
PR- 133
3. "NO TRAILER LABEL."
Trailer labels not on the tapes as indicated, ignored and end
of file treated as end of data.
4. "READ ERROR ON INPUT TAPE."
Redundancy on reading trip card. Program will attempt to read
again.
5. "WRITE ERROR ON A3, IGNORED."
6. "FIVE TRIES HAVE BEEN MADE TO WRITE TAPE B________PUSH START
TO ERASE GAP."
Permanent redundancy on write, if start is pushed a gap is
erased and skipped and writing is attempted again.
7. "ERROR IN I.D. CARD IGNORED."
8. "ERROR IN PARAMETER CARD. JOB TERMINATED."
9. "NUMBER OF ZONES MISSING FROM PARAMETER CARD."
10. "NO. FILES OUTPUT MISSING FROM CONTROL CARD."
11. "NO OUTPUT IN COLS. 67-72 OF LAST CARD."
Tape to which a trip criteria card applies not indicated.
Criteria card is not used.
12. "MORE THAN ONE OUTPUT IN COLS. 67-72 OF LAST CARD." More than
one output tape specified on a criteria card. Criteria card is not
used.
13. "NO HEADER CARD ON EQUIVALENT DECK, IGNORED."
14. "THE FOLLOWING ZONE EQUIVALENT IS EITHER OUT OF SORT OR IS A
DUPLICATE-CURRENT ZONE IS _____(sequence zone)_______
_____(zone equivalent)_____ ."
15. "ZONE EQUIVALENT LIST IS TOO LARGE."
16. "PROBLEM AS SPECIFIED EXCEEDS AVAILABLE STORAGE BY____ CELLS."
Errors 8, 9, 10, 14, 15, 16 all result in a return to the
senior monitor.
A-42
PR-133
G. Other Messages
1. " ______________ CARDS FAILED TO MEET GIVEN CRITERIA."
2. "END OF FILE ON INPUT. DIAL NEW INPUT."
3. "END OF A3 OUTPUT TAPE. DIAL NEW OUTPUT."
A-43
9. PR-134, TRIP LENGTH DISTRIBUTION PROGRAM
IBM 7090/7094
A. Identification
Deck No.: BS0134
Written by: Bunyan, September 1963, Alan Voorhees and Associates
Assembly date: May 22, 1965
B. Purpose
1. To prepare BCD tables, by purpose, of trip length distribution
from binary interzonal traveltimes (skim trees) and binary zone-to-zone
volumes.
2. To give a summary total, by purpose, of person trips and
person hours of travel.
C. Data Requirements1
1. Tape inputs
a. Binary trip tables or skim trees
2. Card inputs (in order required)
a. Call card
b. Identification card
c. Parameter card
(1) Parameters
Card columns Contents
6 Number of input volume tapes (can be
up to 9)
37-39 Number of zones on input
___________________________
1 See section "El' of the Appendix for standard data formats.
A-44
PR-134
d. Origin zone selection card (optional)
This control card and the following card may be used to
optionally select certain origin and destination zones for the trip
length frequency accumulation. If the origin selection card is present,
the destination selection card may be left out if all destination zones
are to be accumulated. Both cards must adhere to the selected zone
format described in section "E."
e. Destination selection card
f. Tape assignment card (optional)
Field Tape Normal tape
assignments
1 Skimmed trees A4
2 Binary trip table
purpose 1 B5
3 Binary trip table
purpose 2 A5
4 Binary trip table
purpose 3 B6
5 Binary trip table
purpose 4 A6
6 Binary trip table
purpose 5 B7
7 Binary trip table
purpose 6 A7
8 Binary trip table
purpose 7 A8
9 Binary trip table
purpose 8 A9
10 Binary trip table
purpose 9 B9
Only those fields that are needed should be used.
A-45
PR- 134
D. Program Operation
BS0134 is called from the binary tape by means of the program call card,
and control is transferred to it. The program then reads in the "1" and
"2" cards, prints them off-line and stores the information.
The program then reads the first skim tree record and then the first
purpose input tape followed by the next input tape. (If alternate
channels are used, two purposes are read at a time.) The trip length
distribution tables begin to accumulate and the next two inputs are
read. This process continues until all the inputs for the current
origin zone are read and then the program repeats the process until all
zones have been processed.
It should be noted that the identification word (giving the zone being
processed and the total number of zones) is not checked by the program.
Only the number of zones specified will be processed, terminating when
these have been completed, though the volume tapes may contain more
zones than specified.
When all zones specified have been processed for all inputs, a BCD table
of trip length distribution is written out for each input. This table
includes a summary of total trips, total person hours of travel and
average trip length. Trips are sorted into intervals of 1 minute, with
a maximum trip length of 200 minutes. Any trips which exceed 200
minutes are placed into the 200 minute category. A printer plot of
traveltime against percent of trips is also written out for each input
tape.
E. Timing
BS0134 requires approximately 2 minutes to prepare tables of trip length
distribution for 5 input tapes of 419 zones each.
F. Error Messages
1. "ERROR IN IDENTIFICATION CARD, IGNORED"
No "1" punch in column 72 of I.D. card. It was accepted as
"1" card and run continues.
2. "ERROR IN PARAMETER CARD, JOB TERMINATED"
The parameter card does not have a "2" punch in column 72,
columns 37-39 do not contain the number of zones on input
tapes, or column 6 does not have the number of input volume
tapes.
3. "BAD CHANNEL ASSIGNMENT"
Tape assignment card has an improper channel designation. The
job is terminated.
A-46
PR-134
4. "BAD TAPE NUMBER."
Tape assignment card has an improper tape number. The job is
terminated.
5. "TOO MANY TAPES - - - "
More tapes are assigned than are specified on the parameter
card. The job is terminated.
6. "TAPE TRANSMISSION ERROR, JOB TERMINATED"
7. "PREMATURE END OF FILE, JOB TERMINATED"
Both of these messages are self-explanatory I/O errors. The
input tapes should be checked.
Note: Conditions 2-7 cause control to return to the senior
monitor*
G. Other Messages
1. "END OF OUTPUT TAPE"
The end of the BCD output tape has been reached. Mount
another tape and press start to continue.
A-47
10. PR-135, GRAVITY MODEL PROGRAM
IBM 7090/7094
A. Identification
Deck No.: BS0135
Written by: Brown, WMATS, for IBM 704. Revised for IBM 7090 by
Brown and Bunyan, Alan Voorhees and Associates, and
S. Robertson, BPR.
Assembly date: April 21, 1965
B. Purpose
PR-135 distributes trips by means of the gravity model resulting in the
following information:
1. Binary tables of interzonal trips.
2. Printed tables of trip length frequency by purpose plus total
purpose.
3. Printed tables of accessibility index.
4. A printed comparison, by district and purpose, of actual trip
attractions to the trips attracted by the gravity model.
The program also adjusts model trip attractions and reiterates them to
bring the model attractions into balance with the given attractions.
C. Data Requirements
1. Tape inputs
a. Binary skimmed trees
___________________________
1 See section "El' of the Appendix for standard data formats.
A-48
PR-135
2. Tape outputs
a. Binary trip table for purpose 1
b. " " " " " 2
c. " " " " " 3
d. " " " " " 4
e. " " " " " 5
f. " " " " " 6
g. Total binary trip table
The tapes required for a particular run depend upon the options
used.
3. Card inputs (in order required)
a. Program call card
b. Identification card(s) (up to 3 allowed)
c. Parameter card
(1) Options
Card columns Contents Results
1 "1" Only identification,
parameter, and zone
selection cards are
written on the system
output tape, other BCD
cards are not.
2 "1" No binary trip tables
will be written
3 "1" Total binary trip table
only
4 "1" Do not write out BCD
tables of accessibility
index.
5 "1" Read terminal times from
cols. 79-80 of the
"PAR" cards
6 "1" K factors will be used
A-49
PR-135
(2) Parameters
Card columns Contents
40-42 Number of zones
46-48 Number of districts
54 Number of purposes (total not
included)
58-60 Number of friction factors used
66 Number of iterations of attractions
(initial calculation of distribution
counts as one iteration)
d. Selected zone card (optional)
Specifies those ranges of zones for which attractions
should be balanced by iteration. There should be separate selections
for each purpose. If a card is absent for a purpose all zones are done
for that purpose. This card must also contain a purpose number. This
is not indicated in the description of the standard zone selection card.
For this case only, the purpose to which the selections on a card apply
is punched in card column 68. It is also possible to continue
selections on another card by punching a "," (comma) in column 67. In
most applications the user should iterate attractions for all zones and
for all purposes.
e. Tape assignment card (must be present)
Field Tape Normal tape
assignments
1 Binary skimmed trees A5
2 Binary total purpose
trip table B8
3 Binary trip table for
purpose 1 B5
4 Binary trip table for
purpose 2 A9
5 Binary trip table for
purpose 3 B6
A-50
PR-135
Field Tape Normal tape
assignments
6 Binary trip table for
purpose 4 A6
7 Binary trip table for
purpose 5 B7
8 Binary trip table for
purpose 6 A7
Only those fields that are needed should be used.
f. Zonal parameter file identification card
Card columns Contents
4- 6 "PAR"
g. Zonal parameter cards (one per zone)
Card columns Contents
1- 3 Zone number
4- 6 District number
7-12 Purpose 1 productions
13-18 " 2 "
19-24 " 3 "
25-30 " 4 "
31-36 " 5 "
37-42 " 6 "
43-48 " 1 attractions
49-54 " 2 "
55-60 " 3 "
61-66 " 4 "
67-72 " 5 "
73-78 " 6 "
79-80 Terminal time, if option 5 used
A-51
PR-135
All zones must have a district number, unless the number of zones
equals the number of districts, in which case the program will assume
all district numbers identical with the zone numbers. If district-zone
equivalents are used, the program accumulates all summaries by district
and balances the attractions on a district basis rather than on a zonal
basis. It is recommended that district numbers be coded equal to zone
numbers. The zone numbers must form an unbroken increasing sequence
beginning with one. If P is the number of purposes specified on the
parameter card, then the first P production fields and the first P
attraction fields will be used by the program. Terminal times are
rarely inserted in this manner as they are generally added by using
program 130, skim and update trees. If terminal times are added during
the gravity model program, the user should realize that the times in the
trip length frequency tables will not include terminal times. This
results in a "driving time" trip length frequency distribution. Blanks
and zeros are treated as equivalent in the punched card data.
h. End of zonal parameter file card
Card columns Contents
3- 6 "ENDP"
i. Traveltime factor file identification card
Card columns Contents
4- 6 "TIM"
j. Traveltime (F) factor cards (one per time interval)
Card columns Contents
4- 6 Time interval
7-12 Purpose 1 traveltime factor
13-18 " 2 " "
19-24 " 3 " "
25-30 " 4 " "
31-36 " 5 " "
37-42 " 6 " "
The time intervals are integer minutes and must form an
unbroken, increasing sequence beginning with one. The program only uses
as many fields of traveltime factors as there are purposes. Blanks and
zeros are treated equivalently.
A-52
PR- 13 5
k. End of traveltime factor file card
Card columns Contents
3- 6 "ENDT"
l. End of file card (if K factors are used)
Card columns Contents
1 "7" and "8" punches
m. K factor file identification card (if K factors are used)
Card columns Contents
4- 6 "KAY"
n. Interzonal trip adjustment (K) factor cards (if K factors
are used)
These factors are used to modify the trips between
specified zone pairs due to some predictable socioeconomic bias in the
gravity model distribution. They may be applied to movements from a
single (or range of) production zone(s), to a single (or range of)
attraction zone(s). The production zones must be in increasing order,
low to high, and ranges of production zones must not overlap.
Production zones may be repeated if the zone or range of zones is
exactly the same as used immediately before. If zones are repeated in
this way, the user should be careful that only one K factor may be
applied to any single zone pair.
The program reads only the number of fields from the K
factor card which corresponds to the number of purposes. Blanks are
interpreted to mean that no K factor is to be used for that purpose. A
decimal zero is not a valid K factor.
Card columns Contents
1- 3 First zone of a range of production
zones.
4- 6 Last zone of a range of production
zones. Same as columns 1-3 if this
is to bea single zone.
7- 9 First zone of a range of attraction
zones.
A-53
PR-135
Card columns Contents
10-12Last zone of a range of attraction zones. Same as cols. 7-9, if this is
to be a single zone.
13-18 Purpose 1 K factor
19-24 " 2 " "
25-30 " 3 " "
31-36 " 4 " "
37-42 " 5 " "
43-48 " 6 " "
o. End of K factor file card (if K factors are used)
Card columns Contents
3- 6 "ENDK"
D. Program Operation
Program 135 reads, edits, and stores all the cards up through the End of
Traveltime Factor File Card. It also computes the storage required,
tests to see if adequate storage is available, and initializes the
counters in the main program for thus particular run. If any coding
errors are found, it writes a message on the system output and either
continues or terminates depending upon the severity of the error.
The interzonal time record for the first production zone is read in and
stored. Next the first K factor card is read, edited, and stored (if
they are to be used). The total traveltime is computed by adding the
applicable terminal times (if option 5 is specified) to the interzonal
time read. Otherwise the time is used as read from the time file. The
traveltime c or corresponding to this time is then obtained. For each
attraction zone, a value (V) equal to the product of the applicable
traveltime factor, number of attractions, and K factor (if required) is
computed and stored. Each attraction zone is processed in sequence
until all are accounted for. This continues until all attraction zones
have been processed, for each purpose, for the production zone. The
summation of V for a particular production zone and purpose (called the
"accessibility index") is accumulated for that zone and purpose, and is
saved for later use. The program then distributes the available
productions to each attraction zone using the gravity model formula.
These trips are then accumulated, by purpose, in the tables of trip
attraction and the tables of trip length distribution.
A-54
PR-135
The entire process above is repeated for each production zone in
sequence, and all the tables are accumulated by purpose. After all the
trips attracted to a zone are accumulated, the ratio of the given
attractions to the trips attracted is computed and saved. The printed
tables specified above are written on the off-line print tape.
If more than one iteration was specified in the parameter card, the
program computes new attractions by multiplying the original attractions
by the ratio described above, and repeats the entire distribution
process.
During the final iteration binary interzonal trip tables are written (if
requested) and the printed summaries for analysis are again written on
the system print tape. Up to one binary trip table per purpose, plus a
total purpose table, may be written out. The program is limited to a
maximum of 999 districts and zones and six purposes. In addition, the
following inequality must hold:
A (5P + 4 + IP + J) + 2P (T + D) + T <29,544
Where:
Z = number of zones
P = number of travel purposes
T = number of traveltime factors used
D = number of districts
I = 1, if "K" factors are used
= 0, if no "K" factors are used
J = 1, if terminal times are to be read from parameter cards
= 0, if no terminal times are to be read
E. Timing
Approximately 12 minutes of IBM 7094 computer time are required to
process 419 zones for 6 purposes with 7 binary output tapes and 2
iterations of attractions. Time is significantly reduced if binary
output and the printout of accessibility index is suppressed.
A-55
PR- 13 5
F. Error Conditions
1. "INVALID CARD, COL. 72 IN ERROR"
2. "CODE ERROR IN TRAVELTIME FACTOR"
3. "NO TRAVELTIME IN THIS RECORD"
4. "CODE ERROR IN TRAVELTIME"
5. "CODE ERROR IN CENTROID PARAMETER"
6. "DISTRICT OUTSIDE SPECIFIED RANGE"
7. "DISTRICT MISSING FROM PAR. CARD"
8. "CORRECT ERRORS IN TIME FACTORS"
9. "CODE ERROR IN TERMINAL TIME"
10. "CENTROID OUTSIDE SPECIFIED RANGE"
11. "NO CENTROID IN THIS RECORD"
12. "CODE ERROR IN CENTROID"
13. "THE FOLLOWING PARAMETER CARDS ARE IN ERROR"
14. "THESE TRAVELTIME FACTOR CARDS HAVE ERRORS-"
15. "WRONG LABELS ON BCD INPUT FILE"
16. "CORRECT ERRORS IN ZONE PARAMETERS"
17. "INCORRECT TRAILER RECORD"
18. "ERROR IN PARAMETER CARD, RUN TERMINATED"
19. "ERROR IN CONTROL CARD, RUN TERMINATED"
20. "WRONG IDENT ON K FACTOR FILE"
21. "K FACTOR RECORD OUT OF SORT - ZONE _______ TO ZONE ______"
All of the above error messages are the result of program
input card edits and refer to the card read immediately before the
message. All cause control to be returned to the senior system.
22. "TOO MANY TAPES --- "
A-56
PR- 13 5
23. -BAD CHANNEL ASSIGNMENT"
24. "BAD TAPE NUMBER"
The three messages above refer to the tape assignment card and
refer to edits of the information in it.
25. "OVERFLOW IN ACCESSIBILITY INDEX, JOB TERMINATED"
The accumulation of accessibility index for a production zone
exceeded the limits of the computer.
26. "PROBLEM AS SPECIFIED IS TOO BIG FOR THIS MACHINE"
Self-explanatory
27. "NO TRAVELTIME FOR ZONE __________"
Indicated production zone is out of sequence or missing from
the binary skimmed trees.
28. "ZERO TRAVELTIME, ZONE __________ TO ZONE __________"
A-57
II. PR-151, FACTOR TRIP TABLE PROGRAM
IBM 7090/7094
A. Identification
Deck No.: BS0151
Written by: Vogt-Ivers Associates, modified by Robertson, BPR
Assembly date: July 20, 1964
B. Purpose
To modify or update a binary trip table or skim tree tape or entries
through:
1. Multiplication by a constant,
2. Substitution of a constant,
3. Addition of a constant, or
4. Subtraction of a constant
C. Data Requirements
1. Tape inputs
a. Binary trip tables
2. Card inputs (in order required)
a. Call card
b. Identification card
c. Parameter card
(1) Parameters
Card columns Contents
37-39 Number of zones on input tape
___________________________
1 See section "El' of the Appendix for standard data formats.
A-58
PR-151
d. Control cards2
Card columns Contents
4- 6 First origin zone in this range
10-12 last " " " " "
16-18 First destination zone in this range
22-24 last " " " " "
25 Modifying symbol3
26-30 " constant4
34-36 First of next range of origin zones
40-42 last " " " " "
46-48 First of next range of destination
zones
52-54 last " " " " "
55 Modifying symbol3
56-60 " constant4
72 "3" (necessary)
___________________________
2 Up to 100 control cards, but origin zones must be in order
(although all origin zones need not be specified).
3 "X" = Multiply by the constant
"S" = Substitute the constant
"A" = Add the constant
"M" = Subtract the constant
4 If "XI' is specified the constant is punched as 000.00
(assumed decimal point between columns 28 and 29, or 58 and 59). For
any other type modification, it is specified as a whole number right-
justified on column 30 or 60.
A-59
PR- 151
e. Tape assignment card (must be last card)5
Field Tape Normal
Assignments
1 Input tape unit A5
2 Output tape unit B5
D. Program operation
The cards described under "Card inputs" are read, checked for validity,
printed off-line, and stored. These cards may be in any order providing
the tape assignment card is last. If any data cards are in error, the
program prints a message and returns control to the controlling monitor.
When the tape assignment card is reached, any necessary reassignments
are made and the program goes into execution.
A tape record is read and the identification word is tested for proper
sequence and record count. Then the next record is read from the input
and previous record is processed.
The origin zone is checked to determine if any modification is to be
applied. The proper destination zones, as required, are modified as per
the control cards and the modified record is moved to an output area and
writing on the output tape is started. If no modification is specified,
the record is copied as is onto the output tape. The program then reads
another record and repeats.
A counter is incremented each time a record is read and compared with
the number of zones. When the proper number of records have been
processed, the output tape is file-ended and both tapes are rewound.
The number of records processed is printed off-line, an end-of-job
message is printed on and off-line, and control is returned to the BELMN
control program.
Any errors cause control to return to the monitor.
E. Timing
The program runs at nearly tape speed, so time is dependent upon the
tape units used.
___________________________
5 This program is fully buffered and input and output tapes
should be placed on opposite channels to achieve optimum program speed.
A-60
PR- 151
F. Error Messages
1. "INVALID CARD, COL. 72 IN ERROR"
Column 72 does not contain a 0, 1, 2, or 3.
2. "IMPROPER MODIFYING SYMBOL, ORIGIN ZONE =____________________"
Column 25 or 55 of a data card does not contain an X, S, A, or
M.
3. "IMPROPER ID WORD, ZONE =_________________________"
The indicated record number on the input tape is not in
correct sequence.
4. "MISSING OR IMPROPER PARAM CARD"
Parameter card not found.
5. "TOO MANY TAPES_______________________________________"
More tapes are assigned than are specified on the parameter
card.
6. "BAD TAPE NUMBER"
Tape assignment card has an improper tape number.
7. "BAD CHANNEL ASSIGNMENT"
Tape assignment card has an improper channel designation.
All errors return control to the senior monitor.
A-61
12. PR-183, INTERZONAL VOLUMES SUMMARY PROGRAM
IBM 7090/7094
A. Identification
Deck No.: BS0183
Written by: Manning, BPR, December 1962; revised April 1964 by
Seiders, BPR.
Assembly date: April 15, 1964
B. Purpose
To accumulate and print selected interzonal interchanges from a binary
trip table.
C. Data Requirements1
1. Tape inputs
a. Binary trip table
2. Card inputs (in order required)
a. Gall card
b. Identification card (up to 10)
c. Parameter card
(1)Parameters
Card columns Contents
37-39 Last zone number
41-44 Number of sets of origin and
destination selection, right-
justified
___________________________
1 See section "E" of the Appendix for standard data formats.
A-62
PR- 183
d. Identification card for set (1 per set). A "1" punch is
required in column 72.
e. Control card (origin zone selection. A "3" punch is
required in column 72.) (UP to 5 per set.)
f. Control card (destination zone selection). Same as
standard control card except a "5" is punched in column
72. (UP to 5 per set.)
g. Tape assignment card (unique for this program).
Card columns Contents
12 Channel - A or B
13 Unit 0 thru 9
72 "0" (zero)
D. Program Operation
The program reads in the sets of selected origins and destinations
first, then it reads in a trip record and checks the table of origins to
see if it is selected. If the record is selected in the origin
selections the volumes for selected destinations are accumulated. When
all the records have been read in and the accumulations completed, the
set totals are written out together with their identification.
I
Following the program call card, which is read by the control program,
are the program cards in the following order:
1. Identification cards for page headings, up to 10 cards -
2. Parameter card, I card -
3. First set identification card, 1 card -
4. First set origin selection cards, up to 5 cards -
5. First set destination selection cards, up to 5 cards -
6. Second set identification card, etc....
7. At end of last set, tape assignment card, 1 card - (Maximum of
65 sets)
After PR-183 is located on the library tape by the BELMN control program
and loaded into core storage, control is transferred to it. The
identification cards (up to 10) are read in and then the parameter card
is read in and the parameters stored for program use. Next the sets of
origin (up to 5 cards per set) and destination selections (up to 5 cards
per set) lead by their set identification cards (up to 65 sets) are read
in until the tape assignment card is encountered. After the tape
assignment card is read in, the program reads in the first trip record,
checks it for errors and looks into the origin selection table for each
set. When it finds a set in which the record is selected it accumulates
the volume according to the set's destination selections. When it has
read in the last record and processed it, writing out begins. At the
top of each page identification cards are written out, then the set
identification card and, on the same line, the sum accumulated for the
set.
A-63
PR- 183
E. Timing
It takes about two minutes to process a 552 zone tape for about 40
selections.
F. Error Conditions
1. "ONLY 65 SETS ALLOWED"
Maximum number of separate volume accumulations exceeded.
2. "TOO MANY ID CARDS _______ NO PARAMETER CARD"
3. "CARD IN ERROR - 77 RETURNED FROM CARD" Improper origin or
destination selection card.
4. "SELECTED ORIGIN ZONE______SET_______ IS LARGER THAN______"
Origin zone selection out of sort.
5. "ORIGIN ZONE______SET_______IS LESS THAN RECORD BEING
ACCUMULATED______"
Origin zone out of sort.
6. "DEST. ZONE ERROR______AT______FOR ORIGIN ZONE______SET______"
Invalid destination zone.
7. "RECORD NUMBER______WORD COUNT WRONG______"
Improper word countin identification word on indicated record.
8. "TAPE RECORD______WRONG ID"
Improper record number in identification word on indicated
record.
9. "ERROR ON TAPE______COULD NOT READ CORRECTLY, NHEK______
TRIPS FROM ORIGIN ZONES 1 THRU______SHOULD BE VALID"
10. "ERROR IN TAPE READ OPERATIONS NHEK = (operation error code)
DATA FOR ORIGIN ZONES 1 THRU______SHOULD BE VALID."
In both 9 and 10 a tape error terminated accumulations; origin
zones processed prior to error are OK.
11. "END-OF-FILE DETECTED WHILE TRYING TO READ RECORD (ORIGIN
ZONE) ______
TRIPS FROM ORIGIN ZONES LESS THAN______SHOULD BE VALID"
12. "END-OF-TAPE REACHED AT RECORD (ORIGIN ZONE)______ON TAPE
UNIT______PRINT RESULTS FOR ONE INPUT TAPE ONLY."
All errors return control to the submonitor.
A-64
13. 501, EDIT PROGRAM
14. 502, EDIT PROGRAM
IBM 1401/1410
A. Identification
Deck No.: 501 (Program #1)
502 (Program #2)
Written by: H. C. Galloway and E. J. Michener BPR. 1961.
B. Purpose
This "general" edit program is designed to be applicable to any data
editing situation. The program edits up to 50 fields of data for
unacceptable characters and can transfer these fields into any desired
format; in this particular battery the format must be acceptable to the
IBM 1401 trip linking program (see page A-85).
C. Requirements
The two programs referenced are very similar. Program deck 501 has an
upper limit on any field length of 5 digits. Program deck 502 has an
upper limit on any field length of 10 digits. The first deck (501)
should be used whenever possible because it permits greater testing
flexibility and reduces operating time.
D. Data Preparation
Input consists of card or tape records (of 80 characters or less)
containing trip data from an origin-destination survey. These data may
be in any format.
A-65
501, 502
E. Card Formats
Several parameter cards are necessary for testing and/or transferring
fields with this program. The parameter cards that are needed include
one Control Card, N "Routine" cards (N refers to the number of fields to
be tested or operated on and must be between 01 and 50), one "Extra"
card, and one Zone card.
The parameter cards for this program are loaded following the program
deck in the order in which they are described below.
1. One "Control" card (BOTH DECKS)
Card column Contents
01 Punch a 'IC"
02-08 Blank
09-10 Number of fields to be operated on,
(N) Range: 01 to 50
11-80 Identification to be printed on-line
2. N "Routine" cards (DECK 501 ONLY)
One "Routine card is required for each of the N fields to be
tested or operated on.
Card column Contents (DECK 501 ONLY)
01 "R" punch (must be punched)
02 "Routine" card master test switch.
"0" - If "Routine" tests are NOT
required (columns 3-72 are left
blank). "1" if "Routine" tests ARE
required.
03 Number of times EXAM 1 is t o be
used, (1-4, "0" if EXAM I not used).
04 Number of times EXAM 2 is to be
used, (1-8, "0" if EXAM 2 not used).
05 Number of times EXAM 3 is to be used
(maximum of 1, "0" if EXAM 3 not
used).
06 Number of times EXAM 4 is to be
used, (maximum of 1, "0" if EXAM 4
not used).
07 Number of times EXAM A is to be
used, (1-8, "0" if EXAM A not used).
A-66
501, 502
Card Column Contents (DECK 501 ONLY)
The sum of two times column 3 Plus columns 4-7 may not
exceed 8.
08 Number of timesEXAM B is to be used,
(1-4, "O" if EXAM B not used).
09 Number of timesEXAM C is to be used,
(1-4, "O" if EXAM C not used).
10 Number of times EXAM D is to be
used, (1-4,"O" if EXAM Dnot used).
11 Number of times EXAM E is to be
used, (1-4, "O" if EXAM E not used).
The sum of columns 8-11 may not exceed 4.
12-14 Blank
(See separate diagram - "Routine" Card Test Switch -
page A-72.)
15-54 a. EXAMS 2, 3, 4. and A
If any combination of EXAMS 2, 3, 4,
and A are specified in columns 4-7,
the first X fields (where X is the
sum of columns 4-7) should be
punched, beginning in column 15,
with each constant right-justified
in a 5-column field in the same
order that the EXAMS appear in
columns 4-7.
15-54 b. EXAM 1
If EXAM 1 is specified in column 3,
the last 2Y fields, ending in column
54, (where Y is the number punched
in columns 3) are punched with the
high and low constants to be used in
the tests, with the low constant
field to the left of the high
constant field. For example: The
first high constant would be right-
justified in a 5-digit field and
ending in column 54; the first low
constant would be right-justified in
a 5-digit, field ending in column
49; the second set of constants
would end in columns 44 and 39
respectively; etc.......
All fields punched in columns 15-54
must be 5-column fields punched with
leading zeros. All unused fields
should be blank.
A-67
501, 502
Card Column Contents (DECK 501 ONLY)
55-62 EXAMS B, C, D, And E
If any combination of EXAMS B, C, D,
and E are specified in columns 8-11,
the first Z fields (where Z is the
sum of columns 8-11) should be
punched, beginning in column 55,
with the card column numbers of the
"other" fields in a 2column field in
the same order that the EXAMS appear
in columns 8-11. Leading zeros must
be supplied.
63-72 Message to describe field being
tested. This will be printed on-
line in case of an error and must be
entered when a "Routine" test is to
be used.
73-74 Test field number, from 01 to N, in
unbroken sequence.
75-76 Input field high order card column
number.
77 Input field length, 1-5 digits only.
78-79 Output field high order column
number. (The range is 01 through W,
where W is as defined in columns 7
and 8 of the "Extra" card.) These
columns should be blank if the field
is to be omitted from the final form
of the edited data record.
80 Output field length. 1-5 digits
permitted. Blank field is to be
omitted from the final form of the
edited data record. Output field
length must be equal to or greater
than input field length.
3. N "Routine" cards (DECK 502 ONLY)
One "Routine" card is required for each of the N fields to be
tested.
Card column Contents (DECK 502 ONLY)
01 "R" punch (must be punched)
02 "Routine" card master test switch.
"O" - If "Routine" tests are NOT
required (columns 3-72 are left
blank), "I" - If "Routine" tests ARE
required.
A-68
501, 502
Card column Contents (DECK 502 ONLY)
03 Number of times EXAM 1 is to be
used, (1-2, "0" if EXAM 1 not
used).
04 Number of times EXAM 2 is to be
used, (1-4, "0" if EXAM 2 not used).
05 Number of times EXAM 3 is to be
used, (maximum of "l" "0" if EXAM 3
not used).
06 Number of times EXAM 4 is to be used
(maximum of "1," "0" if EXAM 4
not used).
07 Number of times EXAM A is to be
used, (1-4, "0" if EXAM A not
used).
The sum of two times column 3 Plus columns 4-7 may
not exceed 4.
08 Number of times EXAM B is to be
used, (1-4, "0" if EXAM B not
used).
09 Number of times EXAM C is to be
used, (1-4, "0" if EXAM C not used).
10 Number of times EXAM D is to be
used, (1-4, "0" if EXAM D not used).
11 Number of times EXAM E is to be
used, (1-4, "0" if EXAM E not used).
The sum of columns 8-11 may not exceed 4.
12-14 Blank
(See separate diagram - "Routine" Card Test Switch-
page A-72.)
15-54 a. EXAMS 2, 3, 4, and A
If any combination of EXAMS 2, 3, 4,
and A are specified in columns 4-7,
the first X fields (where X is the
sum of columns 4-7) should be
punched, beginning in column 15,
with each constant right-justified
in a 10-column field in the same
order that the EXAMS appear in
columns 4-7.
A-69
501, 502
Card column Contents (DECK 502 ONLY)
15-54 b. EXAM 1
If the EXAM I is specified in column
3, the last 2Y fields, ending in
column 54, (where Y is the number
punched in column 3) are punched
with the high and law constant field
to be used in the tests, with the
law constant field to the left of
the high constant field. For
example: The first high constant
would be right-justified in a 10-
digit field, ending in column 54,
the first law constant would be
right-justified in a 10-digit field,
ending in column 44, the second set
of constants would end in columns 34
and 24 respectively; etc..
All fields punched in columns 15-54
must be 10-column fields punched
with leading zeros. All unused
fields-should be blank.
55-62 EXAMS B, C, D. and E
If any combination of EXAMS B, C, D,
and E are specified in columns 8-
11, the first Z fields (where Z is
the sum of columns 8-11) should be
punched, beginning in column 55,
with the card column numbers of the
"other" fields in a 2-column field
in the same order that the EXAMS
appear in columns 8-11. Leading
zeros must be supplied.
63-72 Message to describe field being
tested. This will be printed on-line
in case of an error and must be
entered when a "Routine" test is to
be used.
73-74 Test field number, from 01 to N, in
unbroken sequence.
75-76 Input field High order card column
number.
77 Input field length, 1-10 digits.
Zero is punched for 10-digits.
78-79 Output field high order column
number. (The range is 01 through W,
where W is as defined in columns 07-
08 of the "Extra" card). These
columns should be blank if this
field is to be omitted from the
final form of the edited data
record.
A-70
501, 502
Card column Contents (DECK 502 ONLY)
80 Output field length. 1-10 digits
permitted. Blank, if field is to be
omitted from the final form of the
edited data record. Output field
length must be equal to or greater
than input field length.
4. One "Extra" card (BOTH DECKS)
Card column Contents (BOTH DECKS)
01 "E" punch (must be punched)
02-06 Blank
07-08 W, the number of digits in the
output record. The range of W is
from 01 through 99.
09-10 V, the number of data cards to be in
each blocked tape record. The range
of V is from 01 through 50, but W
times V must be less than or equal
to 4200.
11 Master "Pull" switch.
a. If no "Pulling" is desired,
punch a zero and leave columns 12-29
blank.
b. If "Pulling" is desired, punch
the number of columns to be checked,
1-6 is permitted.
12-29 Punch the 2-digit column number and
the single test digit alternately in
columns 12-14, 15-17, etc. Unused
positions are left blank when column
11 is less than 6. Example: Assume
that you wish to test column 16 for
a 1, 2, 3, 4, 7, or 9 digit.
Columns 12-29 would be punched as
follows: 161162163164167169.
30 "Extra test Master Switch." If No
"Extra" tests are required punch a
zero and leave columns 31-80 blank.
If "Extra" tests are required,
(See - J. Options).
31-80 "Extra" Test Switches (See J.
Options).
A-71
Click HERE for graphic.
A-72
501, 502
5. One Zone card (BOTH DECKS)
Card column Contents (BOTH DECKS)
01 A load punch and a zone test switch punch
are needed in this column. A "+" (12
punch) is the load punch. The test switch
punch is as follows: Punch a Zero if
column 1 is to be skipped; punch a "1" if
column 1 is to be tested for a zone
punch.
02-80 "0" - If a card column is Not to be
tested for a zone punch. "1" - if a
card column is to be tested for a
zone punch.
F. Output
Output is on one or more magnetic tapes containing edited trip
data. Regardless of the original form of the data, the edited
cards or tape records are written on tape unit one.
Error records will be printed out on-line with an error message
indicating the card column that contains the erroneous zone punch
or bad blank. The error records are also punched out and sent to
the normal punch stacker. They may be corrected and resubmitted to
the edit program again and later merged with the previously
accepted records.
The record format of the output from the 1401 Edit program should
be standard to be used as input to the 1401 Trip Linking. This
standard format is shown on a separate page - Standard Format
Table, page A-74).
G. Method
The features of the General Edit program follow in the same order
that each is performed on a particular data card.
A data card (or tape record), may be "pulled" if a given digit is
present in a specified column. The pulled data card goes to
special read stacker "1," and the pulled tape record is punched as
a card and sent to special punch stacker "4." These are not error
cards, they are only data cards that are not to be processed with
the regular set of data cards because of some distinction. The
pulling is controlled by the "pull" switch on the "Extra" card.
The next feature involves testing for zone punches in the card. A
zone punch is an "11" or "12" punch in a card; zone punches in a
field will often cause erroneous conclusions in the IBM 1401
compare operations. It is possible to check each column on the
card for a zone punch or to bypass certain columns
A-73
501, 502
STANDARD FORMAT TABLE
Standard Output Record Format from IBM 1401 Edit Program1
Card columns Contents2
4- 6 Zone of origin
10-12 Zone of destination
15 Purpose from
18 Purpose to
24 Mode of travel
28-30 Trip factor in tenths. Example: 12.1
36 Blank (reserved for general purpose code)
49-51 Start time
52-54 Arrival time
71-76 The sample number, right-justified
77-78 Person number
79-80 Trip number
___________________________
1 Output is standard in this instance only, because the IBM
1401 Trip Linking Program requires standard input. Actually the
edit routine can create any desired format for output records.
2 Contents of card columns not specified may vary in any
desirable manner. However, the edit program must be set up so that
output from it is in the above format.
A-74
501, 502
which may contain legitimate zone punches. This test is controlled
by "Zone" card. If a data card (or tape record) isn't "pulled,"
then its mns will be edited for zone punches. Every column tested
which contains a zone punch will cause an error message, ZONE PUNCH
XX, to be printed (see error messages). The XX represents the
variable column number.
"Bad" blank testing is the next feature. Random blanks within a
given field, which is not completely blank, usually represent a
punching error. These blanks will often cause erroneous
conclusions in the IBM compare operations. The individual card
columns will be checked only if a given field on a data card is
being tested later by "routine" or "extra" tests and the entire
field is not blank. Every individual column which contains an
erroneous blank will cause an error message, BAD BLANK XX, to be
printed. The XX represents the variable column number. Each of
the N fields, as specified by the "Routine" cards, are considered
in this manner.
A data card will be rejected at this point if it contains any zone
punch errors and/or bad blank errors (see error messages). If no
errors of this type are present, the Routine Program continues and
testing and transferring is done for each of the N fields. A
"Routine" test for a given field must be composed of a logical
combination of the following:
Group 1
EXAM 1 L ó Fi ó H
EXAM 2 Fi = C
EXAM 3 Fi > C
EXAM 4 Fi < C
Group 2
EXAM A Fi not = C
EXAM B Fi < Fother
EXAM C Fi ó Fother
EXAM D Fi = Fother
EXAM E Fi not = Fother
A-75
501, 502
Fi = Data field to be tested.
L = Lower value constant for EXAM 1 test.
H = Higher value constant for EXAM 1 test.
C = Constant for EXAM 2, EXAM 3, EXAM 4, and EXAM A.
Fother = Field for EXAM B, EXAM C, EXAM D, or EXAM E.
Group 1 contains the four components of the "OR" type. Group 2
contains the five components of the "AND" type. If a "Routine"
test contains only the "OR" type, the particular field value of the
data card must satisfy only one of the components for a success.
If a "Routine" test contains only the "AND" type, then the field
value on the data card must satisfy every one of the components for
a success. If both types are present in a "Routine" test, then
only one of the "OR" components and all of the "AND" components
must be satisfied by a particular field value for a success. A
"Routine" test for a given field is controlled by its "Routine"
card. There is a "Routine" card corresponding to each of the N
fields. After the "Routine" test is completed, and if no success
is encountered the error message, the field number, the input field
high order column, and the input field length will be printed on-
line.
Take the following example to illustrate the construction of a
logical "Routine" test: Assume that the two digit field, "Tract,"
can have the values 1-50, or 60, or 70, or 80, or 90. A "Routine"
test is necessary to compare the data card field value with the
acceptable ones. Thus a one is punched in column 2 of the
"Routine" card for this field to indicate testing. Since EXAM 1 is
needed once and EXAM 2 is needed four times, a 1 is punched in
column 3 and a 4 is punched in column 4. Zeros are punched in
columns 5-11, since these components are not used. Constant 00001
and constant 00050 are punched in columns 45-49 and 50-54,
respectively. Constants, 00060, 00070, 00080, and 00090, are
punched in columns 15-19, 20-24, 25-29, and 30-34, respectively.
An error message) such as "TRACT NO" is punched in columns 63-72.
Deck 501 is being used as the constants for this "Routine" test
exceed 4.
The transferring or omission of a particular field is also
controlled by its "Routine" card. In each case, the output field
length must be greater than or equal to the input field length.
Thus, within the above limits, the field length can be increased.
If input field length is less than output field length and the
specific field value on a data card is nonblank the appropriate
number of leading zeros is inserted. Thus, it is possible to
rearrange the order of the fields or leave the order unchanged, to
increase the length of certain fields, or to delete the data of
certain fields from the final form of the data record. After a
"Routine" test and/or transfer have been performed on each of the
N fields, the data card will be in its edited form. At this point,
"Extra" testing could be considered (see - J. Options, page A-78.)
A-76
501, 502
At the time that the first error is encountered, the actual data
card (or tape record) is printed on-line as well as the error
message. This is to assist in the rapid determination of the
error(s). Also, the data card (or tape record) is punched and sent
to the normal punch stacker to facilitate later removal of the bad
cards from the original deck. The bad cards must be corrected and
then used as data for a new run of the program.
H. Program Usage
1. Operator setup instructions
a. Input on cards
If the input data are on cards the following
procedure is used:
Sense switch A "on," all other sense switches "off."
Output tape on tape unit 1.
The data are loaded directly behind the parameter
cards in the following order:
(1) One control card (has a "C" coded in column 1).
(2) N routine cards (all have an "R" coded in column 1).
(3) One Extra card (has an "E" coded in column 1).
(4) One Zone card (has a "+" (12 punch) in column 1).
(5) All of the data cards.
b. Input on tape
If the input data are on tape the following
procedure is used:
(1) Sense switch E "on," if, and only if, the first
record on the particular input reel is identification. The program
user must supply this information, and this identification is not
transferred.
(2) Sense switch G "on."
(3) All other sense switches "off."
(4) Output tape on tape unit No. 1.
(5) Sense switch F "on," if the last input reel has been
processed completely and an end of reel halt has been encountered.
A-77
501, 502
The parameter cards are loaded in the card reader in
the following order:
(1) One Control card (has a "C" coded in column 1).
(2) N Routine cards (all have an "R" coded in column 1).
(3) one Extra card (has an "E" coded in column 1).
(4) One Zone card (has a "+" (12 punch) coded in column 1).
The input data tape reel is mounted on tape unit No. 4.
The output tape reel is mounted on tape unit No. 1.
2. Procedures to run program
a. Mount tapes as just described.
b. Load the program deck, data cards (if data are on
cards), and the parameter cards as just described, (each parameter
card must be used).
c. Set sense switches as described.
d. Turn punch on.
e. Hit load key.
f. For halts see on-line printed instructions or halt list.
g. If input is on tape, set sense switch "F" when the
end-of-reel halt occurs after the last input reel has been
processed and then hit start.
I. Tapes
Unit 1 Output (correct records)
Unit 4 Input (all records if cards on tape)
J. Options
1. When data are in card form: an unlimited number can
follow the zone card, sense switch A must be "on," all other sense
switches must be "off."
2. When data are on tape: The 1401 General Edit program
accepts tape records containing only 80 characters or less. If the
records are blocked or longer than 80 characters it will be
necessary to make a preliminary run using the Tape Record Separator
program.
A-78
501, 502
When data are on tape sense switch G must be "on" and all
other sense switches "off" EXCEPT - a) when the first record on a
particular input reel is identification, sense switch E must be
"on" and b) when the last input reel has been processed and an end
of reel halt has been encountered sense switch F must be "on."
3. "EXTRA" Tests
After a "Routine" test and/or transfer has been performed
on each of the N fields, the data card will be in its edited form.
At this point, "Extra" testing will be considered.
"Extra" tests are of a more complex nature - those
involving two or more fields. Typical "Extra" tests are the
conditional, "if - then 1, " type. "Extra" tests might actually
serve as "Routine" tests when using Deck 501, but several fields
would be longer than 5 digits.
"Extra" tests must be constructed for each different set
of data cards and the whole program deck (501 or 502) must be re-
autocoded in most cases. Constants must be added to the program
deck when they are needed for new "Extra" tests. Each "Extra" test
error message is a 10-digit fields and the set of "Extra" test
error messages are stored sequentially as constants in core
storage. "Extra" testing is controlled by the "Extra" card,
columns 30-80. The limit is 50 "EXTRA" tests.
"Extra" tests are easily written by using a system of two
constant entrance instructions and two constant exit instructions
per test, and several basic rules. The last "Extra" test marks the
end of testing on a data card (or tape record), which appears at
the end of the program. If no errors have been found on the data
card, the reassembled, edited card will be sent to a storage block
in core memory. When a specific number (V) of these have
accumulated, the whole block is sent to tape unit one as a
permanent record.
K. Timing
Running time data on this program are approximate only. Recently
some 34,000 records were edited and several items of data in these
records were transferred in 90 minutes. Differences in running
time, however may be encountered depending on the number of fields
edited and/or transferred as well as the actual number of records
processed.
L. Error Messages
Cards containing errors are printed out and the errors are labeled.
(See G. Method.)
A-79
501, 502
M. Program Halts (DECK 501 ONLY)
Location Symbol Explanation
9940 HALTC1 Illegal punch in column 1 of "Control"
card. Check sequence of parameter
cards. Correct and start over.
9976 HALTC2 Illegal punches in columns 9-10 of
"Control" card. Check N, number of
fields. Correct and start over.
10157 HALTRI Illegal punch in column 1 of "Routine"
card. Check sequence of parameter
cards. Correct and start over.
10174 HALTR2 Illegal punch in columns 73-74 of
"Routine" card. Check sequence of
cards.
10259 HALTR3 Illegal punch in column 3 of "Routine"
card. Check limits for EXAM 1.
Correct and start over.
10260 HALTR4 Illegal punch in column 4 of "Routine"
card. Check limits for EXAM 2.
Correct and start over.
10261 HALTR7 Illegal punch in column 7 of "Routine"
card. Check limits for EXAM A.
Correct and start over.
10278 HALTR5 Illegal punch in column 5 of "Routine"
card. Check limits for EXAM 3.
Correct and start over.
10295 HALTR6 Illegal punch in column 6 of "Routine"
card. Check limits for EXAM 5.
Correct and start over.
10408 HALTRB Total of two times column 3 Plus
columns 4-7 exceeds 8 on "Routine"
card. Correct and start over.
10479 HALTR9 Illegal punch in column 8, 9, 10, or
11 of "Routine" card. Check limits
for EXAMS, B, C, D, and E. Correct
and start over.
A-80
501 o 502
Location Symbol Explanation (DECK 501 ONLY)
10534 HLTR10 Total of "Routine" card columns 8-11
exceed 4. Correct and start over.
10588 HLTR11 Illegal punch in column 77 of "Routine"
card. Check limits on input.field
length. Correct and start over.
10660 HLTR12 Illegal punch in "Routine" card.
Output field length is greater than 5.
10687 HLTR13 Illegal punch in "Routine" card. Input
length, column 77, is greater than
output field length, column 80.
Correct and start over.
10848 HALTE1 Illegal punch in column 1 of "EXTRA"
card. Correct and start over.
10905 HALTE2 Illegal punch in column 11. of "EXTRA"
card. Correct and start over.
10975 HALTE3 Illegal punch in column 11 of "EXTRA"
card. Correct and start over. Range
1-6.
1111046 HALTE4 Illegal punch in columns 9-10 of "EXTRA"
card. The value of "V" must be
between 1 and 50. Correct and start
over.
11082 HALTE5 Illegal punch in columns 7-8 of "EXTRA"
card. Value of "W" must be between
1 and 99. Correct and start over.
11113 HALTZ1 Illegal punch in column 1 of "Zone"
card. Must be a + punch (12 punch)
AND a zero or a one in this column.
Correct and start over.
11148 HALTZ2 Illegal punch in columns 1-80. Must be
a zero or a one in each column of the
"Zone" card. Correct and start over.
11458 HLTRT2 End-of-Reel Halt. This halt means that
the input reel on Unit 4 has been
completely read. The used input reel
should be removed and the next reel
(if any) should be mounted. Depressing
the start key will resume the processing.
If no more input, sense switch "F" on
and hit start for End-of-Job routine.
A-81
501, 502
Location Symbol Explanation (DECK 501 ONLY)
11503 HLTRT1 Tape Read Error. Correct tape and
start over.
13308 NONE Last Card, end of run.
13427 HLTWT2 End-of-reel halt. Output reel on unit
one is full. Remove filled reel and
replace with empty reel. Depress start
to resume processing.
13481 HLTWT1 Tape write error. Mount new tape and
start over.
14014 SWERR Error in columns 30-80 of the "Extra"
card.
N. Program Halts (DECK 502 ONLY)
Location Symbol Explanation (DECK 502 ONLY)
9986 HALTC1 Illegal punch in column I of "Control"
card. Check sequence of parameter
cards. Correct and start over.
10022 HALTC2 Illegal punches in columns 9-10 of
"Control" card. Check N, number of fields.
Correct and start over.
10189 HALTR1 Illegal punch in column 1 of a "Routine"
card. Check sequence of parameter
cards. Correct and start over.
10206 HALTR2 Illegal punch in columns 73-74 of
"Routine" card. Check sequence of
cards. Correct and start over.
10291 HALTR3 Illegal punch in column 3 of "Routine"
card. Check limits for EXAM 1.
Correct and start over.
10292 HALTR4 Illegal punch in column 4 of "Routine"
card check limits for EXAM 2. Correct
and start over.
10293 HALTR7 Illegal punch in column 7 of "Routine"
card. Check limits for EXAM A.
Correct and start over.
A-82
501, 502
Location Symbol Explanation (DECK 502 ONLY)
10310 HALTR5 Illegal punch in column 5 of "Routine"
card. Check limits for EXAM 3.
Correct and start over.
10327 HALTR6 Illegal punch in column 6 of "Routine"
card. Check limits for EXAM 4.
Correct and start over.
10440 HALTR8 Total of two times column 3 plus columns
4-7 exceeds 8 on "Routine" card.
Correct and start over.
10511 HALTR9 Illegal punch in column 8, 9, 10, or 11
of "Routine" card. Check limits for
Exams B, C, D, and E. Correct and
start over.
10566 HLTR10 Total of "Routine" card columns 8-11
exceed 4. Correct and start over.
10620 HLTR11 Illegal punch in column 77 of "Routine"
card. Check limits on input field
length. Correct and start over.
10711 HLTR12 Illegal punch in column 80 of "Routine"
card. Check limits on output field
length. Correct and start over.
10783 HLTR13 Illegal punch in "Routine" card. Input
length, column 77, is greater than
output field length, column 80.
Correct and start over.
10959 HALTE1 Illegal punch in column 1 of "Extra"
card. Check sequence of parameter
cards. Correct and start over.
11016 HALTE2 Illegal punch in column 11 of "Extra"
card. Correct and start over.
11086 HALTE3 Illegal punch in column 11 of "Extra"
card. Correct and start over.
Range is 1-6. ,
11157 HALTE4 Illegal punch in columns 9-10 of "Extra"
card. The value of "V" must be between
1 and 50. Correct and start over.
A-83
501, 502
Location Symbol Explanation (DECK 502 ONLY)
11193 HALTE5 Illegal punch in columns 7-8 of "Extra"
card. Value of "W" must be between
1 and 99. Correct and start over.
11224 HALTZ1 Illegal punch in column 1 of "Zone"
card. Must be a + punch (12 punch)
AND a zero or a one in this column.
Correct and start over.
11259 HALTZ2 Illegal punch in columns 1-80. Must be
a zero or a one in each column of the
"Zone" card. Correct and start over.
11562 HLTRT2 End-of-Reel Halt. This halt means that
the input reel on unit 4 has been
completely read. The used input reel
should be removed and the next reel
(if any) should be mounted. Depressing
the start key will resume the
processing.
If no more input, sense switch "F" on
and hit start for end-of-job routine.
11591 HLTRT1 Tape Read Error. Correct tape and
start over.
13408 NONE Last Card. End-of-Run.
13527 HLTWT2 End-of-Reel Halt. Output reel on unit
one is full. Remove filled reel and
replace with empty reel. Depress
start to resume processing.
13581 HLTWT1 Tape write error. Mount new tape and
start over.
14114 SWERR Error in columns 30-38 of the "Extra"
card.
A-84
15. 401, TRIP LINKING PROGRAM
IBM 1401/1410
A. Identification
Deck No.: 401
Written by: T. Synott, BPR, revised by C.E. Sweet, Jr.,
BPR
Assembly Date: March 24, 1965
B. Purpose
This program links all trip records with a "purpose to" or a
"purpose from," of "serve passenger" or "change mode of travel"
according to the concepts outlined in this volume beginning on
page IV-4. If desired it will also determine the zones of
production and attraction for each trip record and classify
records according to a standard general trip purpose
classification.
C. Data Preparation
Input data consists of one or more magnetic tapes containing trip
records formatted by the IBM 1401 Edit Program and sorted by any
of the sort routines according to sample number, person number,
and trip number; the field of major sort is the sample number.
The format is the same as that shown in the Standard Format Table
on page A-74 of this volume, except that only the sample number
may appear in card columns 71-76. Columns 61-70 may contain any
information desired for subsequent processing.
D. Card Format - Parameter Card
A parameter card is necessary to indicate the order of priority
for the modes of travel and the trip purposes used in the study.
The parameter card is loaded directly behind the program deck.
A-85
40l
Card columns Contents
1-10 Order or priority (from highest to lowest)
for the modes of travel used in a particular
study (maximum of 10 modes). Single digit
numbers are entered starting in column 1 and
unused columns are blank. Codes of 0 through
9 are allowed.
11-22 The trip purpose codes used in the survey,
maximum of 12, must be punched in a special
order from left to right. Single digit
numbers, 0 through 9, are allowed; (the two
zone punches are also allowed, if necessary).
The purpose codes of 0 through 9 can be
assigned in any order to the trip purpose
codes which are punched into card columns 11
through 20; the 11-zone punch is assigned to
the column 21 code and the 12-zone punch is
assigned to the code in column 22, if they
are used.
Trip purpose codes must be punched in the following order:
Card columns Contents
11 Home purpose code
12 Work purpose code
13 Shop purpose code
14 School purpose code
15 Social-recreation purpose code
16 Eat-meal purpose code
17 Personal business purpose code
18 Serve-passenger purpose code
19 Change-mode purpose code
20 Medical-dental purpose code
21 Miscellaneous purpose code No. 1, if necessary
(11-zone punch only)
22 Miscellaneous purpose code No. 2, if necessary
(12-zone punch only)
23-80 Blank
A-86
401
E. Output
Output data consist of one or more magnetic tapes containing
unchanged, linked, and adjusted records. Each linked record has
an 11-zone punch in column 60 and each adjusted record has a 12-
zone punch in column 60, for identification purposes. The format
of the output records from the linking option would be the same
as the input format except for linking identification punches in
column 60. The general purpose option permits the addition of a
general purpose in column 36. The output format from the general
purpose option is shown on page A-74, except that card column 60
is used for the linking identification punches and only columns
71-76 are used for the sample number. When both options are
used, the output format is the same as is shown on page A-74,
except for the linking identification punches and the sample
number field. The Trip Table Builder does not interrogate card
column 60.
A printed output is also included. An option provides for
printing all unchanged records as they are processed. After
processing a record, another option provides that the linked or
adjusted record may be printed and identified. After all of the
records have been processed, a line of totals is printed. The
totals include - the number of records read, the number of
records adjusted, the number of records requiring linking, the
number of linked records, and the number of records that required
no changes.
F. Method
This program consists of two basic options. The first option
(trip linking) causes each record to be examined to see if it
requires linking. Any record with a "purpose to" or a "purpose
from" of "serve passenger" or "change travel model' will be
linked. A home-to-home trip or trip codes in error in the
original data can be converted to a home-to-personal business
trip. Since all records have been sorted by sample number,
person number and trip number, the computer can trace all of the
trips which require linking in order to locate both the first and
last trip record for each group of records to be linked. The
records to be linked may be printed out and then the program
combines the necessary data from the first and last trip record
into one record which completely describes the linked trip. The
mode of travel code is assigned in accordance with the order of
priority in the parameter card. The "purpose to" and "purpose
from" are then checked for a home-to-home trip. At this point a
linked record or the record to be adjusted may be printed. A
home-to-home trip is then adjusted by changing the "purpose to"
of the first trip card to the personal business code and then
changing the "purpose from" code to the personal business code in
the last trip card of the group of records to be linked. At this
point an adjusted trip may be printed out.
The second option (general purpose) consists of two additional
steps. These steps put the basic trip data in a revised format
as required for gravity model analysis. Each trip record can be
examined to determine the zone which produces the trip and the
zone which attracts the trip. These zone numbers
A-87
401
are then transferred to the fields which previously contained the
zones of origin and destination. Each triprecord is then
examined to deter-mine the general purpose of the trip. The code
to identify the general purpose is inserted into column 36. The
following general purpose codes are always assigned based upon
the trip purpose codes as they are specified in the parameter
card. The program does not allow the general purpose codes to be
varied.
Home Based Trips
Purpose "to" or "from" General Purpose
Work 1
Shop 2
Social-recreational 3
School 4
Eat-meal 5
Personal business 5
Medical-dental 5
Miscellaneous No. 1 2
Miscellaneous No. 2 2
Nonhome Based Trips
Purpose "to" and "from" do not have a
home purpose code 6
The output record is written out on tape unit 3 in a format
identical to the input except for the following: 1) the linking
option provides identification codes in column 60; 2) when not
using the general purpose option, the zone numbers will remain as
origins and destinations; 3) the general purpose option changes
the zone numbers to production and attraction zone numbers and
inserts a general purpose in column 36.
G. Program Usage
1. Mount input tape on tape unit 2 and output tape on unit
3.
2. Load the condensed deck followed by the single control
card into the reader.
3. Set sense switches for the options desired (see I.
Options).
A-88
401
4. Sense switch G is normally "Off." This switch is turned
"on" in conjunction with switches E and F to bypass all printing,
switch G controls the printing of all error messages, end of tape
reel messages and the end of job message. The purpose of this
switch is to provide for a user without an on-line printer. The
Halt locations should be consulted when using this option.
5. Sense switch D must be turned "on" at the start of
processing the last input tape; a message is written and a halt
occurs at the end of each input so that the sense switch may be
changed, when necessary. In the case of a single input tape
sense switch D is "on" at the beginning.
6. Push LOAD.
7. For all halts (see L. Program Halts).
8. For all messages, follow printed instructions or see K.
Error Messages.
H. Tapes
Input tape(s) must be mounted on tape unit 2, and output tape(s)
on tape unit 3. This program requires that there be no header
labels on the input tapes.
I. Options
1. If Sense switch B is "on" - only the general purpose
option is to be used. No trip records will be linked if this
switch is "on."
2. If Sense switch C is "on" - only the trip linking
option is to be used. The general purpose will not be added and
the zones of production and attraction will not be determined if
this switch is "on."
3. If Sense switches B and C are "off" - both the linking
and general purpose options are to be used.
4. Sense switch E controls the printing of the linked and
adjusted records. If sense switch E is turned "on," the linked
and adjusted records will not be printed.
A partial run of the program might be checked with Sense
switch E "off" to see if the program is operating on the purpose
codes in the required manner. With Sense switch E turned "off,"
each recor d to be linked will be printed followed by the message
"record to be linked"; second, the linked record will be printed
followed by the message "linked record"; third, any record to be
adjusted will be printed followed by the message "record to be
adjusted"; and last, the adjusted record is printed followed by
the message adjusted record." After the partial run has been
checked, the full run could be made with Sense switch E "on" to
cut down on the running time. The switch may be turned on and
off during operation.
A-89
401
5. A fifth option is also available, but it should not be
used unless absolutely necessary. The option to print each
unchanged record followed by the message "unchanged record" is
controlled by sense switch F. The printing will occur with Sense
switch F "off." The use of this option for an entire run will
more than double the running time of this program. This switch
may be turned on and off during operation.
6. A sixth option is controlled by switch G in conjunction
with switches E and F. If switches E, E and G are "on," all
printing is bypassed.
J. Timing
The running time on this program is approximate only. Recently,
22,000 records were run in about 45 minutes on an IBM 1401. Both
the linking and general purpose options were performed on these
data records and some printing was obtained.
K. Error Messages
Special error messages will be printed for two halt conditions
(see HAITI and HALT, in L. Program Halts). For each case, the
carriage is double spaced and the card which was in the print
area is printed on the first line. On the second line, the B
address register is printed first followed by the card which is
in the input area. The B address register gives the location of
the next sequential instruction after the halt (to identify the
halt), and the input are a provides the next card to be
processed. These data should enable the user to locate the cards
which are causing these particular errors. These halts are
irrevocable.
L. Program Halts
Message Symbol Location Explanation
"END OF INPUT REEL CHNGE 3495 End-of-reel on tape
ON UNIT 2. MOUNT unit 2. For multiple
NEW TAPE AND SWITCH input reels, mount the
D ON IF LAST INPUT. next input tape on
PRESS START TO unit 2, check if
CONTINUE. switch D is needed
and press start
Last card printed, HALT1 3881 Press start to print
B address register, the error message.
and the card in The error message will
the input area assist in locating
printed. the card which has
caused the error, as
the number of trip
cards to be linked
has exceeded the
maximum of 30. See
ERROR, halt location
7155.
A-90
401
Message Symbol Location Explanation
Last card printed HALT 4274 Press start to print the
B address register error messages. There is an
and the card in the invalid unequal compare and
input area printed. the error messages will assist
in locating the card which has
caused the error. See ERROR,
halt location 7155.
Total and "END HALT3 4777 End-of-job.
OF JOB."
"BAD PURPOSE CODE HALT4 6162 Invalid purpose codes in trip
IN ORIGINAL CARD. purpose columns. The card
PUSH START TO has been printed. Push start
MAKE A PERSONAL to make a home to personal
BUSINESS TRIP business trip out of it. New
OF IT." card is printed.
None ERROR 7155 This halt is caused by HALT or
HALT1. Check the address at the
beginning of the second line of
the error message to identigy
the halt location. See K. Error
Messages.
"END OF OUTPUT HALT7 7203 End of reel on tape unit 3.
REEL ON UNIT 3 For multipled reels, mount a
MOUNT NEW TAPE new output tape on unit 3 and
AND PRESS START press start.
TO CONTINUE."
"READ ERROR TAPE X" None 7385 Tape read or write error on
or tape unit 2 or 3. Press start
"WRITE ERROR TAPE X" to try 10 or more times. For
a read error, skip record
manually, if permissible. For
a write error, mount a new tape,
reload the program and begin
again.
A-91
Appendix III
STANDARD FORMATS
The following sections include standard data input and output formats and
standard control card formats for both the BELMN monitor and for subject
programs
1. BELMN Submonitor Control Cards
Title of Card Columns Contents
Remarks 1 "*"
3-72 Any alpha-numeric message
desired
Pause 1- 2 "**"
3-72 Any alpha-numeric message
desired
Program call card 1- 2 "PR"
(For a binary program 4- 6 Program number, right-
number) justified
7-72 Blank or as desired
Program call card 1- 5 "PROG."
(For a 6-character BCD 6 Blank
program name) 7-12 Alpha-numeric program name,
exactly as it appears in
the program.
Time cards 1-2 "TS"-for time at start
1- 2 "TP"-for the time since
last time card
1- 2 "TJ"-for total time since
start
3-72 Anything desired
A-93
Title of Card Columns Contents
Load card 1- 4 "LOAD"
7-72 blank or as desired
System card 1- 6 "SYSTEM"
7-72 blank or as desired
2. Program Control cards
Those cards which remain the same from program to program will be
described here and referred to in the abbreviated program descriptions.
Title of Card Columns Contents
Identification 1-71 These columns will be used
to identify the output data
for off-time printing.
72 "1" (necessary to identify
the card)
Parameter 1-36 Options for this particular
program. Specified by
punching a "1" in the
specific column of the
option desired. If the user
does not wish to express
the option, the card column
should be left blank.
This card varies sufficiently that its content will be described in each
writeup.
72 "2" (necessary to identify
the card)
Zone Selection
This card is used to designate the zones or series of zones to
be selected for processing in a particular program. The zones to
be included are specified in columns 1 to 66, in a format of 6
column fields. In preparing the card, place the first zone right-
justified in column 6. If it is to be a single zone a comma (,)
should follow in column 7. If it is to be the first zone of a
consecutive series, punch -the last zone of the series in column 12
(right-justified), followed by a comma if more zones are to follow.
Additional single zones or series of zones may be selected by using
the successive 6 column fields through card column 66. Any combi-
nation of grouped and single zone selections may be made as long as
column 66 is not exceeded. A "3" punch in column 72 is required to
identify the zone selection card.
A-94
For example, suppose zones 6, 9-15, 18-20, 27, and 133 are to
be selected. The control card would be as follows:
Columns Contents
6 "6"
7 "," (comma)
12 "9"
17-18 "15"
19 "," (comma)
23-24 "18"
29-30 "20"
31 "," (comma)
35-36 "27"
37 "," (comma)
40-42 "33"
72 "3"
Tape Assignment
This card allows the user to designate, at run time, the
specific input and output tape units to be used by the program. It
is composed of two-column fields separated by commas. The last
tape punched must be followed by a blank. The normal assignments,
as described in the program description, will be used if the user
does not reassign a particular tape unit. If a tape unit is to
remain unchanged the user may punch the corresponding field with a
zero, or a comma may be punched immediately following the preceding
comma. The first blank column which is encountered will terminate
the reassignment of tape units. This card is identified by a "0"
(zero) punched in column 72.
A-95
Field Number Columns Contents
1 1- 2 Channel and unit for Tape 1
3 "," "," (comma)
2 4- 5 Channel and unit for Tape 2
6 "," "," (comma)
3 continue as above
72 "0" (zero)
When this card is required in a particular subject program, the
tape units to be used in that program will be defined in terms of
the Tape Assignment Card field number as used directly above.
The tape assignment card should always be present if the option
to read control cards from the card reader is used.
3. Binary Tape Formats
(a) Binary Network Descriptions
The binary network description consists of a single
record on tape composed of 4N+1 words, when N is the number of
nodes in the system. The first word contains four times the
highest node number (the count of words in the record excluding the
first word). Taken in groups of four, the remaining words of the
record describe the links from a common node (A node). In each
word, bits 6-17 (decrement) indicate the connecting node (B node).
Thus, the A node is determined by word position in the record and
the B node is designated in the decrement portion of the word. The
remainder of the word contains the descriptive information about
the link. Unused words are filled with zeros.
The complete word format is:
Word Bits Contents
Sign Director of link
1- 4 Turn prohibitors for links connected
at the B Node
5 Not used
6-17 B node
18-19 Municipality or jurisdiction code
20 Flag
A-96
Word Bits Contents
21-26 Distance (in 63rds) from A to B
27-29 Not used
30-35 Time (in 63rds) from A to B
Further information on the network description and
its creation is available in the Traffic Assignment Manual(1).
(b) Binary Loaded Network
This file is composed of three records. The first
record is the same as the network description (see above), except
that in each word the tag (bits 18-20) is blank and the address
(bits 21-35) contains link volume rather than time and distance.
To eliminate overflow possibilities, the volume in the record is
one-fourth the actual volume assigned to the link.
The second record is a turn table containing a "2"
in the decrement of the first word and the remaining word count in
the address. The turn table consists of two words for each four-
way arterial and for each freeway node. The relative position in
the record determines the A node of the word pair beginning with
the first designated turn node and continuing to the last
designated turn node. The decrement contains the B node, and the
address contains one-fourth of the turn volume between the B node
indicated and the highest node connected to Node A.
(c) Binary Trip Table
This tape is in the form of a single file composed
of N records, where N is the number of zones. Each record contains
N+1 words. The first word of the record is the identification word
with the decrement containing the origin zone number and the
address containing N. The second word contains the integer trips
from the origin zone to zone one. The third word contains the
trips to zone two, and so on until all zones are accounted for, The
origin zones are in ascending order on the tape.
(d) Binary Skim Tree
The binary skim tree file is exactly the same as the
binary trip table file (see above) except that trips are replaced
with whole minute times between zone pairs.
4. BPR Trip Record Formats
Detailed descriptions of the information contained in the
various types of survey cards are available in the Traffic
Assignment Manual(1). The procedures to follow in building trip
tables from these cards are also described in this publication.
A-97
Appendix IV
DETAILS OF BELMN OPERATIONS
The user must initiate the BELMN submonitor by calling in the two
programs which comprise the control program (PR-101 and PR-102).
This may be done in several ways:
(1) Using a small program called the BELMN loader under the
control of the Senior System.
(2) Mounting the Library Tape on unit Al and pressing "Load
tape."
(3) Using a binary BELMN loader in the on-line card reader
and
pressing "Load cards."
In all of these cases the following sequence of instructions must
be placed in core storage and executed:
1 8 16
BELMN REWX T
RTBX T
RCHX BELMN+6
TCOX BELMN+3
CLOCKE NOP HUB
TRA START
IORP SELFLD,,-1
MONITR BCI 1,
SELFLD BOOL 75
START BOOL 64000
NOCLOK BOOL 135
HUB EQU 6
X refers to Channel (A or B)
T refers to Unit (1-10)
These instructions must also remain in storage, as described above,
to allow re-initiation of the control program and to insure it is
resident in core storage. The BELMN loader should be located
starting at location 2150 (octal), though by revising the transfer
vectors (see Traffic Assignment Manual(1)) this may be changed as
desired.
A-99
The BELMN loader reads the first two records from the tape unit
specified in the loader (this may be varied) and places them in
storage. The first record (PR-101) is loaded into locations 100-
2000 (octal), and second record (PR-102) is loaded into locations
64000-64777 (octal). Included as part of the second record is the
resident portion of the BELL system which is loaded into locations
0-77 (octal) and 65000-77777 (octal) of core storage. The first
record contains the transfer table, the input-output subroutines,
and the other subroutines used by the subject programs. The second
record is the portion of the control program which performs the
various operations required to-link subject programs together and
maintain continuous operation. These operations are requested by
means of several control cards which may be prepared by the user.
Control of processing must reside with BELMN for these cards to be
valid. As BELMN was originally developed for use under the control
of the BELL Monitor, the BELL system is also included with BELMN to
make available the BELL subroutines.
Format details for the control cards used with BELMN are summarized
in appendix III, part 1. The uses of these cards will be described
in the following material. Communication with the machine operator
to allow input-output tape changes and other run-time modifications
is accomplished with Remark and Pause Cards. The message on a
Remark Card is written on-line and on the system print tape. A
Pause Card, in addition to being written on-line and on the system
print tape, causes the machine to halt. When the operator presses
"START" program execution continues.
When a Program Call Card is encountered, the BELMN control program
searches the BELMN program library tape until it finds the required
program. It then begins loading the subject program into storage.
Two types of Program Call Cards are now available; one for programs
with a binary number as the program name, the other for programs
with a BCD program name of up to 6 characters. The first word of
the program record on the program library tape contains the program
name in one of two forms: (1) as a binary number in the decrement
(left half) of the word, or (2) as a BCD word of 6 characters.
Time cards are used to keep track of the running time of an entire
job or various portions thereof. The use of the three time cards
as described in the Traffic Assignment Manual(l) is no longer
required. If they are omitted, the BELMN control program
automatically clocks each program and records the running time on
the system print tape. However, the "TJ" card should be used as
the normal end to the processing of BELMN programs and to cause a
return to the senior monitor in control. If other control cards
are used for this purpose the machine may halt, or an incorrect
return may be taken. If the user's computer installation does not
have the same clocking method as used in the BELMN Control Program,
the BELMN loader may be used to modify the clocking operation. If
the clock is interrogated through a printer hub other than 6, this
may be changed by modifying the instruction:
HUB EQU 6
A-100
If the user does not desire to make use of the clock at all, the
symbolic location "CLOCKE" in the loader should be changed to:
CLOCKE TSX NOCLOK,4
Two special purpose cards are also available to the user. The
"SYSTEM" card causes a transfer to the BELL system portion of the
control program (be sure that it is still resident in core) to
allow the processing of BELL system control cards. Refer to the
Traffic Assignment Manual(l) for a description of these cards and
their uses. The "LOAD" card simulates a tape load and performs the
same function as pressing "LOAD TAPE" on the console. This allows
the user to initialize a system from tape Al to storage, as
desired.
Each subject program processes the control cards necessary to
specify the parameters for the run. At the end of the subject
program run, control is returned to the BELMN control program. The
programmer should refer to the Traffic Assignment Manual(l) for the
specific return procedures to be employed in given instances. At
this point the control program continues processing BELMN control
cards and initiating subject programs as requested by the user
until control is relinquished to the installation's senior monitor.
By specifying the system which has control (BELL, IBSYS, or FORTRAN
MONITOR) in the BELMN loader, the user is able to gain and
relinquish control in almost any commonly used system. The system
actually in use is specified by using one of the following
instructions in the symbolic cell "MONITR" in the BELMN loader:
8 16 (í = zero)
BCI 1, íMONTR (FORTRAN MONITOR)
BCI 1, íIBSYS (IBSYS)
BCI Anything else (BELL)
Certain tape units are always required for each job run. Tape unit
A2 for card input (unless sense switch 5 is on) and tape unit A3
for printed output are fixed and required by all subject programs.
If BELMN is operated under a system, several system tapes may be
required, including the system tape, an accounting and general
purpose scratch tape, and a tape for punched card output. Other
tapes may be required depending upon the system used. This should
be checked by the user at the installation where runs will actually
be processed. In addition, one tape unit will be required for the
BELMN program library tape. At present, the program library tape
generally is placed on tape unit A8, although this may be modified
by changing the loader as described above. It should also be noted
that any time the BELL system included with the BELMN control
program is in use, it may require some of the above mentioned
system tapes.
The fixed tape requirements of the BELL System may be found in the
Traffic Assignment Manual(1).
A-101
Appendix V
REFERENCES
(1) Traffic Assignment Manual, by the U.S. Department of
Commerce, Bureau of Public Roads, Office of Planning, Urban
Planning Division, Washington, D.C., June 1964; available from
Superintendent of Documents, U.S. Goverment Printing Office,
Washington, D.C. 20402.
(2) Traffic Assignment and Distribution for Small Urb an
Areas, (IBM 1620) by U.S. Department of Commerce. Bureau of Public
Roads, Office of Planning, Washington, D.C., October 1963,
Superintendent of Documents, U.S. Goverment Printing Office - out
of print.
(3) Calibrating and Testing a Gravity Model with a Small
Computer, (IBM 1401) by U.S. Department of Commerce, Bureau of
Public Roads, Office of Planning, Washington, D.C., September 1965;
available from Superintendent of Documents, U.S. Government
Printing Office, Washington, D.C. 20402.
(4) A Comparative Evaluation of Trip Distribution Procedures,
by Kevin E. Heanue and Clyde E. Pyers, presented at 44th annual
meeting of the Highway Research Board, January 1965, to be
published.
(5) A General Theory of Traffic Movement, by A. M. Voorhees,
The 1955 Past President's Award Paper, Institute of Traffic
Engineers, Special Report.
(6) Principles of Social Science, by H. C. Carey, J. B.
Lippincott and Co., Philadelphia, Pennsylvania, 1858-59.
(7) The Laws of Migration, by E. G. Ravenstein, Journal of
the Royal Statistical Society, No. 48, 1885, PP- 167-235, and No.
52, 1889, pp. 241-305.
(8) The Movement of Farm Population, by E. C. Young, Cornell
Agricultural Experimental Station Bulletin 4269 Ithaca, New York,
1924.
(9) a. The Law of Retail Gravitation, by W. J. Reilly,
Fillsburg Publishers, New York, 1953.
b. Methods for the Study of Retail Relationship,
by W. J. Reilly, University of Texas, Bureau of Business Research,
Research Monograph No. 4 (University of Texas Bulletin No. 2994),
November 1929.
A- 103
(10) a. The PIP2/D Hypothesis: The Case of Railway Express,
by G.K. Zipf, Journal of Psychology, vol. 22, July 1046, pp. 3-8.
b. Human Behavior and the Principle of Least
Effort, by G.K. Zipf, Addison-Wesley Press, Cambridge, 1949.
(11) Formulation, Analysis and Testing of the Interactance
Hypothesis, by J. A. Cavanaugh, American Sociological Review, April
1950, PP. 763-781.
(12) The Interactance Hypothesis: A Gravity Model Fitting
Physical Masses and Human Groups, by S. C. Dodd, American
Sociological Review, April 1950, pp. 245-256.
(13) Spatial Interactions and the Urban-Metropolitan
Description, by J. D. Carroll, Traffic Quarterly, April 1955, PP.
149-161.
(14) Estimating and Forecasting Travel for Baltimore by Use of
a Mathematical Model, by A. M. Voorhees and R. Morris, Highway
Research Board Bulletin 224, 1959, PP. 105-114.
(15) Accessibility and Residential Growth, by W. G. Hansen,
Unpublished Master Thesis, Massachusetts Institute of Technology,
1959.
(16) Evaluation of Gravity Model Trip Distribution Procedures
by W.G. Hansen, Highway Research Board Bulletin 347, 1962, pp. 67-
76.
(17) a. Projection of Population, Employment and Trip
Desires from Home to Work (for the San Mateo County Transportation
Study), Stanford Research Institute, pp. 5-6.
b. Manual for the Gravity Model Computer Programs-
-Developed for the San Mateo County Traffic Ways Study, Stanford
Research Institute Project No. IE-3961, July 1962.
(18) Forecasting Peak Hours of Travel, by A. M. Voorhees,
Highway Research Board Bulletin 203, 1958, pp. 37-46.
(19) For example, compare traveltime factors derived for
Hartford, Connecticut (31), Baltimore, Maryland (14), Southeast
Connecticut (32), Washington, D.C. (22), and the Iowa Seven Cities
(35).
(20) Factors Affecting the Amount of Travel, by J. C. Tanner,
Department of Scientific and Industrial Research, Road Research
Technical Paper No- 51, London, 1961.
(21) Graphical and Mathematical Investigation of the
Differences in Traveltime Factors for the Gravity Model Trip
Distribution Formula in Several Specific Urban Areas., by Richard
E. Whitmore, Civil Engineering Department, University of Tennessee,
April 1965.
A-104
(22) The Use of Gravity Model for Forecasting Urban Travel--An
Analysis and Critique, by Richard J. Bouchard and Clyde E. Pyers,
presented at the 43rd annual meeting of the Highway Research Board,
January 1964, to be published.
(23) An Evaluation of Simplified Procedures for Determining
Travel Patterns in a Small Urban Area, by Constantine Ben, Richard
Bouchard, and Clyde E. Sweet, Jr., presented at the 43rd annual
meeting of the Highway Research Board, January 1964, to be
published.
(24) The Adequacy of Clustered Home Interview Sampling for
Calibrating a Gravity Model Trip Distribution Formula, by Kevin E.
Heanue, Lamelle B. Hamner, and Rose M. Hall, presented at the 43rd
annual meeting of the Highway Research Board, January 1964, to be
published.
(25) Manual of Procedures for Home Interview Traffic Study--
Revised Edition, by the U.S. Department of Commerce, Bureau of
Public Roads, October 1954.
(26) External Survey Manual, Niagara Frontier Transportation
Study Manual; New York State Department of Public Works,
Subdivision of Transportation Planning and Programing; Albany, New
York, December 1962.
(27) Truck and Taxi Survey Manual, Niagara Frontier
Transportation Study Manual, New York State Department of Public
Works, Subdivision of Transportation Planning and Programing;
Albany, New York, December 1962.
(28) Vehicular Trip Distribution by Successive Approximations,
by T.J. Fratar, Traffic Quarterly, vol. 8, No. 1, January 1954, PP-
53-65.
(29) Evaluation of Gravity Model Trip Distribution Procedures,
by W.G. Hansen, Highway Research Board Bulletin 347, 1962, pp. 67-
76.
(30) New Orleans Metropolitan Area Transportation Study, vol.
1, 1961, and vol. 2, 1962.
(31) Integrating Land Use and Traffic Forecasting, by C. F.
Barnes, Highway Research Board Bulletin 297, 1961, pp. 1-13.
(32) A Program of Integrated Planning for Long-Range Land Use
and Transportation Development of the State of Connecticut,
Prospectus, December 1962.
(33) a. Gravity Model Procedures Used by Iowa Planning
Survey, by J.J. Pipan, U.S. Bureau of Public Roads, Region 5,
Kansas City, Mo., 1962.
b. A Simplified Method for Forecasting Urban
Traffic, by R.H. Wiant, Highway Research Board Bulletin 297, 1961,
pp. 128-145.
A-105
