PUBLIC AND PRIVATE TRANSPORTATION:
COSTS OF VARIOUS MIXES
by
Michael Jacobs
B.C.E., The Cooper Union
(1962)
Submitted in partial fulfillment of the
requirements for the degree of
MASTER IN CITY' PLANNING
at the
Massachusetts Institute of Technology
1964
Signature of Author
Department ofT.l g ty And Regionial Planning
) .August
24, 1964
Certified by
1%esis Supervisor
Accepted by
Chairman, Departmental Committee
on Graduate Students
ABSTRACT
Title of Thesis: "Public and Private Transportation: Costs
of Various Mixes."
Thesis Advisor: Dr. Aaron Fleisher, Associate Professor of
Urban and Regional Studies.
The question of the efficiencies of various modal
splits is a very important question, but it is also an extremely large one. Certainly, it is not a question to which
there is a single answer; rather, the key to its solution
lies in the accumulation of bits and pieces of pertinent
knowledge.
This thesis is concerned primarily with the costs (as
opposed to the benefits) of the urban transportation system,
and the prime variables investigated are modal split and
urban form. Six different forms of the city, in abstracted
form, are described by specifying their geometry and the
locations and densities of residences and working places.
A previous study, for each of these six cities, has, utilizing an electronic computer, generated traffic flows over a
free surface (i.e., there are no defined transportation networks), and counts of the flows have been taken, in various
directions, through each one-mile square block of area.
The current experiment, utilizing this basic data, defines transrortation networks for the six cities, and assigns to these, for a range of five different modal splits,
the traffic flows for public and private transportation.
Unit costs are then specified, and for each of the thirty
combinations of modal split and city form, computations are
made of capital and maintenance costs, of operating costs,
and of time costs.
The validity of the experiment is, of course, quite
limited, but within the confines of these limitations, the
following observations were made. Increasing the percentage of public transportation generally decreased the per
capita capital costs and operating costs of the total transportation systems, but increased the average door-to-door
journey times. Public transportation was more economical
in areas of higher densities. Subway construction (excluding right-of-way costs) was uneconomical at even the maximum densities used in this experiment.
Per capita capital and maintenance costs were lowest in
the many-centered city and highest in the homogeneous city.
And the average trip times and operating costs for the doorto-door journey were lowest in the central city and highest
in the ring city. It does seem likely, however, that these
observations are very strongly influenced, not only by the
unit costs, but also by the densities of the cities.
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ACKNOWLEDGEMENT
The author would like to extend his thanks to Professor
Aaron Fleisher of the M.I.T. Department of City and Regional
Planning.
His debt to Dr. Fleisher is threefold: for his
original suggestion of the basic topic of this thesis; for
the use of the results from his experiments on travel and
the form of the city; and especially, for his sage advice
during the development of the entire thesis.
Thanks is also extended to Mr. Ronald Rice for the use
of some calculations supplemental to his S.M. Thesis.
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TABLE OF CONTENTS
Page
I. Introduction
1. Discussion of the modal split problem...
2. Further directions of the thesis........
II. Procedure
1. Background..............................
2. Assignment of traffic flows............. . ......
20
3. Selection of transportation facilities.. .......24
26
4. Selection and calculation of costs...... ..
III. Results and implications
1. The results and their interpretation...........34
2. Comparison with the results of other studies...51
3. Recommendations for future study.............57
IV. Bibliography.....................
......
. .
.. 60
V. Appendix A--Total traffic flows................. .. 62
VI. Appendix B--An investigation of various methods
of varying the modal split................... .. 69
VII. Appendix C--Peak directional flows for the
various modal splits......................... .. 73
VIII. Appendix D--Tabulations of peak one-directional
flow characteristics.........................105
IX. Appendix E--Sample calculation of costs..........112
-iii-
TABLE OF ILLUSTRATIONS
Page
Figure 1. The central city..............................11
Figure 2. The quasi-central city.......................13
Figure 3. The many-centered ct............1
Figure 4. The layered city..........................
Figure 5. The homogeneous city..........................15
Figure 6. The ring city....................16
Figure 7. The decision functions........................17
Table 1. Automobile and road costs......................30
Table 2. Bus costs...........
.....
.
.............
.31
Table 3. Rail costs....................................32
Table 4. Summary of costs for the central city..........35
Table 5. Summary of costs for the quasi-central city....36
Table 6. Summary of costs for the many-centered city....37
Table 7. Summary of costs for the layered city..........38
Table 8. Summary of costs for the homogeneous city......39
Table 9. Summary of costs for the ring city.............40
Figure 8. Graph of per capita capital and maintenance
cost vs. modal split.................................41
Figure 9. Graph of per capita operating cost vs. modal
000
...........
42
split. 0.............................
Figure 10. Graph of average door-to-door journey time
vs. modal split......................................43
Figure 11. Traffic flow in the central city.............63
Figure 12. Traffic flow in the quasi-central city.......64
Figure 13. Traffic flow in the many-centered city.......65
Figure 14. Traffic flow in the layered city.............66
Figure 15. Traffic flow in the homogeneous city.........67
Figure 16. Traffic flow in the ring city................68
Figures 17-21. Peak one-directional flows for the
central city.........................
........
75-79
Figures 22-26. Peak one-directional flows for the
quasi-central city...............................80-84
Figures 27-31. Peak one-directional flows for the
many-centered city................................85-89
Figures 32-36. Peak one-directional flows for the
layered city.....................................90-94
Figures 37-41. Peak one-directional flows for the
homogeneous city.................................95-99
Figures 42-46. Peak one-directional flows for the
ring city.......................................10-104
Table 10. Tabulation of peak one-directional flow
characteristics for the central city...............106
Table 11. Tabulation of peak one-directional flow
characteristics for the quasi-central city..........107
Table 12. Tabulation of peak one-directional flow
characteristics for the many-centered city..........108
Table 13. Tabulation of peak one-directional flow
characteristics for the layered city................109
Table 14. Tabulation of peak one-directional flow
characteristics for the homogeneous city............110
Table 15. Tabulation of peak one-directional flow
characteristics for the ring city...................111
-iv-
INTRODUCTION
1. Discussion of the modal split problem
Frequent reference is made these days to the "transportation problem," and much work is being done in the field
But just what is the "trans-
of transportation research.
portation problem?"
Before one can seek out any solutions,
he must know specifically the questions to which he is
seeking the answers.
And certainly, the "transportation
problem" is an exceedingly complex one.
One of the questions it frequently poses inquires as
to the efficiencies of the various modal splits; i.e., given
two or more modes of travel between two points, what will
be the comparative costs and benefits associated with the
various possible combinations of amounts of travel by the
different modes.
There are many criteria which must be
considered before any solutions to this question can be attempted: construction costs of the transportation facilities;
aesthetic and financial effects on property near-by and adjacent to the transportation facilities; transportation
operating costs; speed of travel; comfort and convenience
levels; social acceptability.
Then, too, the evaluation of
the various criteria will vary greatly according to the
perspective through which the problem is being viewed; by
the individual traveler or user of transportation, for
example, or by the planners or decision makers in metropolitan management.
-I-
-1
-2From the point of view of the transportation user,
travel is a cost item (costs being measured in terms of
money, time, and discomfort) to be expended for a return
of some type.
That is, the transportation user will attempt
to minimize the sum of his transportation costs in relationship to the rewards and gains he will reap at the destination of each trip, such as financial gains and residential
and recreational satisfactions. 1
Consequently, the mode of
travel chosen by the traveler will depend on many interrelated factors, especially: the different modes of travel
available to him; his car ownership status; the quality of
transit service relative to the degree of congestion he is
likely to encounter on the roads; and the parking facilities
available at his destination. 2
(It will also depend to
some degree on the amount of transportation being purchased
by the consumer.
Some people purchase so little trans-
portation that mass transportation will always be more
economical.
There are, too, other persons who, for reasons
of age or disability, cannot drive.
However, most people
do purchase enough transportation so that they will allocate
their trips according to the relative costs of the alternative modes of travel available).
1 R.L.
Creighton, D.I. Gooding, G.C. Hemmens, J.E. Fidler,
"Optimum Investment in Two-Mode Transportation Systems,"
(paper presented at the 43rd annual meeting of the Highway
Research Board, January, 1964).
2 J.D. Carroll, Jr., R.L. Creighton, J.R.
Hamburg, "Transportation Planning for Central Areas," journal of the
American Institute of Planners, February, 1961.
I
-3The transportation planners, though, who must decide
where, when, and what kind of transportation facilities
should be built, must view the modal split problem in a
broader light than the individual transportation user.
The
planners must weigh the costs and benefits accruing to all
interested parties: not only the transportation users, but
also the adjacent property owners, the persons who would
be displaced by construction of the transportation facilities,
and the general public (which supplies the revenue with
which the government operates).
It is in this perspective that the present thesis is
viewing the problem of the modal split.
More specifically,
it is attempting to develop a technique and produce some
results, using a range of modal splits and one particular
set of "typical" standards and assumptions, which can be of
some service to the transportation planner and designer.
It is true that much material has already been produced
which offers recommendations on the modal split question. 3
It is also true that much of this material is of a rather
generalized nature.
For example, it can be said that in
medium to low density areas, individual modes of travel
will generally be cheaper, while in very high density areas,
the group modes of travel may well be equal to or even
lower in cost than the individual transportation modes. 4
3 Some
of these studies are cited later in the text, particularly in sections 1.1 and 111.2.
4 R.L. Creighton et. al., op. cit.
L
-4This is certainly useful information, but it does require
considerably more information than this to decide on a
specific type of transportation system for a city.
Then,
too, conclusions are often based almost entirely upon
historical data, which is a necessary, but not a neces-
sarily sufficient criteria upon which to project trends in
transportation.
These should not be construed as criticisms, but
rather as observations; the nature of the modal split prob-
lem is not generally such as to be readily conducive to
specific, reliable, easily obtainable answers or conclusions.
The historical evidence relating to travel patterns and
modal split may seem clear enough:
... It is well known that high densities and starshaped settlement patterns with extensive transit
systems have characterized those large cities which
experienced heavy growth before the advent of the
automobile as a major transport carrier. The growth
of cities since the development of the automobile has
been at lower density and has been less centralized.
This tendency of recent growth to be at low densities, with decentralization of nonresidential activities and with provision for parking, clearly makes
mass transit more difficult to provide. First, any
mass-transportation line will run through terrain
which has a lower population and hence a lower number
of potential passengers per square mile. Second, the
dispersion of nonresidential activities works against
the centripetal-centrifugal movement characteristics
of a highly centralized region. With more dispersed
work places available, there will be a reduction in
the potential number of centrally oriented passengers
per square mile. The CBD with its high density,
centralized, nonresidential activities, fulfills the
ideal conditions necessary for efficient, economical
mass transit. 5
5 J.D.
Carroll, Jr. et al., op.
cit.
-5Or, in other words, transit travel may be said to be predominantly focused on the central business district, whereas automobile travel is diffused throughout the urban area.
It is also true that in all but a few large cities, the
automobile at present accounts for more than 85 percent of
all urban travel, and is usually the dominant form of
transportation for persons entering the downtown area. 6
But historical experience is limited, and the abstraction of even the observed experiences into an hypothesis
on the effects upon the city of different modal splits
is not a simple procedure.
While it often is asserted that highway oriented
urban transportation systems are the undoing of cities
and, conversely, that mass or, better, rapid transit
their salvation, there is little historical evidence
to support a conclusion one way or the other on this
issue....CBD's and central cities have both prospered
and languished with and without rapid transit. Furthermore, relatively less rapid growth has occurred
in CBD's than either central cities or SMSA's as a
whole whether or not rapid transit is available. At
best, rapid transit appears to slightly decelerate the
tendency toward relative dispersion and provides a
very minimal aid, and certainly no guarantees, in
preventing an absolute decline in a CBD. 7
Because, then, of the inconclusiveness of the historical evidence, because of the great variance of costs and
values from city to city, and because of the over-all complexity of the problem, the modal split question must be
construed as being the aggregate of many smaller, more
6 Wilbur
Smith and Associates, "Future Highways and Urban
Growth," New Haven, Conn.: 1961.
7 J.R. Meyer,
J.F. Kain, and M. Wohl, "Technology and Urban
Transportation," Executive Office of the President, Office
of Science and Technology, 1962.
-6specific questions, and great care must be exercised in
answering any of these questions.
The current thesis is
attempting to deal with the question of what costs are
associated with different modal splits for different forms
of city.
The answers obtained will be, of course, partial
answers; many assumptions of unit costs and operating criteria have to be made, so that the conditions under which
the study is being conducted, while intended to be realistic,
nevertheless embrace only a minute proportion of the innumerable sets of conditions which are conceivable.
The
results, then, must be treated with caution; the inferences
drawn from these must be quite limited in their scope of
application.
Still, they should add just that much more
to the slow accumulation of bits of knowledge in the transportation field.
2. Further directions of the thesis
As noted, transportation must be measured in terms of
costs, with respect to the quality of service provided.
Unfortunately, both costs and quality of service contain
many quantities which cannot be easily measured and evaluated in an objective, systematic manner, (e.g., the waiting
period for public transit, noise levels, the views provided
on the journey, the comfort of seating--or standing--facilities, the ability to smoke or read or listen undisturbed
to the radio).
Consequently, rather than grasp for the
elusive and intangible without first investigating the
-7more feasible and promising, this thesis will concentrate
on some of the more readily definable and measurable costs
of urban transportation systems--in general, those to which
a monetary measure can be most easily applied.
These in-
clude physical costs (construction plus maintenance costs)
for the transportation facilities, operating costs, and
time costs (although these costs are given simply in units
of time--no attempt is made to apply a monetary value to
them).
Of course, any set of costs must assume some level of
quality of facilities and services provided.
In this thesis,
the nature of the transportation facilities is considered
to be generally equivalent to modern, present-day, bus,
rail, and highway standards.
A full, more detailed des-
cription of the qualities of the transportation facilities
and services would be difficult to draw, lengthy, and not
always very meaningful in light of the degree of precision
of the cost figures being used.
There are many variables involved in the modal split
problem.
Primary among these is the transportation system
itself; the modal split can embrace many different forms
of travel.
In this thesis, however, the modal split will
hereafter be used to refer to the split between public and
private transportation.
Private (automobile) transportation
and public (mass) transportation will, in turn, embrace
various forms of individual modes and group modes of travel,
respectively.
WOMEN
-8Among the other major variables in the modal split
problem are land use patterns and densities, population
characteristics, and transportation technology.
It would
be cumbersome indeed to investigate all of these in a single
study.
Consequently, in addition to modal split, only city
form will be dealt with in this 'thesis as a major variable.
The general form of the American city today is comprised
of the dense core or central business district surrounded
by lower density "urban sprawl."
But there are many other
possible basic city forms than those of the central city
type of scheme.
Some of these may develop unexpectedly.
Some may be fostered and nurtured by government action if
found suitable in terms of transportation and other factors.
And some may never show their faces in real life.
But since one cannot tell beforehand into which of
these categories any particular city form will fit, and
especially since it is strongly felt that the form of the
city is a very significant variable in the urban transportation problem, the analysis in this thesis will be performed for each of several very different (abstracted) city
forms, and comparisons will be drawn.
PROCEDURE
1.
Background
A common instrument for carrying out the purposes of
transportation studies is the model.
The model, by defini-
tion, is a device used to reduce a problem to a more manageable, more workable scale.
In engineering and the hard
sciences, this reduction may be in a purely physical sense;
the model may aspire to achieve, as closely as possible,
exact duplication of the prototype in every quality except
physical size.
In the "softer" sciences, however, such is
not generally the case.
The problems here are not so
clearly defined, the forces and their effects are not so
predictable, and the methods of solution are not so obvious.
The model achieves workability not through physical reduction, but through simplification; through approximation
and reduction of the number of variables (usually quite
large) which enter into the problem.
The experiment performed in this thesis utilizes models.
They are models of cities and they are not original with
the author of this thesis.
These models were constructed
by Aaron Fleisher in connection with some research he has
performed in the transportation field. 1
Eight different
city forms are defined, of which six are utilized in this
thesis: the central city, the quasi-central city, the many1Aaron Fleisher, "Experiments on the Form of the City and
the Qualities of Travel" (unpublished draft), M.I.T.-Harvard
Joint Center for Urban Studies, 1963.
-9-
-.
10centered city, the layered city, the homogeneous city, and
the ring city. 2
These cities are defined by specifying
only the places of residence and the places of employment,
and it was only the work trip which was being analyzed;
more specifically, the evening rush hour consisting of the
journey from working place to home.
In addition to city form, the other major variable in
the original experiments was the individual's travel decision.
Four decision functions were defined, expressing
four different sets of preferences with respect to the desired length of the journey to work. 3
Trips were distri-
buted, in accordance with the decision function, from
working places to residences for each of the thirty-two
combinations of city form and decision function, and counts
were m'ade of the traffic flow as it passed through each
mile-square block or area.
These included a count of total
flow (in all directions) as well as breakdowns into north,
northwest, west, southwest, south, southeast, east, and
northeast directions.
(Trips were distributed over a free
surface; i.e., they were not confined to any particular
transportation network).
These traffic counts, then, gave a picture of the traffic flows throughout each of the cities for each of the
decision functions.
2 These
In addition, a computation was made
are illustrated in Figures 1 through 6. The other
two forms of city described by Fleisher are two forms of
asymmetric cities.
3 See Figure 7.
-11-
500 living places
31,500 working places
Total population
=
126,000 workers.
Figure 1. The central city.
-12-
500 living places
El
6,100 working places
18,300 working places
Total population = 122,000 workers.
Figure 2. The quai-central city.
-4
-13-
500 living places
10,167 working places
Total population = 122,000 workers.
Figure 3. The many-centered city.
-14-
500 living places
7,500 working places
Total population = 120,000 workers.
Figure 4. The layered city.
-15-
250 living places and 250 working places
Total population = 64,000 workers.
Figure 5. The homogeneous city.
-16-
500 living places
1,633 working places
1,638 working places
Total population = 98,000 workers.
Figure 6. The ring city.
4
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3
DIcis
ION
I
FuNCTION
A
12
24
4
3
I
PE~CISION
FUNCTION
2
0
4
8
'2.
16
20
6
2024
4
3
2
0
I
U-
DECISION FUNCTioNq 3
0
z
4
2
It
3
0
FuNCTION
)EC IS ION
a
TRIP
Figure 7.
L
LENGTH
12.
IN
The decision functions.
MILES
4
16
z4
-18of the average trip length (measured, in the plan view, in
horizontal and vertical directions only) plus its standard
deviation.
The major observations drawn were: (1)the
travel patterns and average trip lengths were dependent
more strongly upon city form, and to a lesser degree upon
the decision function; and (2)for all decision functions
of the six city forms being considered in this thesis, the
central city consistently yielded the shortest average
Wb
trip length, and the ring city, the longest.
(It would be
well to reiterate that only work trips were being considered
here--a simplification which considerably facilitated the
computations.
The results are still of considerable value,
however, for numerous studies have shown that the work
trip is the single most common type of trip in the metropolitan area.
A recent study, for example, found that 40
percent of all trips during an average day were work trips,
and that the percentage was higher, often 60 or 70 percent,
during the peak hours which play such a significant role
in the design of the transportation system 4 ).
The present thesis will be utilizing the flow diagrams
produced by Fleisher's work: assigning the flows to prescribed transportation networks, dividing the flows into
various splits between private and public transportation
(100%-0%, 75%-25%,
50%-50%,
25%-75%,
0%-100%),
and then
computing costs for the various transportation systems.
4 F.B.
Curran and J.T. Stegmaier, "Travel Patterns in Fifty
Cities," Highway Research Board Bulletin 203, 1958.
-19With six city forms, four decision functions, and five modal
splits, there are 120 city form-decision function-modal
split combinations for which to compute costs--an ambitious
undertaking with only a desk calculator available for assistance in performing the arithmetic.
However, since the
travel patterns in the cities do not vary much with the de-
cision functions 5 , it is possible to simplify the procedure
by reducing the number of different combinations of city
with which this thesis will deal (to 30) by selecting only
one decision function for each city form.
For this reason, too, the choice of one particular
decision function is not a very critical decision.
However,
in another thesis which also utilized Fleisher's work,
Ronald Rice does provide some rationale for doing this. 6
On the maps showing the total number of trip crossings
through each one-mile square, contour lines can be drawn
which represent isolines of trip density.
Considering
these now as three-dimensional topographic surfaces, the
calculation of the volume beneath these surfaces will yield
a measure of total capacity (total number of trip crossings
per square x the number of squares).
Rice has performed
this calculation, and the present thesis has arbitrarily
selected for study, for each city form, only that decision
function which produces a total capacity requirement which
5 See
the flow diagrams contained in Aaron Fleisher, op. cit.
6 Ronald
G. Rice, "Public Transportation in Urban Areas:
Analysis and Expectations," S.M. Thesis, M.I.T., Jan., 1964.
OWN
-20lies closest to the average of the total capacity requirements produced by all four decision functions.
The decision
functions selected in this manner are decision function 4
for the homogeneous city, decision function 3 for the central city, and decision function 1 for the other four city
forms, and all subsequent references to any city form shall
assume these particular decision functions.
2.
Assignment of traffic flows
The first step was to overlay a transportation network
on each of the six cities being studied.
This was also the
first major problem, for there is no general agreement
among authorities as to what is the best transportation
pattern for a particular form of city, or as to how to go
about designing an optimum configuration.
For the experi-
ments in this thesis, several forms of radial pattern were
considered, but it was finally decided to use, for all the
cities, a simple square grid pattern with a one-mile spacing
between routes.
The major criterion upon which this de-
cision was based was that the networks ought to be such as
to facilitate the assignment of traffic flows to them from
Fleisher's basic data.
(This calculation could be done
far easier on the grid than on any other pattern considered).
Other criteria which the networks were asked to meet (and
which were met almost as well by some radial patterns as
by the grid pattern) were:
(1)comparisons among the six
cities ought to be facilitated;
(2)the networks ought to
-21facilitate the cost computations; and (3)no person should
live more than one-half mile from the main transportation
network.
Traffic flows (the total flow was assumed to occur
during a one-hour time period) were then assigned to the
networks in the following manner. 7
The transportation
network was placed so as to define or outline the milesquare blocks through which the counts had been made of
the numbers of trips going in the various directions.
North trips through the middle of a block were assigned
half to the route bordering the block on the west and half
to the route bordering the block on the east.
larly for the south, east, and west trips.
And simi-
Of the north-
east trips through a block, half were routed north along
the block's western boundary and then east albng its northern
boundary, while the other half were routed east along the
southern boundary and then north along the eastern boundary.
And similarly for the northwest, southwest, and southeast
trips.
In addition, symmetry was utilized to simplify the
computations for the 256-square-mile cities.
In five of
the cities, only the traffic flow figures for the north-bynortheast octant of the city was used, and the rest of the
city was assumed symmetrical about that octant, while for
the sixth city (the layered city), only the northeast quad7 An
illustrative calculation is included in Appendix A.
-22rant was used. 8
Since the original generation of the trips
was done (by an electronic computer) in a random manner
(though in accordance with the decision functions), some
slight asymmetries were produced in the resultant flow diagrams, and the figures used in the present experiment should
more accurately have been the averages for all eight octants (or four quadrants).
However, these asymmetries did
not seem large enough or significant enough to necessitate
or justify this very large additional calculation. 9
As noted earlier, five modal splits were studied:
100%-O%, 75%-25%, 50%-50%, 25%-75%, and 0%-100%.
(The first
figure represents the percentage of travel by private or
automobile transportation; the second figure, by public or
mass transportation).
The problem then arose as to how to
change the flows by a particular mode of travel along each
of the various portions of the network if the total flow
by that mode were to be reduced by a certain percentage to
achieve a different modal split.
It was felt that this
might simply, rationally, and consistently be done by reducing travel by this mode by an equal percentage from all
segments of the network.
of such a procedure?
8 Diagrams
But what would be the significance
Would it truly be a reasonable approach?
showing the resultant traffic flows for the six
cities are included in Appendix A.
9 Adjustments were made,
however, to correct for the slight
geometric asymmetries present in the quasi-central, manycentered, and layered cities, by taking average flows among
octants (or quadrants) wherever the asymmetry seemed to
have a significant effect.
-23To determine the effects on the flows along the network of various methods of apportionment of a decrease (or
a transfer to the other travel mode), an eight-mile length
of route was set up, with the source for all trips at one
extremity. 1 0
A decrease in travel was then allocated by
several different methods: uniformly (equally) over the
eight miles in one case; entirely to the longest trips in
the second case; in proportion to the number of trips ending
in each mile in the third case; and entirely and equally
among the last four miles in the fourth case.
And it was
found that the percent decrease along each route segment
was equal to the percent decrease in the total flow when
the decrease was apportioned in accordance with the number
of trip-ends in each mile length.
Thus, by applying an
equal percent decrease to all segments of the transportation network, the assumption is being made that the transference of different lengths of trips to the other mode of
travel is being made in direct proportion to the total
number of trips of each length which are being made in the
city; if, for example, auto travel is being reduced from
100% to 75%, the number of automobile trips of each length
is also being reduced to 75%, the total number of personmiles traveled by auto is being reduced to 75%, and the
average trip length by auto does not change.
Although it may be argued that particular modes of
1 OSee
Appendix B.
-24travel may be favored by persons making longer or shorter
trips, the above assumption, stating that changes from one
mode to another will take place equally (percentage-wise)
for all lengths of trips, seems not terribly unreasonable
for this study.
And it certainly does facilitate pro-
cedure.
3. Selection of transportation facilities
Before any costs can be calculated, it is necessary
to define the types of transportation systems and facilities
being used.
Basically, the modal split is being thought
of as a split between private transportation (in the form
of automobile travel over a hierarchy of roadways) and
public transportation (in the form of bus transit or rail
transit).
Summaries of operating characteristics are in-
cluded with the summaries of cost characteristics in the
next section. 1 1
There are, of course, many specific types of travel
modes to choose from.
And enough types must be included
to provide some flexibility in designing the system to meet
different capacity requirements.
But too many types of
travel modes can become cumbersome.
Consequently, such
facilities as busways (exclusive bus highways) and reserved
or preferential bus lanes on highways are not included in
this study.
Private transportation (automobile travel) is con1 1See
Tables 1,2, and 3.
-25sidered to take place on a hierarchy of roads comprising
2- and 4-lane major streets, 4- and 6-lane expressways, and
4-, 6-, and 8-lane freeways.
Freeways are divided highways
with fully controlled access (i.e., no direct access from
abutting property, entrances and exits only at specifically
designated points) and grade-separated intersections or
interchanges, and permit continuous, uninterrupted flow.
Expressways--though the terms freeway and expressway are
often used interchangeably--technically have only partial
control of access, and may have occasional intersections
at grade.
Since the configuration of the transportation network
has already been decided upon--a square gridiron pattern
with a one-mile spacing between routes--the required capacity has in a few instances exceeded even the capability
of the 8-lane freeway.
In these cases, two roads are pro-
vided: an 8-lane freeway operating at full capacity plus
another road determined by the remaining capacity requirement.
(Automobiles are assumed always to contain 1.7
persons per vehicle).
In general, public transportation is supplied by bus
transit.
The types of roads on which the buses travel is
determined by the combined capacity requirement of buses
and automobiles on each road, one bus being considered
equivalent to two automobiles for this purpose.1 2
However,
12This conversion is translated into terms of person-trips
in Appendix C.
-26minimum and maximum figures were assumed for efficient bus
operation.
Where the average headway between buses would
be greater than fifteen minutes (at 50 persons per bus this
would mean less than two hundred persons per hour), no bus
service was provided, these persons having to travel instead by automobile.
And where the average headway would
be less than twenty-five seconds (or where the flow would
be greater than 7,200 persons per hour), rail transit would
have to be utilized instead of bus transit.
Both bus and rail transit are assumed to operate at
full capacity during the peak hour.
Also, buses and trains
are assumed to nake one stop per mile, and the average
speeds indicated for these vehicles 1 3 includes time spent
during these stops plus time for acceleration and deceleration.
4. Selection and calculation of costs
Costs of transportation systems are borne by various
parties; they are borne by the government and by the user
of transportation, as well as by the owner and user of land
nearby the transportation facilities.
Some of these costs
are monetary costs, while others are measured in terms of
comfort and convenience.
None of these costs are actually
entirely separable from the others.
But for the purposes of computation and analysis,
costs are broken down in this thesis into three basic cate1 3 1n
Tables 2 and 3.
-27gories: capital and maintenance costs, operating costs,
and time costs.
Capital and maintenance costs are computed
on an annual basis.
(Right-of-way costs, however, are
omitted because they are far too variable, far too dependent
on specific local real estate values).
Because of the
great difference in costs between types of rail facilities,
two alternative costs are calculated whenever rail transit
is necessitated: one cost is applicable in the case where
the railroad can be placed on the surface of the land (surface rail); the other, where it must be constructed below
the surface (subway).
The distinction between operating costs and maintenance
costs is not always clearly defined; road maintenance and
yard and shop costs for buses and trains are grouped with
constructions costs, but, because it was more convenient
(costs were grouped this way by most references), the
maintenance costs of buses, trains, and railroad way and
structures were grouped with operating costs.
Also, for
the same reason, the purchase cost of automobiles was included with the operating costs (in terms of depreciation
per mile).
It is very important to note, too, that the operating
costs are being computed for the one peak hour only--or for
the work trips, in essence.
(Although it would be possible
to assume a typical distribution of trips over the entire
day, the total daily operating costs would depend greatly
upon the degree and quality of transit service provided in
1.
-28the off-peak hours, and would thus necessitate another
major assumption).
Time costs in this experiment are measured simply in
units of time; no attempt is made to apply a monetary value
to these costs.
A measure of time is included as it is
one of the most important of the convenience and comfort
costs 14 , and is a prime consideration in the design of
urban transportation systems.
Selecting the actual unit costs, for all three categories of costs being investigated, was not an easy chore.
Quick reference to just a few sources will indicate the
disparity that exists among the various estimates of the
various types of costs.
And, to a very great extent, these
disparities exist because of the very real, very large
range of values which these costs can assume; because of
the many variable factors wh'ich exert a strong influence
on these costs.
The final cost figures used in this thesis
are composites and averages taken from many sources. 1 5
A
14 For a discussion of the effects of changes in the modal
split (all public transit by bus) on certain other variables, such as street capacity and numbers of casualties,
see R.J. Smeed and J.G. Wardrop, "An Exploratory Comparison of the Advantages of Cars and Buses for Travel in
Urban Areas," Institute of Transport journal, March, 1964.
15Especially: Martin Wohl, "Costs of Urban Transportation
Systems of Varying Capacity and Service," (paper presented
at the 43rd annual meeting of the Highway Research Board,
Jan., 1964); J.R. Meyer, J.F. Kain, and M. Wohl, "Technology and Urban Transportation," Executive Office of the
President, Office of Science and Technology, 1962; Wilbur
Smith and Associates, "Future Highways and Urban Growth,"
New Haven, Conn.: 1961; Keith Gilbert, "Economic Balance
of Transportation Modes," Traffic Engineering, Oct., 1963;
R.L. Creighton, D.I. Gooding, G.C. Hemmens, and J.E. Fid-
-29compilation of these costs is included in Tables 1, 2, and 3.
For the actual cost computations, diagrams were drawn,
for each of the thirty combinations of city form and modal
split, showing the traffic flows in the direction of heavier
flow along each one-mile segment of route (flows were
rounded off to the nearest fifty person-trips), and showing the type of road which would be required by these flows. 1 6
By using the traffic flows only in the direction of heavier
flow, the computations were greatly facilitated.
(It was
only these flows which determined the type of road or transit facility required along the various portions of the
network).
However, for the calculation of operating and
time costs, as well as the required numbers of buses and
railroad cars, total two-directional figures were needed.
What was done in these cases was to multiply the one-directional figures (for flows in the heavier directions only)
by a factor equal to the quotient of the total two-directional flow (this quantity was measured) divided by the
sum of the flows in the peak directions only.
ler, "Optimum Investment in Two-Mode Transportation Systems," (paper presented at the 43rd annual meeting of the
Highway Research Board, Jan., 1964); Arrigo Mongini,
"The Physical and Economic Characteristics of Express
Bus Urban Transit Systems," S.B. Thesis, M.I.T., June,
1961; Delaware River Port Authority of Pennsylvania and
New Jersey, "Southern New Jersey Rapid Transit System,
Haddonfield-Kirkwood Line," 1961; Edward H. Holmes, "Highway Transportation," U.S. Transportation, Resources, Performance and Problems, (papers prepared for the Transportton Research Conference convened by the National Academy
of Sciences at Woods Hole, Mass.), 1960; Ronald G. Rice,
op. cit.
16nese diagrams are included in Appendix C.
-30Construction cost/
mile, in
$millions
Average
operating
speed, in'
miles/hour
Average
capacity,
persons/
hour--one
direction
Freeway
8-lane
3.6
55
9,600
4.7
6-lane
2.7
55
7,200
4.7
4-lane
2.0
55
4,800
4.7
1.1
35
3,200
5.3
4-lane
0.8
35
2,400
5.3
Major Street
4-lane
0.6
25
1,900
5.9
0.4
25
900
5.9
Road
Expressway
6-lane
2-lane
Operating
cost per
personmile, in #
Automobile capacity assumed at 1.7 persons per vehicle.
Operating cost includes gas, oil, tires, maintenance, depreciation, insurance, registration, parking and garaging.
Road maintenance = $1,000/lane-mile per year.
Estimated life of all roads = 35 years.
Interest rate assumed at 5t%.
To compute annual costs, use capital recovery factor (CRF),
where n = life in years and i = rate of interest:
CRF = i/(1
-
(1 + i)-n)
Table 1. Automobile and road costs.
-31-
Capital and maintenance costs
Purchase cost per bus = $30,000 (life of 12 years).
Yard and shop cost per bus = $4,500 (life of 40 years).
To compute annual costs, use capital recovery factor (CRF),
where n = life in years and i = rate of interest (use 5t%):
CRF = i/(l
-
(1 + i)"n)
Operating costs
Operating cost per bus-mile = $.50.
Operating cost includes maintenance and garage, fuel and oil,
administration, insurance, and wages of drivers and other
transportation employees.
Speed and capacity
Seating capacity per bus = 50 persons.
In determining roadway capacities, one bus is assumed equivalent
to two automobiles.
Average speed (including stops and acceleration and deceleration)
= 30 miles per hour on freeways
= 20 miles per hour on expressways
= 15 miles per hour on major streets.
Waiting time per person
= one-half average headway.
Minimum average headway = 25 seconds
-
=
144 buses per hour
7,200 persons per hour (above which,
rail transit must be employed).
Maximum average headway = 15 minutes
4 buses per hour
= 200 persons per hour (below which,
-
no public transit is provided).
Table 2. Bus costs.
-32Capital and maintenance costs
Purchase cost per car = $90,000 (life of 30 years).
Yard and shop cost per car = $8,000 (life of 50 years).
Construction cost per 2-track mile of surface rail
$4,000,000 (life of 50 years).
Construction cost per 2-track mile of subway
= $17,500,000 (life of 50 years).
Construction cost per surface rail station (one per mile)
= $500,000 (life of 50 years).
Construction cost per subway station (one per mile)
= $3,000,000 (life of 50 years).
To compute annual costs, use capital recovery factor (CRF),
where n = life in years and i = rate of interest (use 5t%):
CRp = i/(1
Operatin
-
(1 + i)-n)
costs
Operating cost per car-mile = $.70.
Operating cost includes way and structures, equipment, power,
conducting transportation, traffic, insurance, general and
administrative.
Speed and capacity
Seating capacity per car = 80 persons.
Average speed (including stops and acceleration and deceleration) = 35 miles per hour.
Waiting time per person = one-half average headway.
Maximum capacity = 40 trains per hour, with 8 cars per train
= 25,600 persons per track-hour.
Table 3. Rail costs.
-33The actual processes of the tabulation of the travel
characteristics and the calculation of the various costs
for the thirty different city form-modal split combinations
is far too lengthy to be reproduced in the text; however,
the results of the tabulations (totals for entire cities,
not just octants or quadrants) plus a detailed sample calculation for a representative city form and modal split
are included in appendices. 1 7
17 See Appendices D and B.
RESULTS AND IMPLICATIONS
1. The results and their interpretation
The results of the cost computations are listed in
Tables 4 through 9, each table summarizing the capital and
maintenance costs, the operating costs, and the time costs
for one of the cities.
A protracted verbal description of
each of the minor results listed in these tables would be
quite unnecessary and quite tiresome; however, the implications of the major results certainly bear some discussion.
In Figures 8, 9, and 10, the three basic costs being
investigated--per capita capital and maintenance cost, per
capita operating cost for the work trip, and average time
spent for the complete door-to-door journey--are graphed
against the modal split.
(The costs are reduced to a per
capita basis so as to enable comparison among the six cities,
which happen to have different populations).
One of the
most significant observations to be made from examining
Figure 8 is that the general trend of the physical costs
of the transportation systems (capital or construction
costs plus maintenance costs) is to decrease as the percentage of public or mass transportation increases.
In
four of the six cities, the cost curve does actually take
a slight upward swing after the percentage of public transportation reaches about seventy-five percent, and in another
of the cities, the homogeneous city, this upward swing in
fact begins at about the twenty percent mark.
-34-
It is sug-
-35Percent Modal Split:
100-0
75-25
50-50
25-75
0-100
I. Capital and Maintenance Costs (in $1,000)
Annual road construction cost 33,735 27,471 21,572 15,750 12,267
Annual road maintenance cost
1,944 1,768 1,512 1,280
944
Total annual road cost
35,679 29,239 23,084 17,030 13,211
Annual bus purchase cost
915 2,078 3,463 4,194
Annual bus yard & shop cost
74
167
279
338
Total annual bus cost
989 2,245 3,742 4,532
Annual train purchase cost
-93
303
681
Annual train yard & shop cost
-7
23
52
Annual construction cost of
surface rail track & stations
--1,063 3,189 6,379
Annual construction cost of
subway track and stations
4,843 14,529 29,058
Tot. an'l surface rail cost
1,163 3,515 7,112
Total annual subway cost
4,943 14,855 29,791
Total capital and maintenance
costs (with surface rail)
35,679 30,228 26,492 24,287
Total capital and maintenance
St
costs (with subway)
"
30,272 35,627
Per capita capital & maint.
costs (w. surf. rail) (in $)
283.17 239.90 210.25 192.75
Per capita capital & maint.
"I
i
240.25 282.75
costs (with subway) (in $)
II. Operating Costs (in dollars)
Auto cost on major street
17,766
Auto cost on expressway
11,475
Auto cost on freeway
32,624
Bus cost
Rail cost
Total operating cost
61,865
49.10
Avg. op. cost/person (in C)
5.10
Avg. oper. cost/mile (in C)
24,855
47,534
197.26
377.25
16,392 17,299 12,583
78
12,919 5,790 3,825
18,895 9,907
928
2,879 5,590 7,703 9,034
348 1,192 2,687
51,085 38,934 26,231 11,799
40.54 30.90 20.82
9.36
4.21
2.16
3.21
0.97
III. Trip Time (in person-hours)
Total traveling time on main
transportation network
30 ,852 38,769 49,562 63,865 69,051
Average headway for buses
(in minutes)
-3.98
2.48
1.93
1.64
Average headway for 4-car
--2.12
trains (in minutes)
1.86
1.65
Total waiting time for
public transit
-993 1,218 1,343 1,387
Total preliminary traveling
time to transp'tion network
8,994 13,031 17,033 20,983
5 ,250
Total time for all journeys 36 ,102 48,756 63,811 82,241 91,421
Average journey time,
door-to-door (in minutes)
1 7.19 23.22 30.39 39.16 43.53
Average journey speed,
door-to-door (in m.p.h.)
3 3.57 24.85 18.99 14.73 13.26
Table 4. Summary of costs for the central city.
-36-
Percent Modal Split:
100-0
75-25
50-50
25-75
0-100
I. Capital and Maintenance Costs (in $1,000)
Annual road construction cost 29,433 23,885 19,830 15,152 13,827
1,976 1,792 1,528 1,216 1,064
Annual road maintenance cost
30,409 25,677 21,358 16,368 14,891
Total annual road cost
1,156 2,562 4,184 5,319
Annual bus purchase cost
429
337
206
93
Annual bus yard & shop cost
5,748
1,249 2,768 4,521
Total annual bus cost
328
105
Annual train purchase cost
25
8
Annual train yard & shop cost
Annual construction cost of
---1,063 3,189
surface rail track & stations
Annual construction cost of
4,843 14,529
subway track and stations
1,176 3,542
cost
rail
Tot. an'l surface
4,956 14,882
cost
Total annual subway
Total capital and maintenance
30,409 26,926 24,126 22,065 24,181
cost (with surface rail)
Total capital and maintenance
I
"
"
25,845 35,521
cost (with subway)
Per capita capital & maint.
249.25 220.70 197.75 180.86 198.20
(in $)
cost (w. surf. rail)
Per capita capital & maint.
i
t
"
211.84 291.16
cost (with subway) (in $)
II. Operating Costs (in dollars)
29,443
Auto cost on major street
18,474
Auto cost on expressway
23,771
freeway
on
Auto cost
Bus cost
Rail cost
71,688
Total operating cost
58.76
Avg. op. cost/person (in C)
5.53
Avg. oper. cost/mile (in C)
265
30,700 25,194 17,487
10,841 5,554 1,932
12,340 5,860
3,085 6,396 9,163 11,457
-- n
412 1,275
56,966 43,004 28,994 12,997
46.69 35.25 23.77 10.65
1.00
2.24
3.32
4.40
1I. Trip Time (in person-hours)
Total traveling time on main
38 ,071 47,930 59,086 74,294 80,725
transportation network
Average headway for buses
5.50
3.15
2.26
1.86
-(in minutes)
Average headway for 4-car
---2.28
2.22
trains (in minutes)
Total waiting time for
1,332 1,582 1,647 1,740
-public transit
traveling
preliminary
Total
5 ,083 8,714 12,609 16,417 20,278
time to transp'tion network
,154 57,976 73,277 92,358102,743
43
journeys
all
Total time for
time,
Average journey
2 1.22 28.51 36.04 45.42 50.53
door-to-door (in minutes)
Average journey speed,
30.04 22.36 17.69 14.03 12.62
door-to-door (in m.p.h.)
Table 5. Summary of costs for the quasi-central city.
-37Percent Modal Split:
100-0
75-25
50-50
25-75
0-100
I. Capital and Maintenance Costs (in $1,000)
Annual road construction cost 26,536 21,858 18,245 15,230 14,139
Annual road maintenance cost
1936 1,872 1,608 1,248 1,088
Total annual road cost
28,472 23,730 19,853 16,478 15,227
Annual bus purchase cost
1,347 2,966 4,654 6,346
Annual bus yard & shop cost
109
239
375
511
Total annual bus cost
1,456 3,205 5,029 6,857
Annual train purchase cost
Annual train yard & shop cost
Annual construction cost of
surface rail track & stations
Annual construction cost of
subway track and stations
Tot. an'1 surface rail cost
Total annual subway cost
Total capital and maintenance
cost (with surface rail)
28,472 25,186 23,058 21,507 22,084
Total capital and maintenance
St
I
I
St
It
cost (with subway)
Per capita capital & maint.
cost (w. surf. rail) (in $)
233.38 206.44 189.00 176.29 181.02
Per capita capital & maint.
"
I
I
I
cost (with subway) (in $)
II. Operating Costs (in dollars)
Auto cost on major streets
31,780 39,033 35,331 20,039
Auto cost on expressways
26,672 16,406 4,165
539
Auto cost on freeways
15,262 3,504
971
Bus cost
3,212 6,685 10,174 13, 666
Rail cost
Total operating cost
73,714 62,155 47,152 30,752 13,666
Avg. op. cost/person (in 0) 60.42 50.95 38.65 25.21 11.20
Avg. oper. cost/mile (in 0)
5.39
4.55
3.45
2.25
1.00
III. Trip Time (in person-hour
Total traveling time on main
transportation network
41,829 55,543 69,141 81,187 91,109
Average headway for buses
(in minutes)
-5.58
3.26
2.33
1.84
Average headway for 4-car
trains (in minutes)
Total waiting time for
public transit
-1,335 1,623 1,761 1,868
Total preliminary traveling
time to transp'tion network
8,667 12,544 16,431 20,333
Total time for all journeys
65,545 83,308 99,379113,310
Average journey time,
door-to-door (in minutes)
23.07 32.24 40.97 48.87 55.73
Average journey speed,
door-to-door (in m.p.h.)
29.14 20.86 16.41 13.76 12.06
Table 6. Summary of costs for the many-centered city.
-38Percent Modal Split:
100-0
75-25
50-50
25-75
0-100
I. Capital and Maintenance Costs (in $1,000)
Annual road construction cost 33,059 27,043 20,155 15,802 14,139
1,968 1,780 1,664 1,332 1,088
Annual road maintenance cost
35,027 28,823 21,819 17,134 15,227
Total annual road cost
Annual bus purchase cost
1,076 2,614 4,487 6,050
Annual bus yard & shop cost
87
211
361
487
Total annual bus cost
1,163 2,825 4,848 6,537
Annual train purchase cost
Annual train yard & shop cost
Annual construction cost of
surface rail track & stations
Anhual construction cost of
subway track and stations
Tot. an'l surface rail cost
Total annual subway cost
Total capital and maintenance
cost (with surface rail)
35,027 29,986 24,644 21,982 21,764
Total capital and maintenance
"
St
I
it
cost (with subway)
Per capita capital & maint.
291.89 249.88 205.37 183.18 181.37
cost (w. surf. rail) (in $)
Per capita capital & maint.
It
Sf
ft
SI
"t
cost (with subway) (in $)
II.
Operating Costs (in dollars)
Auto cost on major streets
Auto cost on expressways
Auto cost on freeways
Bus cost
Rail cost
Total operating cost
Avg. op. cost/person (in 0)
Avg. oper. cost/mile (in 0)
239
22,174 23,719 21,137 18,823
14,482 12,477 14,334
665
30,928 16,861 1,552
3,111 6,460 9,755 13,031
67,584 56,168 43,483 29,243 13,270
56.32 46.81 36.24 24.37 11.06
2.24
1.02
4.30
5.17
3.33
III. Trip Time (in person-hours)
Total traveiang time on main
34 ,805 44,760 60,962 77,525 87,034
transportation network
Average headway for buses
1.58
1.99
2.84
4.86
-(in minutes)
4-car
Average headway for
trains (in minutes)
Total waiting time for
-1,156 1,405 1,488 1,579
public transit
Total preliminary traveling
time to transp'tion network
5 ,000 8,570 12,410 16,195 19,954
Total time for all journeys 39 ,805 54,486 74,777 95,208108,567
Average journey time,
19.90 27.24 37.39 47.60 54.28
door-to-door (in minutes)
Average journey speed,
32.84 23.99 17.48 13.73 12.04
door-to-door (in m.p.h.)
Table 7. Summary of costs for the layered city.
-39Percent Modal Split:
100-0
75-25
50-50
25-75
0-100
I. Capital and Maintenance Costs (in $1,000)
Annual road construction cost 16,114 14,866 14,139 14,139 14,139
Annual road maintenance cost
1,392 1,200 1,088 1,088 1,088
Total annual road cost
17,506 16,066 15,227 15,227 15,227
Annual bus purchase cost
546 1,497 2,266 3,147
Annual bus yard & shop cost
44
121
183
254
Total annual bus cost
590 1,618 2,449 3,401
---Annual train purchase cost
-..
Annual train yard & shop cost
Annual construction cost of
surface rail track & stations
Annual construction cost of
subway track and stations
Tot. an'l surface rail cost
Total annual subway cost
Total capital and maintenance
cost (with surface rail)
17,506 16,656 16,845 17,676 18,628
Total capital and maintenance
SI
It
It
it
cost (with subway)
Per capita capital & maint.
cost (w. surf. rail) (in $)
273.53 260.25 263.25 276.19 291.06
Per capita capital & maint.
I
It
t
I
tf
cost (with subway) (in $)
II. Operating Costs (in dollars)
Auto cost on major streets
40,738 33,828 21,750 11,967
Auto cost on expressways
-----Auto cost on freeways
-Bus cost
1,174 3,218 4,878
Rail cost
Total operating cost
40,738 35,002 24,968 16,845
Avg. op. cost/person (in C) 63.65 54.69 39.01 26.32
Avg. oper. cost/mile (in C)
5.90
5.07
3.62
2.44
775
6,773
7,548
11.79
1.09
III. Trip Time (in person-hours)
Total traveling time on main
transportation network
27P,619 30,759 36,199 40,632 45,681
Average headway for buses
(in minutes)
-12.08
7.37
4.98
4.25
Average headway for 4-car
trains (in minutes)
Total waiting time for
public transit
-1,096 1,833 1,877 2,222
Total preliminary traveling
time to transpItion network
2 ,667
4,026 6,395 8,317 10,515
Total time for all journeys 30 ,286 35,881 44,427 50,826 58,418
Average journey time,
door-to-door (in minutes)
28.39 33.64 41.65 47.65 54.77
Average journey speed,
door-to-door (in m.p.h.)
22.80 19.25 15.54 13.59 11.82
Table 8. Summary of costs for the homogeneous city.
._J
-40Percent Modal Slt
100-0
75-25
50-50
25-75
0-100
I. Capital and Maintenance Costs (in $1,000)
Annual road construction cost 22,351 20,376 18,557 14,139 14,139
Annual road maintenance cost
2,048 2,048 1,768 1,088 1,088
24,399 22,424 20,325 15,227 15,227
Total annual road cost
Annual bus purchase cost
1,455 3,004 4,508 6,005
Annual bus yard & shop cost
242
484
117
363
Total annual bus cost
1,572 3,246 4,871 6,489
-Annual train purchase cost
Annual train yard & shop cost
Annual construction cost of
surface rail track & stations
Annual construction cost of
subway track & stations
Tot. an'l surface rail cost
Total annual subway cost
Total capital and maintenance
cost (with surface rail)
24,399 23,996 23,571 20,098 21,716
Total capital and maintenance
SI
It
"
I"
cost (with subway)
Per capita capital & maint.
cost (w. surf. rail) (in $)
248.97 244.86 240.52 205.08 221.59
II.
Operating Costs (in dollars)
Auto cost on major streets
49,647 57,809 38,148 19,026
Auto cost on expressways
23,941
Auto cost on freeways
-Bus cost
3,128 6,479 9,708 12,959
Rail cost
Total operating cost
73,588 60,937 44,627 28,734 12,959
Avg. op. cost/person (in C)
75.09 62.18 45.54 29.32 13.22
Avg. oper. cost/mile (in C)
5.69
2.22
4.71
3.45
1.00
III. Trip Time (in person-hours)
Total traveling time on main
transportation network
4 ,565 60,048 68,968 77,621 86,212
Average headway for buses
(in minutes)
-6.72
3.62
2.42
1.81
Average headway for 4-car
trains (in minutes)
Total waiting time for
public transit
-1,327 1,478 1,482 1,478
Total preliminary traveling
time to transp'tion network
4 ,083 7,048 10,208 13,522 16,333
Total time for all journeys 50 ,648 68,423 80,654 92,625104,023
Average journey time,
door-to-door (in minutes)
31.01 41.89 49.38 56.71 63.69
Average journey speed,
door-to-door (in m.p.h.)
25.53 18.90 16.03 13.96 12.43
Table 9. Summary of costs for the ring city.
-413 80
3 60
(3
CENTRAL
Ciry
(WITH
CENTRAL
CITY
(WITH SViSWAY)
SVRFACE RAIL)
RAILc)
SbUAC
QvASI-CrEITRAL Crr4 (wr
QVASI -CE1TRAL CITY (WI H SUBWAY)
340
MAWY-CEMTERED CITY
3
(0i)
LA-YERED Crry
@
HomoGrisior
00
RiNs
s Crry
CIT
T
0-1"
-J
2
U
2
Uj
z
2 40
z
2 20K
N-0
CL
CL
2 00
(d601
0
Z5RA-IO
Figure 8.
OF
so
PV8LIC TO TOTAL
100
75-
TRANSPoR-TAToN
(IN
&1v)
Graph of per capita capital and maintenance costs
vs. modal split.
w
-42o
(
CENTRAL CITY
Ccri
QuAsi-c_TRAu.
70
MANY-cENTCAC£ CITY
L^L-iERED Crry
@ HomoGENEOVS
IN) Ri
60
CIry
' CrY
zI"i
U
AO
0
30
U
I-
20
LU
OL
10
0
S60
0
RATio
OF
PVsLrC
To TOTAL
-75TRANSoVRTATI0N (Ir
too
-r.)
Figure 9. Graph of per capita operating costs vs. modal split.
no
-4370
60
z
5,0
140
LU
z
0
30
0
CENTRAL Cn-Y
0l
0U
20
__
VASI-CENTRAL
CrrY
MANY-CENTERED CITY
@LAYEREO
CITY
@ HOMOGENEOVU
CITY
RING CITY
10
0
Z5
0
RATIO
so
100
-75
OF PVuLC -ro TOTAL TRANSPORTATION
(IN I,)
Figure 10. Graph of average door-to-door journey time vs.
modal split.
-1
-44gested here that one of the limitations under which the experiment has operated--the predetermination and fixity of
the densities of the cities--has played a significant role
in fashioning these idiosyncrasies of the cost curves; density, which was held constant in this experiment1 , is actually a significant variable.
Thus, in four of the cities,
operating under the defined unit costs and operating characteristics, the densities may have been such that after
the percentage of public tranlsportation reached seventyfive percent, further increase in mass transit was uneconomical; additional buses had to be bought while the roads
(the least expensive and the lowest capacity carrying used
in this experiment) had yet sufficient surplus capacity to
have carried many of these additional transit riders by
automobile.
And in the case of the homogeneous city, which
had a much lower residential density and a much smaller
total population than any of the other cities, this point
where additional mass transit becomes uneconomical may have
been reached much earlier on the scale of percentages of
public transportation.
For this experiment, then, it is
suggested that the density of the homogeneous city was too
low for an efficient transportation system at all points
on the curve; or conversely, the one-mile spacing of the
transportation routes on the grid network was too close
for the given density.
1 See
Figures 1 through 6.
-45In general, however, increasing public transportation
has increased economy in this study; the savings in roadway requirements resulting from replacing private transportation with public transportation has generally outstripped the cost of the additional transit facilities.
But this statement does require some qualification.
Es-
pecially, in the case where rail transit was required, the
general trend was significantly altered.
While surface
rail, in the cases of the two cities which required some
rail transit, did not significantly affect the general
downward direction of the cost curves, such factors as
noise and right-of-way costs may well prohibit the construction of such facilities in areas of high enough density to require rail transit.
And this would necessitate
underground or subway facilities, which, as can readily be
seen in Figure 8, caused steep rises in the physical costs
of the systems. 2
(In fact, the right-of-way costs in such
dense areas may just as easily prove exceedingly expensive
for freeways, and in dense areas a system utilizing a combination of automobiles and buses on expressways and major
streets may well turn out to be the superior transportation
in terms of physical cost).
2 Although
not considered in this study, elevated rail facilities or elevated all-bus highways are other possibilities for the densely populated areas; however, these would
still have significantly higher construction costs than
the corresponding surface facilities. And any savings in
right-of-way costs, or increases in costs for easements
for light, air, etc., would be hard to gauge except in
specific situations.
-46Comparing the physical costs of the various cities,
it is noted that, with public transportation greater than
about twenty-five percent, these costs were lower for the
central, quasi-central, many-centered, and layered cities
than for the ring city, and lower for the ring city than
for the homogeneous city.
This was not unexpected, as the
first group of cities contains the greatest concentrations
of trips 3 , which would seem to be a requisite for efficient
mass transportation.
Carrying the breakdown a little fur-
ther, the cost for the many-centered city was the lowest
on the graph for all values of modal split.
At first glance
this seemed a bit surprising, for the central and quasicentral cities do have even greater concentrations of trips
than does the many-centered city.
However, for that range
of modal splits where there is a considerable amount of
private transportation, these greater trip concentrations
required more freeways.
And, while the freeways are super-
ior in terms of capacities and travel speeds, they also
have higher cost to capacity ratios than the expressways.
As for those modal splits where public transportation is
dominant, the greater trip concentrations required more
rail transit, which, apparently, still was not competing
economically with bus transit at these densities.
The low-density homogeneous city had very definitely
3 See
the flow diagrams in Aaron Fleisher, "Experiments on
the Form of the City and the Qualities of Travel" (unpublished draft), M.I.T.-Harvard Joint Center for Urban
Studies, 1963.
Pp
the greatest physical transportation costs for almost the
entire range of modal splits (except where public transportation is less than approximately twenty percent).
It
appears that the reasons for this were that this city,
lacking sufficient concentrations of trips, was least
suited for public transit, and that, at its low density,
it had to use a predominance of two-lane major streets,
which have the lowest ratio of capacity to cost of all the
roads used in
this experiment.
With respect to the operating costs in the various
cities, it can be seen from Figure 9 that these costs exhibit an approximately linear relationship with the modal
split for all six cities; operating costs vary inversely
with the percentage of public transportation.
The central
city, which utilizes the most rail transit and the most
freeways (which have the lowest operating costs among the
various forms of public and private transportation, respectively, used in this study), did indeed have a significantly lower per capita operating cost than all the other
cities for the entire range of modal splits.
Four of the
other five cities were grouped rather closely together,
but the sixth, the ring city, consistently exhibited a
significantly higher level of per capita operating costs.
On the surface, this seemed somewhat surprising, for it is
not so obvious that greater operating costs were being encountered here than in, say, the homogeneous city.
How-
ever, this was probably accounted for by the fact that the
-48average trip length was significantly greater in the ring
city than in any of the other cities 4 , so that, all else
being about equal, this city would then yield the highest
per capita operating cost for the total journey.
The graph of the average journey times (Figure 10) is
similar to that of the per capita operating costs.
In this
case, the average door-to-door journey times seem approximately to vary directly with the percentage of public
transportation.
And again, the central city exhibited a
consistently lower average journey time than all the other
cities, while the average journey time for the ring city
was the highest for the entire range of modal splits.
(Of
course, these figures, too, reflect the fact that the
average trip length was longest in the ring city and shortest in the central city.
It will be seen from Tables 4-9
that while the central city--having the highest proportion
of high-speed roads and transit facilities--did also yield
the fastest average travel speeds over the entire range of
modal splits, the homogeneous city--having generally the
lowest proportion of high speed transportation facilities-produced slower average travel speeds than the ring city).
When analyzing the average journey times and speeds,
however,
4 From
a very basic assumption made in
this experiment
Tables 10-15 (in Appendix D), the average trip lengths
are 9.62 miles for the central city, 10.62 miles for the
quasi-central city, 11.20 miles for the many-centered city,
10.89 miles for the layered city, 10.79 miles for the homogeneous city, and 13.19 miles for the ring city.
Op
-49must be borne in mind.
This is, that speeds of travel were
taken to be independent of congestion; all routes were designed so that their capacities were never exceded, and all
vehicles were assumed to travel at the design speeds of
these routes.
In reality, of course, increased traffic
flow on a road (even at levels below the capacity of the
road) does often decrease the average speed of travel on
that road.
However, this error, particularly with proper
law enforcement on the road system, is probably not a large
one as long as roadway capacities are not being exceeded;
certainly not large enough to necessitate the complicated
and lengthy adjustment in the calculations which would be
required to correct for it.
Another important limitation on the experiment is the
Parking may not
omission of the time required for parking.
be a significant factor in low density areas, but in high
density areas it will almost certainly require large expenditures both in terms of time and money.
In this ex-
periment, however, neither parking time nor capital expenditures for parking facilities have been included; these are
not difficult calculations, but they do require significant
additional assumptions.
Furthermore, unlike all other time
and operating costs measured in this experiment, these
parking costs will not be the same for the home-to-work
journey as for the work-to-home journey.
Consequently,
they have been omitted here, and their inclusion is left
to any interested subsequent researchers.
-50In summary, then, the following general observations
have been gleaned from the results of the computations.
Increasing the percentage of public transportation decreased the per capita physical cost of the total systems.
Public transportation was more economical in areas of higher
density.
Subway construction (excluding right-of-way costs)
was uneconomical at even the maximum densities used in this
experiment.
Increasing the percentage of public trans-
portation decreased per capita operating costs but increased the average door-to-door journey time.
And, concerning the differences among the various
cities, the many-centered city was the most efficient in
terms of physical cost of the transportation system, but
ranked only about average with respect to operating cost
and journey time.
The central city was the most efficient
in these latter two categories, but required about an
average expenditure for the physical costs of the system.
The ring city yielded the highest operating costs and
journey times and one of the highest physical costs, and
seemed in general to be about the most inefficient city
form.
The homogeneous city did exhibit a higher physical
cost, but this may well have been due to a density that
was too low and inefficient for the experiment, and, furthermore, it still ranked considerably better than the ring
city in terms of operating costs and average journey time.
These observations, of course, must be taken in light
of the nature of the experiments and its limitations.
This
-51study represents just one more bit of knowledge to be added
to the results of the many other studies which have been
undertaken in the transportation field, and any inferences
drawn from the observations herein should be very carefully
reconciled with the validity and scope of the results.
2. Comparison with the results of other studies
If there is a single lesson to be learned from previous
transportation studies, it is probably that group (mass)
and individual (automobile) modes of transportation do not
function completely independently; each has its own advantages and disadvantages, and, consequently, its own set
of functions which it can efficiently serve.
Indiscriminate
replacement or substitution of one mode by the other will
likely lead to considerable waste and inefficiency.
Typi-
cal statements to this effect can be found in a study conducted by Wilbur Smith and Associates:
...(W)hile transit does not serve the majority of
trips in any urban area, it is valuable for those
particular movements or trip linkages that are concentrated in space and time, especially in high-density urban complexes. Thus, transit is a valuable
adjunct to freeways in serving peak-hour movements
along heavy travel corridors leading to and from the
central business district, particularly in big cities.
...Urban transportation needs will usually require
that highways be augmented by public transit and that
transit be fostered even though, at best, it will but
hold its present levels.
...Rapid transit, with its high peak-hour passenger capacities, is a desirable element in the
total urban transportation system wherever there are
sufficient concentrations of people to warrant such
facilities.
...Just as freeways do not obviate the need for
transit, neither can rapid transit be regarded as a
0
-52substitute for needed new freeways. 5
And even the Automobile Manufacturers Association has stated:
Metropolitan freeway systems will contribute to
the economic vigor of downtown areas by sharply reducing downtown traffic congestion. These systems
are designed to allow two-thirds of peak-hour downtown
traffic, which now is forced to pass through downtown
to other locations, to by-pass the central area entirely.
At the same time, some portions of our metropolitan
areas, and particularly their downtown centers, must
continue to depend on existing or improved public
transit facilities. These transit facilities meet
basically different transportation needs than automobiles...6
A good comprehensive transportation plan, then, should
utilize and coordinate the advantages of both the public
and private forms of transportation.
The claim that group and individual modes of transportation are not interchangeable has also been reaffirmed
in a study performed for a specific city.
A mathematical
model, based on such factors as the numbers of persons
living and working in various zones and the travel times
between zones, was used to estimate origins and destinations of travel, and, consequently, existing and future
traffic patterns in the Baltimore metropolitan region. 7
The model was used to predict the future traffic volumes
that would occur on a proposed highway system and, also,
5 Wilbur
Smith and Associates, "Future Highways and Urban
Growth," New Haven, Conn.: 1961.
6Highway Economics Research Committee of the Automobile
Manufacturers Association, Inc., "Urban Transportation,
Issues and Trends," 1963.
7j. Booth and R. Morris, "Transit vs. Auto Travel in the
Future," journal of the American Institute of Planners,
May, 1959.
OWN
-53the volumes that could be expected if specific mass transit
improvements were made.
Tests of the model were said to
have indicated its reliability and versatility.
The results
indicated that Baltimore transit services, no matter how
extensive, cannot be considered a substitute for highway
improvements; nor will they drastically reduce highway
building requirements.
This is all in agreement with the results of the experiment performed in this thesis, which indicated that the
mass transit facilities, and especially rail transit, were
not efficiently serving the low-density areas, and that
the freeways and expressways, with no mass transit, were
not economically meeting the needs of the high-density areas.
In anothler study, conducted by the Maryland-National
Capital Park and Planning Commission, urban form was considered as one of the prime variables in the transportation
problem.8
Four alternative patterns of urban development
were proposed for the region: a sprawl pattern (development
according to the largely unrestricted forces of private
enterprise, as is common today); an average density pattern (similar to the sprawl pattern but with more public
control--contains both high and low density residential
areas); a satellite pattern (urban development in the central core and in small cities some distance away, with no
development in between); and a corridor pattern (similar
8 Maryland-National
Capital Park and Planning Commission,
"On Wedges and Corridors," 1962.
-54to the satellite pattern, but with development permitted
along the main transportation routes from the central city
to the outer or satellite city).
Preliminary cost studies indicated that the cost for
rapid transit was significantly lower in the sprawl and
average density cities than in the corridor city, which in
turn required a slightly lower expenditure than did the
satellite city.
While the city forms explored here are
not precisely comparable to those investigated in the main
body of this thesis, the results obtained by the MarylandNational Capital study are, on the surface, nevertheless
somewhat surprising.
For it seems as though the corridor
and satellite cities would have the greater concentrations
of trips, and would, consequently, be the more efficient
forms for mass transit.
Unfortunately, the dilemma is not
easily resolved, as the study does not fully describe its
criteria and methods of procedure for the cost analyses.
Many studies, such as the Maryland-National Capital
study, have been primarily concerned with either mass transit or highways.
But there has been, too, at least one
attempt to develop a general method for determining costs
of total transportation systems. 9
(Although, little em-
phasis is placed in this study on the varying types of
urban form).
9 R.L.-
Specifically, the authors, trying to define
Creighton, D.I. Gooding, G.C. Hemmens, and J.E. Fidler, "Optimum Investment in Two-Mode Transportation Systems," (paper presented at the 43rd annual meeting of the
Highway Research Board, Jan., 1964).
---
Pp
-55a means of optimizing investment in a two-mode transportation system, have developed a method of constructing "cost
surfaces" for various modal splits and trip densities.
And
based on the results of their computations, they have come
to two major conclusions. (Although they strongly emphasize
that because of the limited number of examples studied, as
well as some other limitations on their procedure, the inferences must be treated with caution).
The first conclusion states that some gain will almost
always be produced by initial investment in rail facilities,
expressways, or any combination of these facilities.
The
reasoning behind this lies in the fact that investment cost
is a small proportion of travel or operating cost (10 to
20 percent when placed on an equivalent basis, such as
daily cost), yet it will cause substantial reductions in
the travel costs.
The present thesis seems to be in agree-
ment with this conclusion.
For example, taking a typical
figure of sixty cents per person for the peak hour operating cost for an all-private transportation system (the
equivalent cost for an all-public transportation system
would be considerably lower, but great inefficiencies of
operation would be encountered during the off-peak hours
which would be difficult to figure quantitatively), the
total per capita daily cost would be about six dollars
(assuming peak-hour flow at about ten percent of total
daily flow).
The total yearly operating cost, then, even
excluding week-ends, would be $6 x (5 days/week) x (52
__4
A
-56weeks/year) = $1,560 or six time the average per capita
yearly physical cost of about $260.
seem fairly clear.
The implication would
The operating costs should generally
be weighted more heavily than physical costs in planning
new investment in high-speed transportation facilities.
The second major conclusion declares that greater
gains appear to be produced by exclusive investment in expressways or rail rapid transit than by investment in a
combination of these two types of facilities.
The reason
for this is stated to be that capital requirements for
combination investments are high, and full utilization of
each type of facility cannot be expected.
But this is not
in agreement with the results of this thesis, which indicated that investment solely in either roads or transit
facilities for the two cities where rail transportation was
necessitated, was more expensive than for a combination of
roads and transit facilities.
However, this thesis did
not assume any inherent loss in efficiency of utilization
of the facilities for a combined public-private transportation system; nor was any such inherent inefficiency discovered in the process of carrying out the experiment.
Furthermore, it has earlier been noted that a system
of transportation combining both group and individual modes
of travel is generally thought to be the most effective
and most desirable type of system.
If a combined system
of highways and rail transit is uneconomical, the implication would appear to be that the most desirable type of
-57transportation system, both financially and in terms of
quality of service, would be a system of highways serving
both automobile and bus transportation.
And this is
what the results of this thesis, within
the validity of the experiment, seem to suggest: a compromise between the lower costs of bus transit and the superior operating characteristics (such as time, comfort, and
convenien'ce) of the automobile. 1 0
This policy suggestion
is well summed up in the following statement.
Comparisons of the economic feasibility of alternate transit proposals usually indicate that new rapid
transit routeg should be carefully integrated with
freeway construction, and that motor buses should be
used. Rail rapid transit will be limited primarily
to areas where it now exists or where it can be readily adapted to existing railroad lines. 1 1
3. Recommendations for future study
The subject of study in this thesis has by no means
undergone a completely thorough analysis.
Many assumptions
had to be made and many criteria and standards had to be
chosen.
For example, while the unit costs selected do
represent the author's best attempt at defining a set of
"average" or "typical" costs, the resultant set of costs
is hardly definitive.
Furthermore, the standard deviation
1OKeith Gilbert, in "Economic Balance of Transportation
Modes," Traffic Engineering, October, 1963, states,
"It appears that an overall average population density
of at least 10,000 persons per square mile would be
The results
necessary for economical rail operation."
of this thesis would put this figure at an even higher
density, but this is without the inclusion of rightof-way costs.
1lWilbur Smith and Associates, op. cit.
-58which should be attached to any "average" cost would, due
to so many significant variables, be so large as to render
the use of such a cost, in any specific situation, exceedingly dangerous without thoroughly investigating the
actual cost.
And the results obtained are, of course, ex-
tremely dependent upon the cost figures used.
Consequently, it is suggested that the experiment
performed in this thesis could profitably be re-done to
investigate the effects of other variables on the problem;
many more sets of curves could be obtained for other city
forms, for other unit costs, for other population densities,
for other transportation networks, for other performance
standards, etc.
Of course this could be a very ambitious
undertaking, depending on the scope and thoroughness of
the investigation, requiring a great deal in the way of
time and facilities.
But even with limited resources,
particular variables could be selected for study.
Especially,
it is suggested that a significant variation in the results
would be obtained by varying the densities of the cities
used in this experiment, and that this investigation could
be readily carried out.
Altering unit costs or transporta-
tion networks would also probably effect great changes in
the results obtained, but the investigation of these variables would likely prove to be much less systematic and
much more time consuming.
Finally, it should be noted that the computations performed in this experiment (on a desk calculator) would
-59probably be readily adaptable for solution by an electronic
computer.
Such a tool could considerably expedite the mech-
anics of any investigation, and could, consequently, greatly
reduce the number of man-hours required for a study and/or
greatly increase the possible scope of such a study.
-1
BIBLIOGRAPHY
Booth, James and Morris, Robert. "Transit vs. Auto Travel
in the Future." Journal of the American Institute of Planners. May, 1959.
Carroll, J. Douglas, Jr., Creighton, Roger L., and Hamburg,
John R. "Transportation Planning for Central Areas." Journal
of the American Institute of Planners. February, 1961.
Chicago Area Transportation Study. "Survey Findings." Volume I. 1959.
Creighton, Roger L., Gooding, David I., Hemmens, George C.,
and Fidler, Jere E. "Optimum Investment in Two-Mode Transportation Systems." (Paper presented at the 43rd annual
meeting of the Highway Research Board, January, 1964).
Curran, Frank B. and Stegmaier, Joseph T. "Travel Patterns
in Fifty Cities." Travel Characteristics in Urban Areas.
(Highway Research Board Bulletin 203). 1958.
Delaware River Port Authority of Pennsylvania and New Jersey. "Southern New Jersey Rapid Transit System, HaddonfieldKirkwood Line." April, 1961.
Fleisher, Aaron. "Experiments on the Form of the City and
the Qualities of Travel" (unpublished draft). M.I.T.-Harvard
Joint Center for Urban Studies. 1963.
Gilbert, Keith. "Economic Balance of Transportation Modes."
Traffic Engineering. October, 1963.
Highway Economics Research Committee of the Automobile Manufacturers Association, Inc. "Urban Transportation, Issues
and Trends." 1963.
Holmes, Edward H. "Highway Transportation." U.S. Transportation, Resources, Performance and Problems. (Papers prepared
for the Transportation Research Conference convened by the
National Academy of Sciences at Woods Hole, Mass., 1960).
Maryland-National Capital Park and Planning Commission. "On
Wedges and Corridors." 1962.
Meyer, John R., Kain, John F., and Wohl, Martin. "Technology
and Urban Transportation." Executive Office of the President,
Office of Science and Technology. 1962.
Mongini, Arrigo. "The Physical and Economic Characteristics
of Express Bus Urban Transit Systems." S.B. Thesis, Massachusetts Institute of Technology. June, 1961.
-60-
-61Moses, Leon N. and Williamson, Harold F. "The Value of Time,
Choice of Mode, and the Subsidy Issue in Urban Transportation." Northwestern University.
Owen, Wilfred. The Metropolitan Transportation Problem.
The Brookings Instiute. 1956.
Proceedings of the Second Annual Spring Conference of the
Organizataon of Cornell Planners. March, 1959.
Rice, Ronald G. "Public Transportation in Urban Areas:
Analysis and Expectations." S.M. Thesis, Massachusetts
Institute of Technology. January, 1964.
Schnore, Leo. "The Use of Public Transportation in Urban
Areas." University of Wisconsin.
Smeed, R.J. and Wardrop, J.G. "An Exploratory Comparison
of the Advantages of Cars and Buses for Travel in Urban
Areas." Institute of Transport journal. March, 1964.
Smith, Wilbur and Associates. Future Highways and Urban
Growth. New Haven, Connecticut: 1961.
Wohl, Martin. "Costs of Urban Transportation Systems of
Varying Capacity and Service." (Paper presented at the 43rd
annual meeting of the Highway Research Board, January, 1964).
APPENDIX A--TOTAL TRAFFIC FLOWS
The diagrams in this appendix show the total traffic
flows in both directions for the six cities.
The symbols
in the lower right-hand portion of the diagrams indicate
(l)the directions of the flows on each route mile, and (2)the
octant or quadrant from which the traffic flows were derived.
The cities are assumed to be symmetrical about this octant
or quadrant, and the figures shown are, in all cases, the
actual flows along the indicated route segments.
An illustrative example of the assignment of traffic
flow to the transportation network is provided below.
The
original traffic count was taken on a free surface, through
the middle of the one-mile squares formed by the grid, in the
north, northeast, east, southeast, south, southwest, west,
and northwest directions.
These are indicated by dashed
arrows, while the final flows (along the transportation network) are indicated by solid arrows.
4--40-
40
-AND
\1'
THUS:
RI
zoo
_
R=
8oo
y (oo+ 200+300++oooo
+s0oo)
=(2,600) = 1,300 Pin So N s
-62-
140
10
-630
I
(2
zsO
2s a
0
0
C)
0
0
0
0
a
Figure 11. Traffic flow in
the central city.
I
-6411 6
f31
98
In
I.-
I68
22Z
2 2 z
Ao
I
-77
U'
0
<N
0
926
848
25-r.
45
2
2
2.23
5ZzI
N
0
4-
o0
-737
698
2,100
to
47
0
0
N
1,217
5.04
,063
1,081
641
os
0
1=
ob-
'I,
NO
1
1o
1.321
N
,
Ge81
9
O|
1, 1 zo
1,
N,
709
1,43
,
N
4
1060
~2,
0
S3
295
760
~0
'a
In
735
o
%n-
A -74-
932
2540
967
N4
o 0
0e
,
0
1
o0
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N
%4
1,906
... 0
86 r
1
1,1 z I
1"-
7711
1,0~10
'75
-788
0
54q9
689
N n
0%
N
(fl
1,1971
1
(,900
,599
r 3Z
N
796
N_
-
N
7,4IG
4,705
|
w
Figure 12. Traffic flow in
the quasi-central city.
4f~
%'
54G
1091
348
0)
N
O0
o0
0
5-42
35'6
5,61
1,365
0
0
4,
-65216
224
259
25t
(46
119
.59
7S$
262
249
9,4
54
200
211
0
0
'I,
o0
N 0
0
o0
I, 554
982
-'
,
,
-t ry
1
2,300
2,102
1,330
1,229
683
1,093
1,344
2,41f
1,801
1.G6S
1,446
,
G
V33 9
5'80
945
1,5~09
Ts
1,101
C"
U,
i
1~-
1,824
N
8941
1, 069
1,.099
1,709
I')
245'O
1=
9,292
,
,
1,119
0\
0
N
N
N
N
1,695
1,262
a,
en
2,0~7
2,867
1,112
'S
t'~
rN
0
2, 4 570
1,075,
1.90(
1,090
,q.
1,3.5'O
1,2.03
(ft
N
(V.
|
2,229
,332
3.3
,4'49
0
t
617
3,093
1 02.5
N
1,736
0.
4734
3,253
6)
Figure 13. Traffic flow in
the many-centered city.
N 0
0
N
'a 0
0
'I,
'a
,
761
633
1,420
to 0
(E~
Cd)
AlL
3,4,53
.1
-6693
109
1Z1
I9 5
203
158
2.06
-T337
o4
C
00
an-eto
0
a-
309
T
M
m
T
MIT
o * % M000
5A0
366
160
I0OA
o
%N
670
16
76
ao
a
629
0
4z
0
C)
N
oo
0'~
67.0
427
772.
3A Z
916
29
1,13,4
,012
111
1,097
897
411
a
0
0
76
NN
1,19(
7141
N
1,6G9
42.8
1,407
5-9
1,647
*r
1~-
Z
16G
I,2T6
9395'
16
-12.4
0
ab4)a-a
0
N
,
291
0
wDC
-
tw
w
I,97z
2,137
1,009
t,405
ri
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CS
tiN
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1,941
1,
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308
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1,341
906
A Z3
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0
0
N
a-
0
a--
tv
G
r--Cr-O
0
1*
2,445
1,5(7
2,2,
2,S20
2,042
2,10s
98
1,838
89
,400
43Z
6179
291
0
3
a-D
2,719
3,033
3,027
3,5'00
3,243
3,592
2,331
2,A3 1
i,917
1,49 2
2S
,
'446
877
7-11
1,405
85
0
I.
-j
__4__5__
5'012
CDor-
qt,
t
t- 2
2
-70
2 Z 7 2,0
3,247S-
$5^658
(o,2
5't.
Figure 14. Traffic flow in
the layered city.
1,60'6
6,162
N0
I
NS
\ N
,99
1,007
'I-
OD %
593 9
s'l
238
2,359
-67ISS8
187
( 65
I 60
163
15~5
N
-N
O0
51g6
54 8
~
I5
15,
-I
for
505
53.1
'1334
1T8
SO
'I,
o
,i
129
12
I36
A57
,
37
42.o
I
743
689
,
rho
1o0
In
971
0%
os)
912
900
98A
496
603
I9n
,
, 857
820
,7 723
-719
'-S
I'
tE7
r
In
10110
1.094
1)102
1,075O
1 0O4
1,195
0%
1,t1e8
1,136
1,206
O~ID
898
In
-~
N
876
, 96 ;
1,02S
1,032
,N
CAN
1,239
1,277
1,213
'-I
tJ~
N
1,207
1,272
It
N
4.
Pigure 15. Traffic flow in
the homogeneous city.
-4-
69
309
1~
670
,
699
774
117
30
360
"7
783
-79C
144
w
WI~)
826
835'
12o
Z
0%
41(-
1 59
I
eN
-68289
IZI
1 eE
A60
so
A8
691
5'6 1
to
C2
-759
-12
9-
0
1,004
8Z3
'493
,280
,'174
3"1
1,569
,496
I~0
N
v
I'
9-
,100
1,323
15'80
0
0
0
1,659
1,-71
'78
59A
I ,914
1
N
994
662
,75-4
1,738
376
37'6
1,426
N
'1~
V ,,2.
I, 5 75'
1. 221
996
(131
I, 679
1, 607
1,777
1,-oz
1,779
N
9'
t I ,
N
1,-709
1,632
I,669
W 9%
N
7-
1, 336
9-12
1,689
/1144
',392
N
4'
&
I,631
1,1327
1,933
1,97r
I')
N
N
1,812
1,908
,
1,545
2,006
N
1, 6o
_7
1,865
Figure 16. Traffic flow in
the ring city.
4,
1,497
6S'7
milk
4AM9
APPENDIX B--AN INVESTIGATION OF VARIOUS METHODS OF VARYING
THE MODAL SPLIT
This section studies the effects of various methods of
varying the modal split.
When the total travel, or total
number of person-miles traveled by one transportation mode,
is reduced, this total reduction can be achieved by numerous
devices: by allocating the decrease in person-miles traveled
entirely to the longest trips, or primarily to the longest
trips, or equally to all lengths of trips, etc.
Four different types or methods of decreasing travel
by a particular mode are studied here to determine the effects
on the flows along the various segments of the transportation
network.
In addition, as it has been suggested in the text
that a simple, consistent means of reduction would be to
reduce all lengths of trip by the same proportion, the conditions are determined in each of the four cases under which
this means of reduction would be applicable.
In each case, the original travel is decreased by 25
percent; the analysis would be the same, however, no matter
what percent decrease was used.
A particular percent was
chosen rather than a general percent (such as "x" percent)
because the resultant expressions would be simpler.
-69-
-70ni
n2
~
n3
fiI
4
n5
I
n6
n7
n8
ile#l-mile#2--mile#3-mile#4-mile#5--mile#6-mile#7--mile#8
origin of all trips
8
ni= total number of trips through mile i =
IAi = trips ending in mile i = ni
Aj
-ni+
nit = number of trips through mile i after decrease = n
S
Ani
8
Therefore,
nit = ni +;>
n, = the total number of trips originated
Let nit = 3n/4
(That is, the total number of trips is
being decreased by one-quarter).
1. The decrease is distributed uniformly.
&(&1) = zA(A2) =...= & (A8) = (1/8)(-n 1 /4)
= -nl/32
111' = ni + 8(-n/32) =3n/4
n 5 ' = n5 - 41/32
n2' = n2 - 71/32
n6'
n3' = n3 - 6n1/32
n 7 ' = n7 - 2n,/32
n4'
n8? = n8 - n1/32
= n4 - 5nl/32
= n6 - 3n,/32
Und er what conditions would nit = 3ni/4 ?
n2'
= 3n2/4 = n 2
-
7n1 /32
7n1/32 = n2/4
n2 = 7n/8
n3'
= 3n3/4 = n3
-
61/32
6ni/32 = n3/4
n3 = 6n1/8
etc .
Therefore,
ni = (9-i)n1 /8
(Th at is, every mile must contain the same number of trip- ends).
2. The decrease is allocated to the longest trips, assuming
ni1/4 F n8
-71-
A(L1) = A(LC2) =...= A (S7)
L (L8) = -n.1i/4
= 0
n, - nl/4 = 3n,/4
n5' - n5 - nl/4
n2 - nl/4
n6' = n6 - nl 4
n3'
n3 - nl 4
n7' = ny - n1/4
n4=
n4 - nl/4
n8' = n8 - n1/4
nt=
=
n2'
Under what conditions would ng' = 3ng/4 ?
n2 ' = 3n
4=n2 - n,/4
n
n3' = 3n3/4 = n3 - nl/4
etc.
n
n3 -n
Therefore, ni = n,
(That is, all trips must end in mile#8).
3. The decrease is allocated in proportion to the number of
trips ending in each mile.
L (L 2)/( A2)
A (1)/61)=
8
+ &(A2)
i) = -ni/4 = L(al)
TA(-
(8)(
=...=
+...+
)
z(A8)
Substituting:
-/4=
t (Lb1)
+
(t62/61)Ls(A1)
+...+
(A8/A1)A(A1)
= (A (A1)/61)(A1+A2+...+A8) = (A(Al)/61)n
1
l(Al) =-
=n/4(ALl/A2)AL(2)
= (A(
+ (t 2/L 2)A(A2) +...+ (A8/A2)L(A2)
2)/A2)(L1+A2+...+ A8) = (6(A2)/,62)nl
AL(A 2) = -(A2)/4
etc.
n
Therefore,
= n,
+
ni n2'
A(Ci) = -(Ai)/4
(-.61/4 - A 2/4 -...-
L8/4)
(1/4)(Al+d2+...+A8) = ni - n/4 = 3n,/4
112 + (-,2/4
-
A3/4
-...-
L8/4)
= n2 - (1/4)(62+A3+...+A8) = n2
n2/4 = 3n2/4
-72And similarly:
n3' = 3n3/4
n4' = 3n4/4
n5' = 3n5/4
n6' = 3n6/4
n7' = 3n 7 /4
n8' = 3n8/4
4. The decrease is divided equally and entirely among the
last iour miles.
d(L1) = L (A2) =
= L(A6)
6jA5)
ni
3)=
A (4)
= 0
= A(L(7) = A(&8) = (-nl/4)/4 = -ni/16
= n1 +4(-nl/16) = 3n,/4
n2' = n2 -.
n/4
n5' = n5+4(-nl/16) = n5~4n1/16
n6' -- n6-3n,/16
n3' - n3-n/4n'
n 4' = n4-n1/4
= n 7 -2n,/16
n8' = n8-nl/16
Under what conditions would nil = 3ni/4 ?
n2'
= 3n2/4 = n2 - n1/4
n2 = n1
And similarly, n3 = n4 = n5 = n
n6' = 3n6/4 = n6 - 3n/16
-n6/4 = -3n,/16
n6 = 3n/4
n7' = 3n7/4 = n7 - 2n/16
-n7/4 = -2n1/16
n7 = n/2
n8' = 3n8/4 = n8 - n/16
-n8/4 = -nj/16
n8 =
11/4
(That is, one-quarter of all the trips must end in each of
the last four miles).
APPENDIX C-PEAK DIRECTIONAL FLOWS FOR THE VARIOUS MODAL SPLITS
The following diagrams give the traffic flows during
the peak hour, in numbers of persons, in the direction of
heavier flow for each one-mile link in the transportation
network.
The figures are rounded off to the nearest fifty
persons, and are broken down into the numbers of persons
traveling by (1)private and (2)public transportation for
modal splits of 100%-0%, 75%-25%, 50%-50%, 25%-75%, and
%-100% for each of the six cities.
The symbols in the lower right-hand portion of the
diagrams indicate the octant or quadrant for which the
traffic flows are given.
The cities are assumed to be
symmetrical about these octants or quadrants, and the figures shown are, in all cases, the actual flows along the
indicated route segments.
The following notation is used:
M2--no. of persons travelling by auto on 2-lane major road
M4--no. of persons travelling by auto on 4-lane major road
E4--no. of persons travelling by auto on 4-lane expressway
E6--no. of persons travelling by auto on 6-lane expressway
F4--no. of persons travelling by auto on 4-lane freeway
F6--no, of persons travelling by auto on 6-lane freeway
F8--no. of persons travelling by auto on 8-lane freeway
B--persons traveling by bus (on the type of roadway indicated for the auto travel; for all-transit systems,
buses travel on 2-lane major roads
-73-
-74R--persons traveling by rail transit (either subway or
surface rail)
When buses were run on the roads with automobiles,
the automobile-carrying capacities of the roads were decreased in the following manner: a decrease of 50 automobile travelers, assuming 1.7 passengers per automobile,
means a decrease of 29.4 automobiles.
Since, in terms of
roadway capacity, one bus is considered the equivalent of
two automobiles, this decrease can be compensated for by
an increase of 29.4/2 = 14.7 buses @ 50 passengers per
bus = 735 persons.
In other words, 735 bus riders must be
compensated for by a decrease in automobile capacity of 50
riders; 2 x 735 = 1,470 bus riders would necessitate a decreased capacity of 100 auto riders; 3 x 735 = 2,205 bus
riders would necessitate decreasing automobile capacity by
150 riders; etc.
All transit facilities are assumed to operate at full
capacity during the peak hour.
-756
0
z
0
0
0
N
N
M
0
0
0
0
0
0
0
0
300- M2
0
1*
£
C
1~,
C
C
C
C
0
0
0
0
0
C
0
N
1oO-M2
SO-M2
Cl
Ed
'I,
0
Ia
1450-M4Z
,
1-
w
C
0
0
0
0
ed
0
I ,Ioo-r-14
1450-M4
'4.
1~
C
C
0
t
C
Z,100-E'4
2,300-E4
1,650-M4
it)-M
800 -Mz
1.45'0-M4
t
1-
_
2u
C
In
I-
N
5'0-
M2
3.050-(6
I~
-q-
3
1r
L
2200-E6
OSO-6
,L
4.9S0-
100 -MtL
700 -mz 33oo-,
'p
IL
II-
0
C
0
C
F6
'a
3,250-F4
o7,05-F6
IL
C
C
C
i.
2O
250-MZ
N
x
'I,
750 -Mz
0,
Mz
N
('4
I',
'A
zSo-
250-MZ
200-M2
2
N
In
In
~0-M2
1*
?I,~S0-F8*E4
(0
ILl
Figure 17.
Peak one-directional flow for central city.
Ratio of private-public transportation: 100%-0o%.
- M2
-76-
a
C3
In
C)
C)
'0
e N
O
0
f
1~
1~
a
a e)
C)
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N
'W
4oo-16
~.1
gIC
f3~
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'ii
In
C)
C)
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a
N
N
350-8
ha
C)
C)
'0
Soo-~
'a' 0
C) C)
'44,
C)
C) I0
C) C)
C)
0
'N
5'-2
14.
'U
'4,
a...
.1
ha
550-8
3 5'0- *
in
faa C)
C
N
7o0-M2
9,63,0-F4
4o-6
8oo-~
1,2oo-B
.4'I-
LL
'4,
5.ZS0-F6
2,450-E&
'00-S
m
to
C
C)
a
C)
.4.
"a
N
-
2,400-Eb
2,300-E4
1. 050.4
I
I,600-MA
1,~100-14
,2-50-M4
'a
N
35O-~
'4.
0
C) C)
'a
14.
1~
4 S0O - M 2
0,
0
3SO-5
x)
14
C)
o
I,I0
0-M-4
1,100-M4
600-M~2
600-M2
200-B
50
-12
SO-M2
00-
N
Io In
C4
M
100-M4
200-B
,
C)
C)
o
C
o
In-
N
o
C)
C)
~ala
0
65*-0-MZ
-
ZoQ-8
FO
z
In
5ff0-tM2
400-M2
400-2
550-Mrl
300-M2Z
-
N
N
'A
I
0
0
N
a
'A
f)
'4,
N
N
N
C)
25'0-r42
ZOO-M2
250-MZ
250-PZ
2S'O- I
ZSO-112
200-M2
50-r12
SOmz
o0
o0
1,750-S
0
C)
0
Z,900 -B
tn
V)
Figure 18.
Peak one-directional flow for central city.
Ratio of private-public transportation: 75%-25%.
Z50-MZ
-77o
o,
T-o-Mz
-MZ-.,-
2
N
N
tN
a VO
el
250-M2
I)
114
~0
N
~d)
N
'I
10
N
6 I
o
N
N
C
a
Ii,
o
a 10
In
400-Ma
50-M2
50M
O
1*
I
-
-
'0
N
700-~ M42
Il
'0
to
1 -4450-- -M,4
2 1o--a.
I.
0
I.400-M4q
IL
6 0li
x'0
0
0
1,050 -t14
1,o0-3
a
a
1,600-M,4
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et
_
0
0
*
2,S-00- F4
,
3.500 -'8
LL
a
'I,
I...
S, Bro-FG
raro-
b
S
tj.
a
a ;D
N
400-112
400-B
t4
2,A4r0'4-
6
a
2,4"o-E5
1, 6S0-%
s
6
ISS0 -'b
Lu
a
a *-
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1
1,S-
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a
FO
E
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a
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__________
,
jg~
a
a U)
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IV)
aSOM
t1
J~I5~0-B
z
a
a
400-M.
400-15
"700-IMu
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aS5o -M4
i________________
--
_6
C.)
9%
8oo-S
1~
Fe
%a'7
a
a
800-112
I
loo --s
a
E
750-M2
--7 50-
4
qOD4-M
a
& &
a
1~~
0
N
(0
1t
E
a
&
o-M
4 0-'B
350-B-
to
N
N
300.-M?2
C2
(14
"I
(1
3e
5,350
a
0
a.;
Figure 19.
Peak one-directional flow for central city.
Ratio of private-public transportation: 50%-50%.
250 -M2
~so-riz
M,
ZSO-P12
250-M2
zso-Mz
2,o-M?
-_____
o
0
o0
S9
m
N
M
N
K:
a
a
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o
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0 __
___
-
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N
fC
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N
0
50-M2
a
a
It.
ao
35-0-112
zoo-Mz
0
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o
a
Ma
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a
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a
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,
r0-M2
1,600-B
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K:
a oea
oa a W
a
350 -MZ
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--a
1.100
1~
550-'M2
o:
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('4
K:
l,700--B
o
s--z
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1~
t fo
I
350-M2
8oo-M44
750- M4
2,300 -3
2,4oo -3
1r
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a
a
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60&50-14
fn-
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2,46-0 -S
2
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1,200-M4
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150-M-2
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1,250-1
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300 -'8
200-2
N
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a a
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a
r
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ro-MR
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ft
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Li)
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65-0-B
.
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o o
%
r0
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a
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Figure 20.
Peak one-directional flow for central city.
Ratio of private-public transportation: 25%-75%.
fa
-790
2 s- -T7
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I.300 --B
2,900-
N
30200-'Bh
go
4,8so-S
7 os-o-&
111 (&50 -R
00
Figure 21.
Peak one-directional flow for central city.
Ratio of private-public transportation: 0%-100%.
-8015"0 - t1
100-12
100-Mr
N
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z
N
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a
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.,
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~ 1,7&o-M-4
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1~
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('4
N
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2:
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.4
Figure 22.
Peak one-directional flow for quasi-central city.
Ratio of private-public transportation: 100%-0O%.
las
a
In
c~i
-, I0- E 4
-.81,SO-p2z
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N
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2
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0
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+
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I
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a
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a
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350-S
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I
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5-0-8
0
Figure 23.
Peak one-directional flow for quasi-central city.
Ratio of private-public transportation: 75%-25%.
200-riz
N
N
N
4
-
200-M2
250-M42
Z50-tz
200-M2
I,
00-M4
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-sr - Mz
0f o - M 2
100--
N
N
a
a
N
a
a
N
z
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0
'4
N
300-M2
soo-o
sero-.
a a
a a1~
a.
z
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N
0
a
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a
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0
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a a
a
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aI Z5Q-194
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M4
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z
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350-IS
350-1
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N
N
a
a
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350-M2
250-t2
a
'A
N
2,400 -E6
2,400-13
4
3,100- F4
3,700-S
a
0
If)
Figure 24.
Peak one-directional flow for quasi-central city.
Ratio of private-public transportation: 50%-50%.
200-
20o-M2
N
a a
a a
N
a
3oo-mZ
zSo- M2
50-P2
N
r
a
0 a
a
a ~0
.
200-112
Z O 2
N
N
'0
'00-M2
I5~O-M2
Ir - mz
a
N N
M?-
-83150-MZ
(00-MZ
z00-Mi
fO-Hz
N
x
a
a
a
15-0o-2 -m
150-M2
A4E0-?
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2S0-tlM2
N
a
1,000-S.
2a
.-
3S0-Mz
800-B
1,000-13
E
N
N
a
'4
C"
a
'4
cv'
a
a (
a
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N
t
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4
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a a
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,-aoo-13
r.
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t
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8 0 -'B
-
5,100-13
N
N
a
In
I',
a
a
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z 10S-3
,250-13
N
a
a
I-
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a
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2,900-13
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a
l4
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a
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I
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r
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M
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gin
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N
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il
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N
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N
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a
a
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3 50-M1
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M
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N
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E
0
a
a
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a
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M2
o-
S'O - m 2
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Z00-13
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"a
-B
a
a
['4'-
Figure 25.
Peak one-directional flow for quasi-central city.
Ratio of private-public transportation: 25%-75%.
0-&
z
a
'A
'A
-
o
'A
-84IO-M 2
1-5'0-m2
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a
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a
C
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M
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fa
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0
to
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to
1117
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o
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M
2,550-B
a
a
4,7s'o -S
a
&
1,40o -"R
Figure 26.
Peak one-directional flow for quasi-central city.
Ratio of private-public transportation: 0O%-100%.
N'
200-'8
-85_M2
N
t
1~
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'1)
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Figure 27.
Peak one-directional flow for many-centered city.
Ratio of private-public transportation: 100o%-0%.
-86Z
2s'o-z
Z-15'0-MZ
. 200-mzZoo-Mz 200-MZ
200-Mz
25,0_M2
N
C"
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r
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in
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,,
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N
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0
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2
I,S
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450-S
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14
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0
0
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0
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0
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Figure 28.
Peak one-directional flow for many-centered city.
Ratio of private-public transportation: 75%-25%.
2. goo-6
,
850-5
-87zoo -M2
220 -M
O -
25-o-M2
2--2
75"o-Mg
Z,-2
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2
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200-112.
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to
a
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± 500-MZ
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a
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I
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,
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en
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Figure 29.
Peak one-directional flow for many-centered city.
Ratio of private-public transportation: 50%-50%.
(0
I
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2oo-192
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N'
r4
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250-192
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N
C
a
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300-Pi2.
2:
a
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a
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N
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a
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Figure 30.
Peak one-directional flow for many-centered city.
Ratio of private-public transportation: 25%-75%.
PO
'A
vr-M
a a
a
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zo o-'3
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a
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ea
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Figure 31.
Peak one-directional flow for many-centered city.
Ratio of private-public transportation: 0%-100%.
-901
0
~
ai'J-A-L
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N
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N
0
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2 0 6E626- 2,450qf'-h
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3,00-MZ
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Figure 32.
Peak one-directional flow for layered city.
Ratio of private-public transportation: 100%-0%.
-
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I~A
150-82
.j., ,iso-h2
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450-MZ
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600-82.
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750-M2
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sq
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1,600-3
Figure 33.
Peak one-directional flow for layered city.
Ratio of private-public transportation: 75%-25%.
Z~
F,
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4
I I 100- 1:5
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a
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ro-
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trol-
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200-112
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N
N
200-M2
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3,
Figure 34.
Peak one-directional flow for layered city.
Ratio of private-public transportation: 50%-50%.
0 -
2,I
m17V-
p
7-U
-I
-930
100-l2
M2
IA00-
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O-M2
i5~o-rl2
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450 -
500-6
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100-MZ
IS0-M2
30 0-8
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400-B
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15~1-M2.
100-m2
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got
N
N
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6So-6
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1,0-
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300-2
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700-B
500-M
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0
3I50-6
4,2-a0o -
4,700-
4,950 -15
S,050-B
4,GO
0
Figure 35.
Peak one-directional flow for layered city.
Ratio of private-public transportation: 25%-75%.
-
-',0
=
I
O
I
L
-94I5'0- N2
--M2 o-M2
V
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0
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a+
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tor
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o
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li 0
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614o-7B
-b
l,200-S
I oo-S
itc
S,00-
C,60-
6,250-S
6,600 -S
Figure 36.
Peak one-directional flow for layered city.
Ratio of private-public transportation: 0O%-100O%.
SIoO-S
2, 3so-IB
-950
22^
0-M
v
-
,,-
-
-
N
N
£
s~s-0-
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I
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S-
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('4
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0
N
N
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400-M2
40 -M
2
N
N
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'I,
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k. 2
1%.d
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0
1.4
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-
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9
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r
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r
>
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o-4
~
1,300-14
oo-
ISO-M2
S5'0-M2
- _MZ______m
--
1.2 0-114
I,Z50 -M4
Figure 37.
Peak one-directional flow for homogeneous city.
Ratio of private-public transportation: 100%-0o%.
T
N
z
\ 150- M2
-96Igo-Mz
zool-Mz
zoo-M2
20 -M
Ir-
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-1
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N
CN
5'00
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N
A
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40
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200-S
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a
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400-112
-4()O-MZ
7
N
N
N
a
'4
a
a
a
a
V
1
CN
a
a
0
N
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fo
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650- M2
6SO-M2
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N
(.4
a
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a
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-M2
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l-N
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a 1
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N
N
M2
4
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N
z
CO
a
g-
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-
N
(.4
a
a a
a "I
N
~0
90o-M4
300-S,
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x
1 ;0
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Bc'0-l'12
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-
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N
a 9oo-84
a
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0
a
a
r*i
N
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3o0-a
9(o-s
10OTSOM
I'O-Mz
M2
N
r
a
a
CS
10--
S0M
aD
zo-
Figure 38.
Peak one-directional flow for homogeneous city.
Ratio of private-public transportation: 75%-25%.
CM
-97200-M2
200-M2
I5'0-Mz
0-M2
(So-M2
15o-M2
N
N
t
0
0
2
-9
M
2
zo -
N
Q
N
2
0~-12
250-
0-M2
200-92
,SOM
200--B
2.o0-M2
'OM
250-B
13
tq
C4 N
N
N
N
t
N
z0
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M2
350-8
400-^S
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N
z
0
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o
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Cl
-
45"o-M2
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450-S
s-o0-s
E
fou
0
0
1'
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N
0
'I,
0
0
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lb
0
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oo-B
0
%n %?
600-2
600-b
(ISIC)-S
N
z
0
0
0
"I
z
'S
650-5i2
N
0
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N
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;0
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Cl
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0
0 0
N
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0
0
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0
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3 5-
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z
, SOO-M2
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N
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N
C%
N
N
150-ZM
10o-MZ
,
,50-M-4
0
0 0
~0
6.fo-MZ
650-0
Figure 39.
Peak one-directional flow for homogeneous city.
Ratio of private-public transportation: 50%-50%.
-M
-98Zoo-M2
N
200-MIZ
N
a
a
t
N
t
I5r0-1
400-IS
z0o-r'i
q
a
41
200-liz
200-MZ
400-S
600 -S
V4j
z
2S0O- M
N
t
N
250-M2
'750 -9
N
a
a
b
N
Q
250-82
I
N
2i00-M2
2S0 _M2_
|
8ro-%
N
-
400--a
z
a
N
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a
a a
N
200O-Mi
-~250-M42
SOO-15
81o-a
via
a
-
2.00--MZ
5350-'B
200-MZ
(So-b
N
-
a
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N
3
00-f 2.
900-S
N
a
a
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N
00-Mz
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a
a a*
a*
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t
a a
a
N
a
a
ico M2
7
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(V)
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goo-a
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1:
a
a
a
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a
a 'U'
a (1
If 0-M 2
150 -4 Z
500-8B
0
N
~ I-
'300-15
"'B
I"
Figure 40.
Peak one-directional flow for homogeneous city.
Ratio of private-public transportation: 25%-75%.
a
ITO-M2
150-M2
I~
a
N CC
Qz
a
-M
N
oof-M2
~
~BIO7-M
T
I oo-Hz
15'0-O ~~ 2
350-13
N
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a a
a a
a
a
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a
6-0-M2
too
N
N
N
15o-M12
N
N
a
a
N
B 5'o-.M2
N
N
a
a
N
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iro-M1
ff0-M
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N
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eA
I
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i
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N
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900-8
1
VI
0
100-'8-
4
I,05'0-
I 900-'s
all
I2I
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700 -'a
1,0 50-3
on
1ie300- 4
-M Z
, l00-M2
, 150-MZ
200-B
6N
N
150
,
II zoo-B
Figure 41.
Peak one-directional flow for homogeneous city.
Ratio of private-public transportation: 0%-100%.
N
I 300 -
:300-_'
N
rl
-100500-lIZ
400-MZ
35o-mz
r
4z
1~
0
4-
0
0
Lu
'1,00-M4
1*
15,OO -
,
, ,50
M4
1,600-Mll
-M4
r
'Il
00
1,15~0 - M4
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Lu
1, 6!ro -Mi
1~
Lu
0
'A
1,8 00-M4A
1,600-M4
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Lu
0~
NT
1,8O-MA4
LU
I,950*-4
M
1,
8S0-M4
jl-00-m4
0
0
0
In
NT
0
1,900-M4
1850-M4
,
'3'U
0
1,-0E4
0
I,900-Mi
(43
N
1, 900-MA
, 2,000-
I, 95 0 -EA
E4
Lu
10
N
1,86-7M4
Gio-
'A
0
0
N
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'A
1,700-M-4
'3-
-so-M1
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00
1,450-M4
M'.
'3-
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1,600-M4
'o0-
'3-
1,400-M4
.,300-M,4
600-MZ
V
193-
2:
0
"7
Figure 42.
Peak one-directional flow for ring city.
Ratio of private-public transportation: 100%-O%.
M2
-101-
10~
-
9a
a
I
)AALII
'S
t
'A
1/300-MA
'A
IA .4-
t
0-
-
14r
&too
B
S
a
a
'A \A
30
5,20-r4
If35o-N~4
~
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a
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4-o -S
r
I,AV5-r4
a
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to
a A
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400-g
1~
fZ00-114
11300-M,4
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1
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400-S
'A
1*
1~
Cr...j.qA
A
a a
a CO
a
a a
a 'A
z a
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3S0-B
1~i
C
q,
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a a
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1* 'A
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2100-t4
1,200- MA
400-11,
3so-S
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a
a
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a
1,100-114
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200--e
a
a a
a 'A
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fa
GO0-MZ
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oz 1-mz
sro..ia
roo-mz
40o-iz
-
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10-3
I
t
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a
a
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C
C
a
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C
a
a
I Soo-13
1-
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1~
a
'A
1~
Figure 43.
Peak one-directional flow for ring city.
Ratio of private-public transportation: 75%-25%.
- 0
65O#1
-102200-iiZ
200 - m z
-M2
250
N
N
r
a
a
'A
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a
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,
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a
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0%
Aa-o..
2
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a
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r
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a
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900-14
9_o-M4
ao-B
1*
x
a
a
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1~
a
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a
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a
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a a
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1,000-M,4
9toM
1,000-5
9 o-
75'0-IZ
t
'A
0%
*
9S-14
a
a
0%
Figure 44.
Peak one-directional flow for ring city.
Ratio of private-public transportation: 50%-50%.
35t-
I-
,
Foo-8
9O0-9
-a.
V,
Soo-
0
9s-0-&
8oo-i$
SOO-M2
SOO-M2
350-MZ
N
a a
a
a
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1-
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________
N
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00
750 -1?,
'o0-B
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32 r
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400-15
4oo-M2
3SOIrI12
300--S
N
t
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300-M2
N
10
I-.
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300-M2
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0
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200-H2N
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to
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t
6
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0
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i,400 -B
t
N
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400-m2
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,300-B
z
'4
0
1
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0
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it,3rSo-
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i,soo-B
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I, 500'I
0
w,
0-i
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£'00 -I-i
1,4O - IS
I,ro0 --S
41,400-8
0
Figure 45.
Peak one-directional flow for ring city.
Ratio of private-public transportation: 25%-75%.
k
3Iro0- M Z
1,100-B
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Figure 46.
Peak one-directional flow for ring city.
Ratio of private-public transportation: 0%-100%.
APPENDIX D-TABULATIONS OF PEAK ONE-DIRBCTIONAL FLOW CHARACTERISTICS
The following tables represent tabulations of various
characteristics taken from the peak directional flow diagrams
given in Appendix C.
The figures listed here are for the
total city, not just the octant or quadrant depicted in the
flow diagrams.
The modal splits are written with the percentage of
private transportation given first; thus, for example, 75-25
represents 75 percent private transportation and 25 percent
public transportation.
PMT is an abbreviation for the number of person-miles
traveled.
-105-
-11
-106Percent Modal Split:
75-25
50-50
25-75
0-100
188
83,200
224
103,000
76
17,000
284
108,600
212
95,400
376
104,000
344
302,800
472
1,200
448
822,000
136
190,800
120
149,800
49,200
128
158,200
158,200
88
90,400
271,800
24
51,600
40
82,400
27,600
24
47,200
47,200
8
14,000
42,000
52
145,400
52
139,400
46,600
20
52,200
52,200
20
51,800
85,600
on 12 mi.
44
160,400
32
129,800
55,800
16
52,000
52,000
36
208,200
8
42,000
14,000
20
103,600
103,600
28
263,000
24
194,000
51,800
on 20 mi.
4
36,200
100-0
2-Lane Major Street
Miles of road
PMT by auto
Mi. of bus rte.
PMT by bus
4-Lane Major Street
Miles of road
PMT by auto
PMT by bus
4-Lane E2xpressway
Miles of road
PMT by auto
PMT by bus
6-Lane Expressway
Miles of road
PMT by auto
PMT by bus
4-Lane Freeway
Miles of road
PMT by auto
PMT by bus
6-Lane Freeway
Miles of road
PMT by auto
PMT by bus
8-Lane Freeway
Miles of road
PMT by auto
PMT by bus
2-Track Rail
Miles of track
PMT by train
Total PMT by Road
Total PMT by Bus
Actual % Auto Travel
--
36,200
12
124,200
24
279,400
840,400
558,000
278,200
1,200
262,000
508,600
702,200
822,000
76.23
50.60
25.19
0.11
--
1102,600
--
100.00
4
4
18,000
Total PMT, all modes, in lesser direction = 109,200
Average Length of Trip = total PMT (both directions)/city pop.
= 1,211,800/126,000 = 9.62 miles
Table 10. Tabulation of peak one-directional flow characteristics
for the central city.
.. . .._----- -
.
...
..
..
.-,.
.
1
-107Percent Modal Split:
75-25
50-50
25-75
0-100
196
92,000
228
105,600
88
19,600
336
142,200
272
130,200
484
155,800
436
442,600
532
3,200
508
817,800
188
264,200
212
265,800
88,800
148
162,600
162,600
48
55,600
166,600
52
110,200
44
88,800
30,200
28
55,600
55,600
8
14,800
44,400
52
138,600
20
57,200
19,200
8
19,200
19,200
4
11,200
36
148,400
28
109,400
36,400
20
66,600
66,600
12
74,000
o--
8
44,400
14,800
4
22,400
22,400
12
97,600
4
33,600
11,200
100-0
2-Lane Major Street
Miles of road
PMT by auto
Mi. of bus rte.
PMT by bus
4-Lane Major Street
Miles of road
PMT by auto
PMT by bus
4-Lane Expressway
Miles of road
PMT by auto
PMT by bus
6-Lane Expressway
Miles of road
PMT by auto
PMT by bus
--
4-Lane Freeway
Miles of road
PMT by auto
PMT by bus
6-Lane Freeway
Miles of road
PMT by auto
PMT by bus
8-Lane Freeway
Miles of road
PMT by auto
PMT by bus
2-Track Rail
Miles of track
PMT by train
Total PMT by Road
Total PMT by Bus
Actual % Auto Travel
---
4
33,600
12
104,000
925,000
704,800
468,600
237,400
3,200
--
220,200
456,500
653,600
817,800
76.19
50.65
25.68
0.36
100.00
Total PMT, all modes, in lesser direction = 371,200
Average Length of Trip = total PMT (both directions)/city pop.
= 1,296,200/122,000 = 10.62 miles
Table 11. Tabulation of peak one-directional flow characteristics
for the quasi-central city.
-108Percent Modal Split:
50-50
25-75
212
97,200
56
14,000
292
123,600
220
104,400
464
152,800
432
436,600
188
280,800
240
332,400
112,000
224
265,000
265,000
76
67,600
203,600
84
185,200
24
53,200
17,400
16
32,200
32,200
4
6,600
20,000
48
141,800
56
147,800
49,000
8
18,800
18,800
48
184,400
8
28,400
9,600
4
13,400
13,400
4
26,600
4
20,000
6,600
100-0
2-Lane Major Street
Miles of road
PMT by auto
Mi. of bus rte.
PMT by bus
4-Lane Major Street
Miles of road
PMT by auto
PMT by bus
4-Lane Expressway
Miles of road
PMT by auto
PMT by bus
6-Lane Expressway
Miles of road
PMT by auto
PMT by bus
4-Lane Freeway
Miles of road
PMT by auto
PMT by bus
6-Lane Freeway
Miles of road
PMT by auto
PMT by bus
8-Lane Freeway
Miles of road
PMT by auto
PMT by bus
172
69,200
--
75-25
0-100
544
544
888,000
2-Track Rail
Miles of track
PMT by train
Total PMT by Road
Total PMT by Bus
Actual % Auto Travel
Total PMT,
all modes,
888,000
679,000
453,000
227,000
--
208,600
433,800
660,200
888,000
76.50
51.08
25.59
0.00
100.00
in lesser direction = 479,000
Average Length of Trip = total PMT (both directions)/city pop.
= 1,367,000/122,000 = 11.20 miles
Table 12. Tabulation of peak one-directional flow characteristics
for the many-centered city.
-
m
-109Percent Modal Split:
100-0
2-Lane Major Street
Miles of road
PMT by auto
Mi. of bus rte.
PMT by bus
4-Lane Major Street
Miles of road
PMT by auto
PMT by bus
4-Lane Expressway
Miles of road
PMT by auto
PMT by bus
6-Lane Expressway
Miles of road
PMT by auto
PMT by bus
4-LaneFreeway
Miles of road
PMT by auto
PMT by bus
6-Lane Freeway
Miles of road
PMT by auto
PMT by bus
8-Lane Freeway
Miles of road
PMT by auto
PMT by bus
2-Track Rail
Miles ofTtrack
PMT by train
Total PMT by Road
Total PMT by Bus
Actual % Auto Travel
196
94,200
---
146
202,900
--
38
79,500
--
50
136,500
--
72
294,500
--
42
225,700
--
--
75-25
50-50
25-75
244
121,400
98
23,300
306
122,700
246
110,300
422
544
125,500
3,200
390
544
362,900 1030,100
148
196,400
65,600
136
160,500
160,500
116
126,500
378,000
--
38
80,100
26,600
44
90,000
90,000
6
9,900
29,600
--
38
106,000
35,700
50
123,800
123,800
----
----
68
244,600
81,700
8
26,100
26,100
--
--
--
--
----
----
----
--
--
--
8
39,000
13,000
--
0-100
---
---
--
--
--
--
--
---
---
--
--
--
--
787,500
523,100
261,900
245,900
510,700
770,500 1030,100
1033,300
--
10.00
76.20
--
50.60
25.37
--
3,200
0.31
Total PMT, all modes, in lesser direction = 274,000
Average Length of Trip = total PMT (both directions)/city pop.
= 1,307,300/120,000 = 10.89 miles
Table 13. Tabulation of peak one-directional flow characteristics
for the layered city.
-110Percent Modal-Split:
2-Lane Major Street
Miles of road
PMT by auto
Mi. of bus rte.
PMT by bus
4-Lane Major Street
Miles of road
PMT by auto
PMT by bus
4-Lane Expressway
Miles of road
PMT by auto
PMT by bus
6-Lane Expressway
Miles of road
PMT by auto
PMT by bus
4-Lane Freeway
Males of road
PMT by auto
PMT by bus
6-Lane Freeway
Mles of road
PMT by auto
PMT by bus
8-Lane Freewa
Miles of road
PMT by auto
PMT by bus
100-0
75-25
50-50
25-75
0-100
392
188,600
488
244,600
188
43,800
544
192,000
412
167,600
544
105,200
420
253,000
544
6,800
496
350,400
--
--
--
--
152
168,600
--
56
51,400
16,800
--
--
--
--
--
--
---
----
----
----
----
----
----
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
----
--
--
--
--
---
---
---
--
---
---
------
--
--
--
--
--
--
--
--
--
--
--
--
---
---
2-Track Rail
Miles of track
PMT by train
---
---
---
---
---
Total PMT by Road
357,200
296,000
192,000
105,200
6,800
60,600
167,600
253,000
350,400
83.01
53.39
29.37
1.90
Total PMT by Bus
Actual % Auto Travel
--
100.00
Total PMT, all modes, in lesser direction = 333,400
Average Length of Trip = total PMT (both directions)/city pop.
= 690,600/64,000 = 10.79 miles
Table 14. Tabulation of peak one-directional flow characteristics
for the homogeneous city.
A
-111Percent Modal Split:
100-0
2-Lane Major Street
Miles of road
PMT by auto
Mi. of bus rte.
PMT by bus
4-Lane Major Street
Miles of road
PMT by auto
PMT by bus
4-Lane Expressway
Miles of road
PMT by auto
PMT by bus
6-Lane Expressway
Miles bf road
PMT by auto
PMT by bus
4-Lane Freeway
Males of road
PMT by auto
PMT by bus
6-Lane Freeway
Miles of road
PMT by auto
PMT by bus
8-Lane Freeway
Miles of road
PMT by auto
PMT by bus
75-25
50-50
25-75
544
224,400
544
675,600
544
901,800
0-100
--
64
36,400
8
--
3,200
204
124,600
204
124,600
480
646,400
214,800
340
326,600
326,600
--
--
--
--
--
--
----
----
----
-------
64
39,200
328
547,600
--
152
315,000
--
---
---
--
544
--
--
--
--
---
--
--
--
--
--
---
---
---
---
--
----
----
----
----
----
--
--
--
--
--
---
---
--
---
---
2-Track Rail
Miles of track
PMT by train
---
---
---
---
---
Total PMT by Road
901,800
682,800
451,200
224,400
--
--
218,000
451,200
675,600
901,800
75.80
50.00
24.93
0.00
Total PMT by Bus
Actual % Auto Travel
100.00
Total PMT, all modes, in lesser direction = 391,200
Average Length of Trip = total PMT (both directions)/city pop.
= 1,293,000/98,000 = 13.19 miles
Table 15. Tabulation of peak one-directional flow characteristics
for the ring city.
APPENDIX B--SAMPLE CALCULATION OF COSTS
In this appendix, the complete set of cost calculations
is performed for the quasi-central city with a modal split
of 25% private transportation and 75% public transportation.
1. Capital and maintenance costs
484 miles of 2-lane major street @ $400,000/mile = $193,6 00,000
48 miles of 4-lane major street @ $600,000/mile =
8 miles of 4-lane expressway @ $800,000/mile
28,E 00,000
=
6,400,000
4 miles of 6-lane expressway @ $1,100,000/mile =
4,4 00,000
Total construction cost of roads = $233,2 00,000
Capital recovery factor (CRF) for 51% interest and 35 yea r
life = .064975.
Therefore, the annual construction cost of
roads = .064975 x $233,200,000 = $15,152,000.
Annual maintenance cost of roads @ $1,000/lane-mile =
$1,000 x (2 x 484 + 4 x 48 + 4 x 8 + 6 x 4) = $1,216,000.
Therefore, $15,152,000 + $1,216,000 =
Total annual road cost = $16,368,000
The flow diagrams are drawn only for the direction of
heavier flow on each road.
Therefore, to obtain two-direction
PMT's (person-miles traveled) for any mode of transportation,
multiply the one-direction PMT's by a proportionality constant k.
This constant k will be equal to the total PMVT for
the city (both directions) divided by the total one-direction
PMT.
(The ratios between the different modes of travel are
assumed constant for the two directions).
-112-
-113Since k = 1,296,200/924,600 = 1.402, the total PMT by
bus = 1.402 x (442,600 + 166,600) = 1.402 x 609,200
= 854,000 person-miles on major streets
= 1.402 x 44,400 = 62,000 person-miles on expressways
Assuming maximum efficiency of bus scheduling (all
buses always run at full capacity during the rush hour),
the capacity of one bus operating on major streets (average
speed of 15 miles per hour, including stops) = 50 persons
per bus x 15 miles per hour = 750 person-miles per bus (for
the one-hour time period).
Therefore, the required number of buses for the major streets
= 854,000/750 = 1,140 buses.
And similarly, the required number of buses for the expressways = 62,000/(50x20) = 62 buses.
Therefore, the total number of buses required = 1,202 buses.
At a cost of $30,000 per bus, an interest rate of 5-,k%, and
a life of 12 years (CRF = .116029), the annual purchase cost
of the buses = 1,202 x $30,000 x .116029 = $4,184,000.
Annual yard and shop costs @ $4,500 per bus (life of 40 years)
= 1,202 x $4,500 x .062320 = $337,000.
Therefore, $4,184,000 + $337,000 =
Total annual bus cost = $4,521,000
Similarly, the total number of PMT's by rail will be equal
to 1.402 x 33,600 = 47,000 person-miles.
And the required number of cars = 47,000/(80 persons per car
35 miles per hour) = 17 cars.
x
-114At a cost of $90,000 per car, an interest rate of 5-f-%,
and
a life of 30 years (CRF = .068805), the annual purchase cost
of the cars = 17 x $90,000 x .068805 = $105,000.
Annual yard and shop costs @ $8,000 per car (life of 50 years)
= 17 x $8,000 x .059061 = $8,000.
For surface rail:
4 miles of track (complete way and structures) @ $4,000,000
per mile = $16,000,000.
4 stations (assuming one station per mile of track) @
$500,000 per station = $2,000,000.
Therefore, annual construction cost for track and stations
(life of 50 years) = $18,000,000 x .059061 = $1,063,000.
For underground rail (subway):
4 miles of track @ $17,500,000 per mile = $70,000,000.
4 stations @ $3,000,000 per station = $12,000,000.
Therefore, annual construction cost for track and stations
(life of 50 years) = $82,000,000 x .059061 = $4,843,000.
Therefore, $105,000 + $8,000 + $1,063,000 =
Total annual surface rail cost = $1,176,000
Or, alternatively, $105,000 + $8,000 + $4,843,000 =
Total annual subway cost = $4,956,000
Therefore, $16,368,000 + $4,521,000 + $1,176,000 = Total annual capital & maint. cost (with surface rail) = $22,065,000.
Or, alternatively, $16,368,000 + $4,521,000 + $4,956,000 =
Total annual capital & maint. cost (with subway) = $25,845,000.
-115And $22,066,000/122,000 persons = Per capita capital and
maintenance cost (with surface rail) = $180.86.
Or, alternatively, $25,845,000/122,000 persons = Per capita
capital and maintenance cost (with subway) = $211.84.
2. Operating costs
(The factor k (= 1.402) is again applied to determine total
two-direction PMT's).
1.402 x (155,800+55,600) person-miles traveled by auto on
major streets @ $.059 per person-mile = $17,487.
1.402 x 26,000 person-miles by auto on expressways @ $.053
per person-mile = $1,932.
1.402 x 653,600 person-miles traveled by bus @ 50 persons per
bus & $.50 per bus-mile = 1.402 x 653,600 x ($.50/50)
= $9,163.
1.402 x 33,600 person-miles traveled by rail @ 80 persons per
car & $.70 per car-mile = 1.402 x 33,600 x ($.70/80) = $412.
Therefore, $17,487 + $1,932 + $9,163 + $412 =
Total operating cost = $28,994
And $28,994/122,000 persons =
Average operating cost per traveler = 23.77#
And 23.770/10.62 miles per traveler =
Average operating cost per mile = 2.240
3. Time costs
(Once again, the factor k (= 1.402) is applied to determine
total two-direction PMT's).
1.402x211,400 PMT by auto on maj. st./25 mph = 11,855 pers-hrs
-I
-1161.402x26,000 PMT by auto on exp'way/35 mph =
1,041 Ders-hrs
1.402x609,200 PMT by bus on maj. st./15 mph = 56,940 pers-hrs
1.402x44,400 PMT by bus on explway/20 mph =
3,112 pers-hrs
1.402x33,600 PMT by rail transit/35 mph=
1,346 pers-hrs
Total traveling time = 74,294 person-lirs.
To compute the waiting time for bus transit, let:
PMT = number of person-miles traveled by bus (per hour)
N = number of persons traveling by bus (per hour)
L = total length of bus route, in miles
d = average trip length by bus, in miles (assume equal to
average trip length by all modes, which is known)
q = avg. flow along bus route, in no. of persons (per hr.)
h = average headway, in hours
w = average waiting time, in hours
W = total waiting time, in person-hours
Then, for the one-hour time period:
h = (number of buses per hour)- 1 = (q/50 persons per bus)-1
h = ((PMT/L)/50)- 1 = 50L/PMT
w = h/2 = 25L/PMT
W = wN = (25L/PMT) x (PMT/d)
W = 25L/d
This is a very interesting result, indicating that the total
waiting time is dependent only upon the length of bus route
and the average trip length, and is not dependent upon the
number of person-miles traveled.
In other words, for example,
if the PMT on a particular length of bus route is increased
-117(average trip length remaining the same), the number of buses
required will increase, and the headway and, consequently,
the average waiting time per person, will decrease.
But
since more people are now waiting for buses, the total waiting
time will remain constant.
Since, in this example, L~
k x (436+48+8) = 1.402 x
492 = 690 miles, and d = 10.62 miles, the total waiting time
for buses = 25 x 690/10.62 = 1,624 person-hours.
And similarly, for rail transit, W = 40L/d.
And since L=
1.402 x 4 = 6 miles, the total waiting time for trains =
40 x 6/10.62 = 23 person-hours.
Also, since it might be useful as a measure of the cost of
control which will be required, the average headway for
buses = 50LB/PMTB (in hours) = 60 minutes per hour x 50
persons per bus x k x 492 miles/k x 653,600 person-miles per
hour = 3,000 x 492/653,600 = 2.26 minutes.
And the average headway for rail transit = 60 minutes per
hour x 80 persons per car x k x 4 miles/k x 33,600 personmiles per hour = 4,800 x 4/33,600 = 0.571 minutes for each
individual car.
Assuming an average of four cars per train,
the average headway for trains = 4 x 0.571 = 2.28 minutes.
Assuming that persons can enter the main transportation
network only at the nodal points, or route intersections at
one-mile spacings (this is not quite accurate in the case of
autos traveling via major streets and possibly via expressways, but the error is a small one), some time is required
-118for traveling to the main transportation network.
The
average distance traveled for this purpose--assuming within
each mile-square block, uniform density, all travel parallel
to the grid, and entrance to the system at the nearest nodal
point--will be one-half mile.
The total preliminary trav-
eling time to the system, then, assuming average pedestrian
travel at 3 miles per hour and average automobile travel at
12 miles per hour on the minor streets, will be 25.68% x
122,000 persons x 0.5 miles/12 miles per hour = Preliminary
traveling time for motorists = 1,305 person-hours.
And = 74.32% x 122,000 persons x 0.5 miles/3 miles per hour =
Prelim. traveling time for transit riders = 15,112 person-hrs.
Therefore, 74,294 + 1,624 + 23 + 1,305 + 15,112 =
Total time for all journeys = 92,358 person-hours
And 92,358 person-hours/122,000 persons =
Average time of journey = 0.757 hours = 45.42 minutes
And 1,296,200 person-miles/92,358 person-hours =
Average speed of complete journey = 14.03 miles per hour