EPA 400-11-76-001
TRANSIT REQUIREMENTS FOR ACHIEVING LARGE
REDUCTIONS IN LOS ANGELES AREA
AUTOMOBILE TRAVEL
3J ^
Q
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C.
NOVEMBER 1976
-------
EPA/400-11/76-001
TRANSIT REQUIREMENTS FOR ACHIEVING LARGE
REDUCTIONS IN LOS ANGELES AREA
AUTOMOBILE TRAVEL
by
JOEL HOROWITZ
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C.
NOVEMBER 1976
-------
111
TABLE OF CONTENTS
Abstract iv
List of Figures v
List of Tables V1-
Introduction 1
Structure of the Model 3
Application of the Model to Los Angeles 18
Sensitivity Analysis 29
Conclusions 32
Acknowledgement 34
References 35
Appendix A: Equations of the Model 37
Appendix B: Inputs and Outputs of the Model 49
Appendix C: Additional Los Angeles Results 53
-------
IV
ABSTRACT
This paper describes the structure and application of a model for
estimating aggregate supply characteristics of bus transit systems that
are capable of carrying substantial fractions of the person trips in an
urban area. Given the number and geographical distribution of trips that
must be carried on transit, the model enables a range of transit options
for carrying these trips to be developed. Each option is characterized
by the number of buses it requires, the geographical area served by transit,
the transit schedule frequency, the transit mode split that must be achieved
in the transit service area, average transit travel time and cost per trip,
and the average travel time and cost that would result if bus travelers
used automobiles.
The model is applied to Los Angeles, California. The results indicate
that large fractions of current person trips in Los Angeles can be carried
on bus transit at a cost that is comparable to the cost of automobile
travel and with an average travel time that exceeds average automobile
travel time by 15 to 20 minutes. However, this requires bus fleets and
transit mode splits that are quite large by current standards. For example,
to carry 20 percent of person trips at a cost equal to the cost of auto-
mobile travel and with an average travel time 17 minutes greater than
average automobile travel time, the transit system must have 9500 buses
and must achieve a 45 percent mode split in the areas it serves.
-------
V-
List of Fi gures
Page
Figure 1 - District Map of Los Angeles 6
Figure 2 - Schematic Diagram of Intra-District Service 8
Figure 3 - Schematic Diagram of Inter-District Service 10
Figure 4 - Nomograph of Los Angeles Results 24
Figure Cl - Reduction in 6 AM - 8PM Automobile VMT as
Function of Fraction of 6 AM - 8 PM Trips Using
Transit' 54
Figure C2 - Components of Bus Travel Time and Cost 55
Figure C3 - Size of Transit Service Area as Function of
Threshold Trip Volume 56
Figure C4 - Transit Service Area for 500 Trip Per Hour
Threshold 58
Figure C5 - Transit Service Area for 1500 Trip Per Hour
Threshold 59
Figure C6 - Transit Service Area for 2400 Trip Per Hour
Threshold 60
Figure C7 - Bus Travel Time - Automobile Travel Time vs. Bus
Travel Cost - Automobile Travel Cost 63
Figure C8 - Bus Travel Time - Automobile Travel Time vs.
Transit Mode Split 64
Figure C9 - Bus .Cost - Automobile Cost vs. Transit Mode Split 65
Figure CIO - Bus Travel Time - Automobile Travel Time vs.
Bus Travel Cost - Automobile Travel Cost 66
Figure Cll - Bus Travel Time - Automobile Travel Time vs.
Transit Mode Split 67
Figure C12 - Bus Cost - Automobile Cost vs. Transit Mode Split 68
Figure C13 - Bus Travel Time - Automobile Travel Time vs.
Bus Travel Cost - Automobile Travel Cost 69
Figure C14 - Bus Travel Time - Automobile Travel Time vs.
Transit Mode Split 70
Figure C15 - Bus Cost - Automobile Cost vs. Transit Mode Split 71
-------
VI
List of Tables
Table 1 - Capital Costs and Service Lives 17
Table 2 - Parameters of the Model 20
Table 3 - Characteristics of Los Angeles Transit Options 22
Table 4 - Response of Model to Ten Percent Changes in
External Parameters 30
-------
TRANSIT REQUIREMENTS FOR ACHIEVING
LARGE REDUCTIONS IN LOS ANGELES
AREA AUTOMOBILE TRAVEL
by
Joel Horowitz
U. S. Environmental Protection Agency
Washington, D. C.
The need to reduce air pollution, energy consumption, and traffic
congestion caused by automobiles has stimulated widespread discussion of
the feasibility and desirability of diverting large numbers of urban area
automobile travelers to other modes. Much of this discussion has been
concerned with issues of travel demand. The problem of identifying
measures that are effective in reducing the demand for automobile travel
-has received particular attention. Several investigators (Ref. 1, 2, 3)
have suggested that if suitable policies influencing travel demand were
implemented, automobile travel in cities could be reduced by 20 to 30
percent. The reduction would be achieved mainly by diverting automobile
drivers to transit and carpools. Traffic reductions of lesser but nonethe-
less impressive magnitudes already have been achieved in some cities through
the implementation of policies to control the demand for automobile travel
(Ref. 4, 5).
The problem of characterizing transit systems that could carry a
large fraction of current urban area automobile trips has received less
attention than demand-related issues. Transit system characteristics that
might affect the feasibility of diverting large numbers of automobile users
-------
-2-
to transit include the number of transit vehicles required, the
geographical area served by the transit system, the relative travel times
of transit and automobile trips, the relative costs of transit and automobile
service, and the mode split that the transit system must achieve. One
possible reason for the relative neglect of these matters in the discussion
of the feasibility of achieving large reductions in urban area automobile
traffic is the lack of a methodology that would enable aggregate characteristics
of transit systems that may be quite different from current systems to be
estimated relatively quickly and inexpensively for use in policy planning.
Techniques of the UTPS type tend to be too cumbersome, costly, and time
consuming for use in policy planning. Simpler techniques frequently are
used to compare the characteristics of alternative modes in a corridor
(Ref. 6, 7, 8, 9), but these techniques have not been generalized for
application to an entire urban area. A model developed by the RAND
Corporation (Ref. 10) does enable aggregate characteristics of a regional
transit system to be estimated quickly and inexpensively. However, this
model assumes a uniform distribution of trip ends over the transit service
area and, hence, does not reflect the spatial structure of travel demand.
This paper describes a model that was developed to estimate aggregate
characteristics of bus transit systems capable of carrying substantial
fractions of person trips — and, by implication, automobile trips — in the Los
Angeles area. The model can be applied to other cities easily and removes
some of the previously described methodological difficulties. Given the
number and geographical distribution of trips that must be carried on the
-------
-3-
transit system, the model enables a range of transit options capable of
carrying these trips to be developed. Each option is characterized by
the number of transit vehicles it requires, the geographical area served
by transit, the transit schedule frequency, the transit mode split that
must be achieved in the transit service area, average transit and auto-
mobile travel times per trip, and average transit and automobile costs
per trip. The model is based on a generalization of techniques that have
been used in corridor-level comparisons of modal options (Ref. 6, 7, 8, 9).
The model is not intended to provide information useful in the detailed
design and evaluation of transit systems. Rather, it provides a relatively
quick and inexpensive means of generating estimates of transit supply
characteristics that can be used in forming preliminary assessments of the
feasibility of proposals for reducing automobile travel in cities and in
identifying options worthy of more detailed analysis.
In the following sections the structure of the model is described,
and the results of its application to Los Angeles are presented. The
sensitivity of the results to variations in input parameters and potential
errors in structural assumptions is discussed. Finally, conclusions based
on the Los Angeles results are presented, and limitations of the model that
might be the topics of further research are discussed.
Structure of the Model
The structure of the model is described verbally in this section. The
equations of the model are presented in Appendix A. Appendix B lists the
model's inputs and outputs.
The model is similar in concept to the previously mentioned corridor
models. Person trip volumes and transit mode splits are specified exogenously.
-------
-4-
Bus service is provided in areas where the volume of person trips exceeds
a specified threshold, and transit trips in these areas are assigned to
bus routes on an idealized street network. Buses are assigned to the
routes in sufficient quantities to both accommodate the demand for transit
trips and achieve or exceed an exogenously specified minimum schedule
frequency. Average transit travel time is computed from estimates of
average walk and wait times, in-vehicle distances, and bus speeds. Average
transit cost per trip is computed from estimates of the purchase prices of
buses and auxiliary facilities, and from estimates of the relationship
between bus miles (kilometers) traveled, bus hours of operation, and bus
operating cost. The average travel time and cost per trip that would be
incurred if all transit trips were carried in automobiles also are computed.
Through repeated runs of the model using different levels of transit mode
split, threshold trip volume for providing bus service in an area, and
minimum schedule frequency, graphical and tabular relationships among the
total number of transit trips, the transit service area, the transit mode
split that must be achieved in the transit service area, transit schedule
frequency, the number of buses needed, the average travel time for bus
trips, the average travel times that would result if the same trips took
place in automobiles, the average cost per bus trip, and the average
cost per trip that would be incurred if the same trips took place in
automobiles are developed. In general, there exists a continuum of transit
options capable of carrying a specified proportion of person trips in a
given urban area. The graphical and tabular relationships summarize the
characteristics of these options.
-------
The model is based on the traffic districts typically defined in
urban area transportation surveys. In the Los Angeles application of the
model, 100 such districts were used (Figure 1). The districts were defined
in connection with the Los Angeles Regional Transportation Study (LARTS)
and have a median area of 25 sq. mi. (64 sq. km.).
The demand for transit trips is developed from exogenously specified,
district level person trip tables and exogenously specified transit mode
split factors. The trip tables give the number of person trips per hour
between each pair of districts according to trip purpose and time of day.
The mode split factors give the fraction of trips of each purpose that will
use transit if service is provided between their origin and destination
districts. The mode split factors do not represent projections of the demand
for transit travel. Rather, they are parameters of the model that are used
to establish supply-side relationships between transit mode split and other
characteristics of the transit system.
The person trip tables and mode split factors are combined to yield
district level transit trip tables according to trip purpose and time of day.
The tables for the various purposes at each time of day are further combined
to yield district level tables specifying total transit trips per hour,
according to time of day, that will take place between each pair of districts
served by transit. These trip tables contain all the transit travel demand
information supplied to the model. In the Los Angeles application, the trip
purposes considered were work and non-work. The times of day considered were
morning peak, afternoon peak, and off peak.
-------
-6-
Figure 1 - DISTRICT MAP OF LOS ANGELES
VENTURA
LOS ANGELES
SAN BERNARDINO
RIVERSIDE
-------
-7-
A transit system that carries a substantial fraction of the trips in
an urban area must serve suburban trips as well as CBD-oriented trips.
Consequently, the model is designed to estimate the characteristics of
transit systems that serve trips whose origins and destinations are
diverse and spread over a large geographical area. The model provides
two types of transit service: inter-district and intra-district. The
inter-district service provides limited-stop, linehaul service for trips
whose origins and destinations are in different districts. The intra-
district service carries trips whose origins and destinations are in the
same district. It also provides collection and distribution service for
inter-district trips. This service design enables trips with widespread
and diverse origins and destinations to be served. It also enables the
model to use the geographically aggregated travel data normally available
in urban area transportation surveys. However, the service design does
not permit the optimization of bus service in high density corridors.
The intra-district service operates within districts and on rectilinear
routes (Figure 2). The spacing between parallel routes and between stops
along a route is equal to an exogenously specified maximum distance that
travelers must walk at each end of a bus trip. For reasons that will be
described later, this walk distance was set equal to 0.5 mi. (0.8 km.) in
the Los Angeles application. An intra-district vehicle begins its route
at a district boundary and proceeds along the route to the opposite district
boundary, making stops along the way to load and unload passengers. When
the vehicle reaches the end of its route, it turns around and traverses the
-------
Figure 2 - SCHEMATIC DIAGRAM OF
INTRA - DISTRICT SERVICE
-H + 1--
DISTRICT BOUNDARY
BUS ROUTE
• BUS STOP
-------
-9-
route in the opposite direction, again making stops along the way. The
vehicle continues this back-and-forth movement along its route throughout
the service period. When in motion, buses move at exogenously specified
automobile speeds. However, buses lose time at stops due to the loading
and unloading of passengers, acceleration, and deceleration. Buses also
lose time when turning around at the ends of their routes.
The street network on which intra-district vehicles are assumed to
operate is a square grid with a grid spacing equal to the maximum walk
distance. The average one-way length of an intra-district bus route
on this network is equal to the square root of the area of the district.
Significant differences between the geometry of real street networks and
the idealized network geometry used in the model will cause errors in the
model's results. The likely magnitudes of these errors are discussed in
the section on sensitivity analysis.
The structure of the inter-district service is illustrated in Figure 3.
The service between two districts i and j operates as follows. An inter-
district vehicle begins its route at a boundary of district i. It proceeds
across district i, making stops to load inter-district passengers at stations
whose spacing along the route is exogenously specified. No passengers are
unloaded along this portion of the route. The stations serve as points of
transfer between intra-district and inter-district vehicles, and each intra-
district vehicle detours from its route as necessary to serve the nearest
inter-district station. After loading passengers at the last station in
district i, the inter-district vehicle proceeds non-stop to the boundary
of district j. It then traverses district j, making stops at stations to
unload but not to load passengers. When it reaches the last station in
-------
-10-
Figure 3 - SCHEMATIC DIAGRAM OF INTER - DISTRICT SERVICE
DISTRICT BOUNDARY
INTER - DISTRICT BUS ROUTE
• INTER - DISTRICT TRANSFER STATION
INTERSECTING INTRA - DISTRICT BUS ROUTES
-------
-11-
district j, the vehicle reverses its route and returns to district i,
stopping at stations in district j to load passengers and at stations
in district i to unload passengers. The vehicle continues to travel
back-and-forth between districts 1 and j throughout the service period.
When in motion, the inter-district buses move at the same speeds as
automobiles. However, the buses lose time at stops and in turning
around at the ends of their routes.
An inter-district bus operating between two districts i and j uses
the same square-grid street network as intra-district vehicles on the
portions of its route that are inside districts i and j. The model does
not contain a network representation for the portion of the route between
districts i and j. Inter-district route lengths and bus speeds are
determined from exogenously specified automobile distances arid speeds.
The length of a bus route between two districts is equal to the automobile
distance between the district centroids plus the distances on the square-
grid network between the district centroids and the district boundaries.
The speed of an inter-district bus is the centroid-to-centroid automobile
speed adjusted for time lost at bus stops.
An intra-district bus traveler walks to the nearest intra-district bus
stop, waits for a bus, and boards the first bus that arrives. If the
traveler's destination is within the maximum walk distance of the route he
has boarded, he rides to the stop nearest his destination, alights from the
bus, and walks to the destination. Otherwise, the traveler must make at
most one transfer to a route that serves his destination. The traveler
walks an average distance equal to half the maximum walk distance at each
-------
-12-
end of his trip. The corresponding average walk time is computed from
this distance and an exogenous!,/ specified walk speed. The traveler
waits before boarding each vehicle he rides for a period whose average
duration is half the headway of intra-district vehicles in his district.
If a transfer is needed, the traveler spends additional time moving between
bus stops at the transfer point. This transfer time is specified exogenously.
In-vehicle distances and transfer frequencies for intra-district
travelers are estimated'by assuming that the intra-district trip density
is uniform within a district. Thus, the number of trips between a point x
in a district and a point y in the same district is assumed to be the same
for all points x and y in the district. The trip densities vary between
districts, depending on the trip volumes specified in the transit trip table
and on the district areas. The uniform density assumption implies
that the average intra-district traveler has an in-vehicle distance equal
to two-thirds of the average intra-district route length in his district.
The average in-vehicle travel time of an intra-district traveler is the
automobile travel time required to traverse this distance plus the time
the intra-district bus spends at stops while traveling along two-thirds of
its route. The average number of transfers per intra-district trip depends
on district size. In the Los Angeles application, there were an average of
0.8 transfers per intra-district trip.
An inter-district traveler walks to the nearest intra-district bus
stop, boards an intra-district bus, and travels to an inter-district transfer
station. There, he transfers to an inter-district bus and rides to a trans-
fer station in his destination district. He then transfers to another intra-
district bus, rides to the stop nearest his destination, and walks from the
-------
-13-
bus stop to his destination. An inter-district traveler must make two
transfers. At each end of his trip he walks an average distance equal
to half the maximum walk distance. The corresponding walk time is
computed from this distance and the average walk speed. The traveler's
average total waiting time is the sum of half the headway of intra-district
vehicles in his origin district, half the headway of inter-district vehicles
operating between his origin and destination districts, and half the headway
of intra-district vehicles in his destination district. The traveler spends
exogenously specified additional time moving between platforms at the
transfer stations.
It is assumed that the ends of the trips between two districts i and j
are uniformly distributed within the districts. Hence, a traveler between
districts i and j travels on a district i intra-district bus an average
distance equal to one quarter of the district 1 intra-district route
length. He travels an equivalent distance on a district j intra-district
bus. He travels on an inter-district bus an average distance equal to the
distance between the centroids of districts i and j. The average in-vehicle
travel times for inter-district travelers are computed from these in-vehicle
distances, automobile speeds within and between districts, and the time
buses spend at stops.
The model averages the walk, wait and transfer, in-vehicle, and total
travel times of all individual travelers in the transit service area, there-
by producing average transit travel times. The average travel time that
would result if all of the transit trips took place in automobiles is
computed from exogenous automobile travel time data.
-------
-14-
Bus schedule frequencies vary across routes and time periods (e.g.,
morning peak, afternoon peak, off peak), depending on passenger flows.
The passenger flow during a particular time period at the maximum load
point of a bus route is developed from the transit trip table for the
time period, the assumed distribution of trip ends within districts, and the
square-grid network geometry. The flow at the maximum load point of a route
divided by bus capacity yields the minimum bus schedule frequency needed to
carry the flow on the route during the time period. The schedule frequency
on the route during the time period is set equal to this value or an
exogenously specified minimum schedule frequency,1 whichever is larger. The
reciprocal of the resulting schedule frequency equals the bus headway that is
used in computing wait times.
The schedule frequencies together with the previously described
assumptions concerning route lengths, stop spacings, and bus speeds
enable the number of buses needed during each time period to be computed.
In addition, bus hours of operation and bus miles (kilometers) traveled
are computed for each time period. The total bus fleet size is set equal
to the largest number of vehicles needed in any time period plus five percent
for spare vehicles. Bus hours of operation and bus miles (kilometers)
traveled are summed over time periods to obtain total bus hours of operation
and bus miles (kilometers) traveled per service day.
The geographical area served by the bus system remains constant
throughout the day and is determined by the average daily volumes of person
trips on potential bus routes. Intra-district service is provided on
-------
-15-
potential intra-district routes where the average dally volume of person
trips exceeds an exogenously specified threshold. Inter-district service
is provided on potential inter-district routes where the average daily volume
of person trips exceeds the same threshhold, subject to the condition that
the routes connect districts in which intra-district service is provided.
The latter condition is imposed because the intra-district service performs
passenger collection and distribution for the inter-district service. The
provision of bus service only on potential routes that have sufficiently
large trip volumes enables the model to take advantage of the tendency of
transit service to be cheaper per trip in high-volume corridors than in low
volume ones.
Bus costs evaluated by the model include bus operating costs and the
capital costs of buses, yards and shops for buses, and inter-district
stations. The cost that would be incurred if transit passengers used
automobiles includes automobile capital and operating costs. Buses and
automobiles are assumed to operate on existing roadways. Hence, roadway
costs are not included in the model. In computing automobile capital costs
it is assumed that households owning two or more cars will dispose of one
car if transit service is available for the work trip of one or more house-
hold members. In computing automobile operating costs, it is assumed that
average automobile occupancies by trip purpose have exogenously specified
values that may exceed one person per car. All costs are expressed in
1974 dollars. Capital costs are annualized with a discount rate of 10
percent per year. Capital costs per service day are computed from the
annualized costs assuming a 255-day service year. Capital costs per trip
are computed by dividing the capital costs per service day by the number of
transit passengers per day.
-------
-16-
The capital costs and service lives used in the Los Angeles appli-
cation of the model are shown in Table 1. Automobile operating cost was
assumed to be $0.08 per vehicle mile ($0.05 per vehicle kilometer, Ref. 11).
Bus operating cost was computed using an equation derived from a cost
estimating algorithm obtained from the Southern California Rapid Transit
District. The equation is
(1) C = 0.246M + 12.43H
where C = Bus operating cost ($/day)
M = Bus miles traveled per day (1 mi. = 1.6 km.)
H = Bus hours of operation per day.
Bus and automobile operating costs per trip were computed by dividing the
daily bus and automobile operating costs by total daily transit trips.
The exogenous variables of the model define the demand for transit
trips, the transit service policies, and the operating characteristics asso-
ciated with a transit option. The model computes the total transit trips,
fleet size, average transit and automobile travel times, and average transit
and automobile costs per trip for the transit option defined by the exogenous
variables. By changing the values of the exogenous variables, the aggregate
characteristics of a range of transit options serving various levels of
demand with various service policies and operating characteristics can be
estimated. In the Los Angeles application of the model, the transit mode
split factors, threshold trip volume for providing service on a potential
bus route, and minimum intra-district schedule frequency were treated as
policy variables. The other exogenous variables were treated as fixed
-------
-17-
TABLE 1 - CAPITAL COSTS AND SERVICE LIVES
Capital Cost9 Service Life
Busb $53,000 15 Yr.
Automobile0 $ 3,400 10 Yr.
Inter-district Stationd $300,000 per berth 25 Yr.
Yards and Shopsb $14,500 per bus 25 Yr.
a. Costs are in 1974 dollars
b. Source: Ref. 8. Assumes 50-passenger seating capacity.
c. Source: Ref. 11
d. Source: Ref. 12. It is assumed that each berth can accommodate up
to 1300 inter-district passengers per hour (Ref. 13).
-------
-IB-
parameters. The values of the policy variables were changed between runs
of the model, whereas the values of the fixed parameters stayed constant.
Through a series of runs, using different values of the policy variables,
graphical and tabular relationships between total transit trips, the
transit service area, the mode split to transit that must be achieved in
the transit service area, fleet size, schedule frequency, average travel
times, and average travel costs were developed. These relationships are
discussed further in the next section,
Application of the Model to Los Angeles
The Los Angeles application is based on travel data obtained from the
Los Angeles Area Transportation Study (LARTS). District level person trip
tables, automobile occupancies, automobile travel times, and automobile
travel distances were developed from the LARTS data. Automobile speeds
and the speeds of buses while in motion were computed by dividing automobile
travel distances by automobile travel times. It was assumed that each
automobile trip incurs a terminal time of 5 minutes in addition to the
LARTS travel time. This terminal time was not included in the speed
computations.
Transit service was provided during three periods of the day: morning
peak (6 AM - 9 AM), afternoon peak (3 PM - 6 PM) and off peak (9 AM - 3 PM
and 6 PM - 8 PM). Collectively, these three periods account for 88 percent
of daily person trips in the Los Angeles area. No service was provided
between 8 PM and 6 AM.
As explained earlier, all of the model's exogenous variables except
the transit mode split factors, the trip threshold for providing bus
-------
-19-
service on a route, and the minimum intra-district schedule frequency
were treated as fixed parameters. The values that were assigned to the
parameters not developed from LARTS data are shown in Table 2. The maximum
walk distance was set at 0.5 mi. (0.8 km.) as the result of a series of
experiments with the model indicating that the 0.5 mi. (0.8 km.) distance
tends to minimize both average passenger travel time and a weighted travel
disutility equal to in-vehicle travel time plus two times out-of-vehicle
travel time. Shorter maximum walk distances increase the number of bus
stops per route. Other things being equal, this reduces both schedule
frequencies and average bus speeds. The resulting increases in wait and
in-vehicle times negate the beneficial effect of the reduced walk distance.
With maximum walk distances greater than 0.5 mi. (0.8 km.), the increase in
walk time is not fully compensated by improved bus speeds and schedule
frequencies.
The.relationship between total transit trips, transit service area,
mode split to transit in the transit service area, fleet size, minimum
schedule frequency, average travel time, and average travel cost that was
developed by repeatedly running the model with different values of the
policy variables is shown in Table 3 and Figure 4. Additional results of
the model are presented in Appendix C. In both the table and the figure,
the total number of transit trips is expressed as a percentage of total
6 AM - 8 PM person trips in the Los Angeles area. Transit service area is
defined by the trip threshold for providing service on a potential bus
route. Maps of the service areas corresponding to various threshold values
are shown in Appendix C. Travel times and travel costs respectively are
-------
-20-
TABLE 2 - PARAMETERS OF THE MODEL3
Parameter Value
Maximum walk distance at each end of
bus trip 0.5 mi.
Walk Speed 3 mi./hr.
Bus Capacity 50 passengers
Minimum schedule frequency for
inter-district buses 5 per hour
Distance between inter-district stations 1 mi.
Bus turnaround time 1 min.
Time lost by buses at each stop 0.6 min.
Time passengers spend moving
between platforms at transfer points 1 min.
a. 1 mi. = 1.6 km
b. Assumes passengers board and alight through separate double-width
doors with an average of 15 passengers boarding per stop (Ref. 13),
-------
-21-
expressed as the difference between average transit travel times and costs
per trip and the average times and costs per trip that would result if all
transit trips took place in automobiles. Automobile travel times and costs
per trip typically are in the ranges 17-19 mia and $0.40-$0.50 respectively,
depending on the geographical coverage of the transit system.
The transit mode splits in Table 3 and Figure 4 represent the mode
splits that must be achieved in the transit service area if the indicated
travel times, travel costs and transit trip volumes are to be achieved.
They are not projections of the mode splits that would result from the
implementation of the various options. The mode splits are averages over
all trip purposes. The travel times, travel costs, and fleet sizes for
each value of the mode split have been averaged over a range of ratios of
work trip to non-work trip mode split. The effects of variations in this
ratio are discussed in the section on sensitivity analysis.
Figure 4 constitutes a nomograph of the Los Angeles application of the
model. The use of the nomograph is illustrated by the dashed lines in the
figure. The nomograph is entered on the horizonal axis of Figure 4a by
specifying the percentage of daily 6 AM - 8 PM person trips that the transit
system must carry. The vertical axis indicates the required mode split to
transit in the transit service area as a function of the relative travel
times and costs of transit and automobile trips. The dashed line in Figure 4a
illustrates a case in which 20 percent of 6 AM - 8 PM trips are to be carried
on transit at an average transit cost per trip equal to the average automo-
bile cost and an average transit travel time that exceeds the average
automobile travel time by 17 minutes. A transit mode split of 45 percent
is required in the service area. This mode split is projected onto
-------
-22-
TABLE 3 - CHARACTERISTICS OF LOS ANGELES TRANSIT
OPTIONS^
Option No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
a
10
10
10
10
10
20
20
20
20
20
30
30
30
30
30
50
50
50
50
50
C_
0
0
0
0.10
0.10
0
0
0
0.10
0.10
0
0
0
0.10
0.10
0
0
0
0.10
0.10
T
15
17
20
15
17
15
17
20
15
17
15
17
20
15
17
15
17
20
15
17
EL
2350
2100
2000
2200
2050
2100
1700
1450
1950
1650
1850
1275
750
1675
1125
1500
750
225
1250
475
MS_
61
38
28
48
31
68
45
33
55
38
76
52
39
63
46
90
65
53
77
60
_V
3500
4000
3000
5000
4500
7000
9500
7500
8500
9000
11000
14000
15000
13000
15000
18000
23000
28000
23000
27000
_F
16
11
8
17
12
17
11
8
19
13
17
13
9
21
14
18
14
9
24
16
(Footnote on next page)
-------
-23-
TABLE 3 (cont'd)
a. Notation:
N= Percentage of daily 6 AM - 8 PM trips using transit
C= Difference between average transit and automobile costs per trip ($).
T= Difference between average transit and automobile travel times
(minutes)
FL= Threshold volume to provide service on a potential transit route
(person trips/hr=)
MS= Transit mode split that must be achieved in the transit service
area
V= Fleet size
F= Minimum schedule frequency on intra-district routes (buses per hour).
-------
-24-
Figure 4 - NOMOGRAPH OF LOS ANGELES RESULTS
100 r
100
£
H
_J
Q.
UJ
O
O
j-
co
2
CC
N
00
50
1000
TRIP THRESHHOLD
40
20
2000
(trips/hr.)
3000
(0
1000 i 2000
TRIP THRESHHOLD (trips/hr.)
4
3000
1000 2000
TRIP THRESHHOLD (trips/hr.)
3000
(a)
0 50 100
FRACTION OF 6AM-8PM TRIPS (%)
LEGEND
1. T= 15, C = 0
2. T = 17, C = 0
3. T = 20, C = 0
4. T = 15, C = 0.10
5. T= 17, C = 0.10
WHERE:
T = DIFFERENCE BETWEEN BUS AND
AUTOMOBILE TRAVEL TIMES (minutes)
C = DIFFERENCE BETWEEN BUS AND
AUTOMOBILE COSTS ( S/TRIP)
-------
-25-
the vertical axis of Figure 4b, which gives threshold trip volume as a
function of mode split, travel time, and travel cost. In the example
under consideration, the figure indicates that service should be
provided on potential bus routes where the average volume of person trips
equals or exceeds 1700 trips per hour. This volume is projected into
Figure 4c, which gives fleet size as a function of threshold volume, travel
time, and travel cost. In this example, 9500 vehicles are needed. Finally,
the threshold volume is projected into Figure 4d, which gives the minimum
intra-district schedule frequency as a function of threshold volume, travel
time, and travel cost. In this example, the frequency is 11 buses per hour.
Summarizing these results, to carry 20 percent of 6 AM - 8 PM person trips
on transit at a cost equal to the cost of automobile travel and with an
average travel time exceeding the automobile travel time by 17 minutes,
transit service must be provided on potential routes where the average
volume of person trips equals or exceeds 1700 trips per hour. The transit
system must carry 45 percent of person trips on these routes. A bus fleet
of 9500 vehicles is needed. The schedule frequency on each intra-district
route should be set at the value needed to accommodate the flow on the route
or at 11 buses per hour, whichever is larger. The same results also are
presented as option 7 in Table 3.
The Los Angeles results of the model are qualitatively reasonable. The
average bus operating cost is roughly $1.00 per vehicle mile ($0.60 per
vehicle kilometer). Bus operating cost is roughly 85 percent of total
bus cost. Average bus speeds are 21 mi./hr. (34 km./hr.) for inter-
district buses and 15 mi/hr. (24 km/hr.) for intra-district buses. The
-------
-26-
high speed of inter-district buses is a consequence of their limited-
stop operation. The speed of intra-district buses reflects an assumption
that passengers board and alight through separate double-width doors (see
Table 2). If conventional boarding and alighting through single-width
doors with non-prepayment of fares had been assumed, intra-district bus
speeds of 10-12 mi./hr. (16-19 km/hr.) would have been obtained.
Increasing the number of trips that transit must carry while keeping
relative transit and automobile travel times and costs constant requires in-
creasing both the size of the transit service area (i.e., decreasing the
threshold trip volume) and the transit mode split in the service area.
Although the number of transit trips could be increased by increasing mode
split without changing the size of the service area, the required increase in
mode split would be greater than the increase that is needed when the service
area is expanded, and travel times and costs would not stay constant.
Increasing the number of transit trips at constant relative travel
times and costs also requires increasing the fleet size and the minimum
intra-district schedule frequency. The fleet size increases because the
transit system must serve a larger geographical area and larger ridership.
The minimum schedule frequency increases because the structure of the
Los Angeles districts and the geographical distribution of trips among
districts are such that the average district size tends to increase as
the service area expands. This increases the average number of bus stops
per route and reduces the average bus speed. The resulting increase in
in-vehicle time must be compensated by a reduction in wait time to maintain
a constant difference between transit and automobile travel times. Wait
-------
-27-
time is reduced by increasing the minimum schedule frequency.
When total transit patronage is held constant, reducing transit cost
at constant travel time and reducing travel time at constant cost require
increasing both the threshold trip volume for providing transit service and
the transit mode split in the service area. This reflects the tendency of
transit to be most efficient in high density corridors and at high mode
splits. The increase in threshold trip volume and corresponding decrease
in the size of the service area tends to reduce the required fleet size,
other things being equal. However, this tendency is counteracted to a
greater or lesser extent by the increase in average passenger flow per bus
route that occurs when the service area decreases while total ridership
stays constant. Thus, reducing travel time or cost at constant rider-
ship sometimes increases the required fleet size and sometimes decreases
it.
The Table 3 results show that it is possible to carry a substantial
fraction of Los Angeles person trips on bus transit at a cost per trip that
is comparable to the cost of automobile travel and with average travel times
that are within 15 to 20 minutes of automobile travel times. However, this
requires bus fleets and transit mode splits that are quite large by current
standards. The fleet and mode split requirements are discussed further
below. Although it is not shown in Table 3, the difference between bus and
automobile costs increases rapidly as the difference between bus and
automobile travel times decreases from 15 minutes. With the bus service
policies assumed in the model, bus travel times that exceed automobile
travel times by less than roughly 12 minutes are not possible.
-------
-28-
The bus fleets required to carry 10 or more percent of Los Angeles
trips with the travel times and costs shown in Table 3 are large and
roughly proportional in size to the number of trips carried in buses. A
fleet of 3000 to 5000 buses, depending on operating policies, is needed to
carry 10 percent of 6 AM - 8 PM trips. To carry 20 percent of 6 AM - 8 PM
trips, a fleet of 7000 to 9500 buses is needed. The current Los Angeles
bus fleet has approximately 2500 vehicles and carries roughly 3 percent of
daily trips.
High transit mode splits are needed to achieve the travel times and
costs shown in Table 3. When 10 percent of daily trips are carried by
transit, 28 to 61 percent of the trips in the transit service area must use
transit if an average transit travel time within 15 to 20 minutes of the
average automobile travel time and a cost of transit travel comparable to
the cost of automobile travel are to be achieved. The required mode split
to transit increases as the fraction of daily trips using transit increases.
All-day mode splits to transit exceeding 28 percent are found in some
European cities. In the United States, transit mode splits of 28 percent
or more usually are experienced only during peak periods. Achieving the
transit ridership levels and travel times shown in Table 3 with mode splits
below the tabulated values would substantially increase the average cost of
transit trips. For example, if the mode split to transit in the transit
service area were 15 percent, then transit travel would be at least twice as
costly as automobile travel, depending on transit operating policies.
The transit service described in Table 3 has a minimum schedule
frequency on intra-district routes of 8 to 24 buses per hour, depending
-------
-29-
on ridership and operating policies. This minimum frequency range applies
to suburban routes as well as central-area routes. Schedule frequencies
equalling or exceeding these values are common in the central areas of U. S.
cities, particularly during peak periods, but are not normal in suburban
areas.
Sensitivity Analysis
The sensitivity of the model to small errors in exogenous parameters
and structural idealizations was evaluated using transit option 7 in Table
3. In the analysis of the model's sensitivity to changes in exogenous
parameters, the policy variables (i.e., threshold trip volume for provision
.of service on potential bus routes, transit mode split in the transit service
area, and minimum schedule frequency on intra-district routes) were held
constant, and the changes in travel time, travel frequency, and fleet size
caused by a 10 percent change in each of several parameters were computed.
The results are shown in Table 4. Travel costs are most sensitive to changes
in bus and automobile operating costs and automobile trip lengths. A 10
percent change in any of these parameters causes a $0.03 per trip change
in the difference between bus and automobile costs. The difference between
bus and automobile travel times is most sensitive to changes in automobile
travel time, bus speeds, and the walk speed. Ten percent changes in these
quantities cause one to two minute changes in the difference between bus
and automobile travel times. Fleet size is most sensitive to bus speeds
and the time buses lose at stops. Ten percent changes in these parameters
cause fleet size to change by 300 to 500 vehicles.
-------
-30-
TABLE 4 - RESPONSE OF MODEL TO TEN PERCENT CHANGES
IN EXTERNAL PARAMETERS
Change In
Parameter
Bus Operating Cost
Bus Capital Cost
Yard and Shop Cost
Cost of Stations
Auto Operating Cost
Auto Capital Cost
Walk Speed
Bus Speeds
Time buses spend at
stops
Time passengers spend
moving between
platforms at transfer
points
Bus turnaround time
Ratio of work trip to
non-work trip mode
split
Auto Travel Times
Auto Travel Distances
Bus Cost
•Auto Cost
($/Trip)
0.03
0.004
0.001
0.001
0.03
0.01
0
0.02
0.01
0
0.002
0.008
0
0.03
Bus Time
-Auto Time
(Minutes)
0
0
0
0
0
0
0.9
1
0.6
0.1
0
0.009
2
0
Fleet Size
0
0
0
0
0
0
0
500
300
0
40
40
0
0
-------
-31-
The structural idealizations tested in the sensitivity analysis are
the square-grid intra-district street network and the uniform distribution
of trips within districts. The square network geometry used in the model
tends to minimize the average lengths of bus routes, other things being
equal. The effect of non-square network geometry was simulated by
increasing the lengths of the intra-district portions of bus routes in the
model by 10 percent. This caused a $0.03 per trip increase in the difference
between the costs of bus and automobile travel, a one minute increase in
the difference between bus and automobile travel times, and a 600 vehicle
increase in fleet size. These changes are similar in magnitude to the
changes caused by 10 percent variations in bus operating costs, bus speeds,
and automobile travel times.
Non-uniformities in the distribution of trips within districts would
cause passenger flows on bus routes and in-vehicle travel times to differ
from the flows and travel times computed in the model, assuming that transit
routes and service policies remain unchanged. The signs of the differences
could be either positive or negative, depending on the nature of the non-
uniformities. To simulate the effects of non-uniform trip distributions,
passenger flows on bus routes and in-vehicle travel times were increased
10 percent over their normal values. Transit routes and service policies
were not changed. This caused a $0.001 per trip increase in the difference
between bus and automobile travel costs, a 2 minute increase in the difference
between bus and automobile travel times, and a 70 vehicle increase in fleet
size. The changes in cost and fleet size are negligible. This is because
most of the buses in the transit option tested operate with excess passenger
-------
-32-
capacity. The change in travel time is similar in magnitude to the
changes caused by 10 percent variations in walk speed, bus speeds, and
automobile travel times.
Conclusions
The results presented here suggest that to achieve the diversion of
a large fraction of Los Angeles automobile travelers to bus transit,
transit schedule frequencies and mode splits must be maintained system-wide
and all day at levels that normally are experienced in U. S. cities only
during peak periods .and in central areas. Depending on the fraction of
travelers that use transit, substantial increases in the bus fleet size may
be needed.
The model upon which these conclusions are based is inexpensive to
use and readily applicable to other cities. The results the model produces
are qualitatively reasonable and do not seem highly sensitive to the model's
structual idealizations. However, the model has some significant limitations.
The model's reliance on exogenously specified trip tables and mode split
factors is, perhaps, its most serious weakness. The implementation of
policies to achieve high transit mode splits undoubtedly would change the
magnitude and geographical distribution of travel demand, as well as
travelers' mode choices. The effects of such changes on transit system
characteristics and the interactions between system characteristics and
travel demand are not treated by the model and are not reflected in the
results presented here.
Another limitation of the model is that it treats only one service
concept: fixed route, fixed schedule service with separate collection/
-------
-33-
distribution and linehaul vehicles. Moreover, this service concept is
evaluated using district level aggregate travel data. Other service
concepts, such as various forms of paratransit, and integrated service
in high density corridors, might be less costly or time consuming under
some circumstances. Improvements in transit performance also might be
achieved through the use of system designs that reflect sub-district
variations in the spatial distribution of trips.
A third limitation of the model is that it is static. Transportation
changes of the magnitudes needed to divert large numbers of automobile
travelers to transit will take many years to implement. During the
implementation period, travel demand, the supply of roadway facilities, and
the costs of travel by bus and automobile among other factors, are likely
to change in ways that depend, in part, on transportation policy. However,
the model assumes that all factors influencing transportation system
characteristics have fixed values. The effects of long-term changes in
these factors caused by transportation policy or exogenous influences are
not treated.
-------
-34-
ACKNOWLEDGEMENT
The author thanks David Syskowski of the Environmental Protection
Agency for his invaluable assistance in developing and operating the
computer programs used in applying the model to Los Angeles.
-------
-35-
REFERENCES
1. W. T. Mikolowsky, Jo R. Gebman, W. I, Stanley and G. M. Burkholz,
The Regional Impacts of Near-Term Transportation Alternatives:
A, Case^Stii(^~o'f Los Angeles, Report No. R-1524-SCAG, preparedly
"fh~e~RA"ND Corporation for the Southern California Association of
Governments, June, 1974.
2. Frederic C. Dunbar, "Evaluation of the Effectiveness of Pollution
Control Strategies on Travel: An Application of Disaggregated
Behavioral Demand Models," Proceedings of the Transportation Research
Forum, Vol. XVI, No. 1 (197FT
3. Joel Horowitz and Steven Kuhrtz, Transportation Controls to Reduce
Automobile Use and Improve Air Quality in Cities: The Need, TheUptions,
and EffectsT'on Urban Activity, Report No. EPA-400/11-74-002, U. S.
Environmental Protection Agencys November 1974.
4. Better Towns with Less Traffic., Conference Proceedings, Organization
for Economic Cooperation and "Development, Paris, France} 1975.
5. Peter L. Watson and Edward P. Holland, Coj^_stjipjT__pjjcTng_-- The
Example of Singapore, International BanFTorltec^nTtucTioirind~~°
Development, Study~of Traffic Restraints in Singapore, Technical
Memorandum No. 13.
6. J. R. Meyer, J. F. Kains and M. Wohl, The Urban Transportation
Problem .Harvard University Presst Cambridge., Massachusetts, 1965.
7. J. Hayden Boyd5 Norman J. Asher9 and Elliot S. Wetzler, Evaluation of
Rail Rapid Transit__a_nd Express Bus Service in the Urban Commuter
Market, Report No. DOT P 6520.1, prepared for the U. S. Department of
Transportation by the Institute for Defense Analyses, October 1973.
8. Kiran Bhatt, "Comparative Analysis of Urban Transportation Costs,"
Transportation Research Record No. 559, pp 101-116, 1976.
9. T. E. Keeler, L. A. Merewitz, and P. Fisher, The Foil Costs of Urban
Transport, Monographs, No. 19-21, Institute o? Urban and Regional
Development, University of Californias Berkeleys California, 1974-1975.
10. J. H. Bigelow, B. F. Goeller, and R. L. Petruschell, A Policy-Oriented
Urban Transportation Model: the San Diego Version, Report No. R-1366-SD/
Appendix 4, prepared by the RAND Corporation for the San Diego County
Environmental Development Agency, December 1973.
11. L. L. Listen and R. W. Sherrer, Cost of Operating an Automobile, U. S.
Department of Transportation9 Federal Highway Administration, April
1974.
-------
-36-
12. Herbert S. Levinson, William F. Hoey, David B. Sanders, and F. Houston
Wynn, Bus Use of Highways: State of the Art, Report No. 143, National
Cooperative Highway Research Program, 1973.
13. Herbert S. Levinson, Crosby L. Adams, and William F. Hoey, Bus Use of
Highways: Planning and Design Guidelines, Report No. 155, National
Cooperative Highway Research Program, 1975.
-------
-37-
APPENDIX A
Equations of the Model
UtsKARY U.S.
-------
-38-
Notation
** Signifies that non-integer values are to be rounded upward to the
next highest integer.
A(I) = Square root of area of district I.
W = Maximum walk distance
M(I) = Maximum walk distance in district I.
NP(I,J) = Average number of person trips per hour from district I to
district J. The average is over the service day.
FL = Trip threshold for providing service on a potential bus route.
Z = Set of districts in which intra-district service is provided
Z(I) = Set of districts J (J £ I) such that inter-district service
is provided between J and I.
LR (1,0) = Length of bus route between districts I and 0. 1=0 signifies
an intra-district route.
D(I,0) = Highway distance between the centroids of districts I and 0
(1*0).
T(I,0) = Automobile travel time between the centroids of districts I
and 0 (I £ 0) excluding terminal time.
DS = Maximum distance between stations on inter-district routes
DS(I) = Average distance between stations on inter-district routes in
district I
S(I,0) = Number of stops on route between districts I and 0. 1=0
signifies intra-distrtct route.
TVEH(I,0) = One-way bus travel time between the ends of route connecting
districts I and 0. 1=0 signifies intra-district route.
V(I,0) = Non-stop bus speed on route connecting districts I and 0.
1=0 signifies intra-district route
TS = Time a bus spends accelerating, decelerating, and loading
and unloading passengers at a stop.
-------
-39-
TRND(I,J) = Round trip bus travel time on route between districts I and
J. I=J signifies intra-district route.
TEX = Bus turnaround time at the end of a route.
N(I,J) = Transit passenger trips per hour from district I to district J
during a time period.*
MN(I,J) = Major direction transit passenger trips per hour on route
between districts I and J (I^rJ) during a time period. MN(I,I)
is total inter-district transit trips per hour into or out
of district I during a time period, whichever is larger.
R(I,0) = Bus round trips per hour during a time period on route between
districts I and J. I=J signifies an intra-district route.
Cl = Passenger capacity of inter-district bus.
Fl = Minimum schedule frequency for inter-district buses.
VEH(I,J) = Vehicles required during a time period on route between
districts I and J (I=£J). VEH(IJ) is total intra-district
vehicles needed in district I during a time period.
F(I,J) = Bus schedule frequency during a time period on route between
districts I and J. I=J signifies intra-district route.
BMT(I.J) = Bus miles (kilometers) traveled per hour during a time
period on route between districts I and J (I^J). BMT (1,1)
signifies miles (kilometers) traveled on all intra-district
routes in district I.
BHT(I,J) = Bus hours of operation per clock hour during a time period on
route connecting districts I and J (I^J). BHT(I,l) refers to
the total of all intra-district routes in district I.
T(I) = Average automobile travel time for trips in district I, excluding
terminal time.
D(I) = Average highway distance for trips in district I.
C2 = Passenger capacity of intra-district bus.
F2 = Minimum schedule frequency on intra-district bus routes.
*Time period refers to periods of the day, such as AM peak, off peak,
PM peak.
-------
-40-
FLOW(I) = Maximum bus passenger flow (in passengers per hour) during a
time period on intra-district routes in district I.
VW = Average walk speed
TPASS(I.J) = Average passenger door-to-door travel time for bus travel
between districts I and J during a time period. I=J signifies
intra-district travel in district I.
TTR = Time required for a passenger to move between bus platforms at a
transfer point.
TPASS = Average bus passenger door-to-door travel time during a time
period.
Nl = Total inter-district bus passenger trips per hour during a
time period.
N2 = Total intra-district bus passenger trips per hour during a
time period.
N = Total bus passenger trips per hour during a time period.
VEH = Total buses in operation during a time period.
BMT = Total bus miles (kilometers) traveled per hour during a time period.
BHT = Total bus hours of operation per clock hour during a time
period.
VEHH(I) = Total buses in operation during time period I.
BMTH(I) = Total bus miles (kilometers) traveled per hour during time
period I.
BHTH(I) = Total bus hours of operation per clock hour during time period
I.
H(I) = Number of hours in time period I.
NH(I) = Total bus passenger trips per hour during time period I.
TPASSH(I) = Average bus passenger door-to-door travel time in time period
I.
DTPASS = All-day average bus passenger door-to-door travel time.
TC(I,J) = Average automobile door-to-door travel time between districts
I and J, including terminal time.
TC
Average door-to-door travel time during a time period that bus
travelers would experience if they used cars.
-------
-41-
FLEET = Bus fleet size
DBMT = Daily bus miles (kilometers) traveled.
DBHT = Daily bus hours of operation
DC(I,J) = Average automobile travel distance between districts I and J.
AVMT = Automobile vehicle miles (kilometers) traveled per hour during
a time period that bus travelers would cause if they used cars.
OCC = Automobile occupancy during a time period.
TCH(I) = Average door-to-door travel time during time period I that bus
travelers would experience if they used cars.
DTC = Daily average door-to-door travel time of bus travelers if they
use cars.
AVMTH(I) = Average automobile vehicle miles (kilometers) traveled per hour
during time period I that bus travelers would cause if they used
cars.
DAVMT = Daily automobile vehicle miles (kilometers) traveled that would
be caused if bus travelers used cars.
P = Transit mode split of work trips in the transit service area.
WT(I) = Work trips per hour using transit in time period I.
-------
_42-
Deflning the Transit Service Area
**
Z(I) = |J* I | NP(I,J) + NP(J,I) > FL, I, J«Z|
Z = {I I W(I) [NP(I,I) + 0.5 Z (NP(I,J) + NP(J,I))] /A(I) > FL}
J *
The expression on the left-hand side of the inequality defining Z is the sum
Of hourly trips originating and terminating along an intra-district route,
originating along the route and. terminating elsewhere inside or outside
the district, and originating elsewhere and terminating along the route.
-------
_43.
Characteristics of Inter-district Service
The following equations apply only to district pairs I,J (l=£ J)
such that J e Z(I). The equations apply separately to each time period
modeled.
LR(I,J) = D(I,J) + 0.5 [A(I) + A(J)]
DS(I) = A(I)/ [A(I)/DS]**
A(J) /DS(J)
TVEH(I,J) = LR(I,J)/V(I,J) + S(I,J) *TS
TRND(I,J) = TRND(J,I) = TVEH(I,J) + TVEH(J,I) + TEX
MN(I.J) = MN(J,I) = MAX [N(I,J), N(J,I)]
R(I,J) = R(J,I) = MAX [MN(I,J) /Cl, Fl]
VEH(ISJ) = VEH(J,I) = [R(I,J)*TRND (I,J)]**
BMT(I,J) = BMT(J,I) « VEH(ISJ)* [LR(ISJ) + LR(J,I)] /TRND
BHT(I5J) = BHT(JJ) = VEH(ISJ)
-------
-44-
Characteristics of Intra-District Service
The following equations apply only to districts in the set Z. The
equations apply separately to each time period modeled.
MN(I,I) = MAX [EN(I,J),EN(J,I)]
FLOW(I) = W(I) [N(I,I) + MN(I,I)]/4.0 A(I)
FLOW(I) is the maximum flow along a bus route caused by the combination of
trips originating and terminating on the route, originating on the
route and terminating elsewhere, and originating elsewhere and terminating
on the route.
LR(I,I) = A(I) + 0.5 DS(I)
S(I,I) = 1+ A(I)/W(I)
TVEH(I,I) = LR(I,I)/V(I,I) + S(I,I)*TS
TRND(I,I) = 2[TVEH(I,I) + TEX]
RCORR(I,I) = MAX [FLOW(I)/C2, F2]
F(I,I) = RCORR(I,I)
VEH(I,I) = 2A(I)*[RCORR dJ)*TRNDd,I)]**/Wd)
BMT(I,I) = 2 VEH(I,I)*LR(I,I)/TRND(I,I)
BHT(I.I) = VEH(I,I)
-------
-45-
Transit Passenger Travel Time
The following equations apply separately to each time period modeled.
The equations apply only to districts I and J in the transit service area.
TPASS(I.J) = [W(I) + W(J)]/2VW
+ 2 TTR + 0.5 S(I,J)*TS + D(I,J)/V(I,J)
I) + TS
+ A(I)* TS/4W(I) + [A(J) + DS(J)] /4V(J,J)
+ A(J)*TS/4W(J), I ^rJ
The first term in TPASS(I,J) is walk time. The second and third terms
are wait and transfer time. The fourth and fifth terms are time in inter
district vehicles. The last terms are time in intra-district vehicles in
the districts of origin and destination.
TPASS(I,I) = W(I)/VW + [1
+ [1-2W(I)/A(I)] TTR
+ [2A(I)/3 + 0.5
+ TS*[2A(I)/3W(I) + 1]
The first term in TPASS(I.I) is walk time. The second term is wait time
and reflects the proportion of intra-district bus passengers making a
transfer. This proportion is [1-2W(I)/A(I)]. The third term is the
average time passengers spend moving between platforms during transfers.
The last two terms are in-vehicle time, including the time required for a
bus stop at an inter-district station.
Nl =
I J « Z(I)
N2 =
N = Nl + N2
TPASS = [ N(I,J)*TPASS(I,J) + N(I,I)*TPASS(I,I)] /N
I J « Z(I) I« Z
-------
-46-
Total Transit System
The following equations apply to each time period K separately.
VEH =
BMT = H(K)[BMT(I,I) + 0.5
Z(I)
BHT =
The following equations are for service in all time periods
FLEET = 1.05 MAX [VEHH(I)]
DBMT = SH(I)*BMTH(I)
DBHT = SK(I)*BHTH(I)
DTPASS = 2[H(I)*NH(I)*TPASSH(I)]/2C"(D*NH(I)]
-------
-47-
The Automobile System
The following equations apply separately to each time period
modeled.
TC = Z) [Nd.D* TC(i,i) + £N(I,J)*TC(I,J)]/[NI + N2]
If I J«Z(I)
AVMT = ]C[N(i»i)*DC(i.i) + SN(I,J)*DC(I,J)]/OCC
I « I J €
The following equations are for service in all time periods.
DTC = SH(I)*NH(I)*TCH(I)/
DAVMT = X1H(I)*AVMTH(I)
-------
Los Angeles Cost Equations
DAILY BUS OPERATING COST = $0.246 DBMT + $12.43 DBHT
BUS CAPITAL COST PER DAY = $4.53 FLEET
INTER-DISTRICT STATION COST PER DAY
= $0.40 [MAX Nl OVER ALL TIME PERIODS]
DAILY YARD AND SHOP COST = $6.25 FLEET
DAILY AUTOMOBILE OPERATING COST = $0.08 DAVMT
DAILY AUTOMOBILE CAPITAL COST
= $0.59 P£H(I)*WT(I)
-------
-49-
APPENDIX B
Inputs and Outputs of the Model
-------
-50-
Inputs
Areas of districts
Average district-to-district automobile travel times
Average district-to-district highway distances
Average walk speed
Passenger capacity of inter-district buses
Passenger capacity Nf intra-district buses
Minimum inter-district schedule frequency
Minimum intra-district schedule frequency
Maximum walk distance
Time required for passengers to move between platforms at bus stops
Time buses spend at each stop
Maximum distance between inter-district stations
Bus turnaround time at the ends of routes
Automobile terminal time
Trip threshold to provide service on a potential bus route
Automobile occupancies by time period
Transit mode split factors by trip purpose
District level person'trip tables by trip purpose and time of day
Cost estimating relationships
-------
-51-
Outputs
The following outputs are provided for each time period:
Inter-district, intra-district, and total bus trips
Average door-to-door travel times for inter-district, intra-district
and total bus passengers
Average wait and transfer times for inter-district, intra-district and
total bus passengers
Average in-vehicle times for inter-district, intra-district, and total
bus passengers
Components of inter-district, intra-district, and total passenger in-
vehicle times attributable to bus stops
Inter-district, intra-district, and total buses in operation
Bus miles (kilometers) traveled by inter-district, intra-district, and all
buses
Average door-to-door automobile travel times for inter-district, intra-
district and all bus passengers
Automobile vehicle miles (kilometers) traveled that inter-district, intra-
district, and all bus passengers would cause if they traveled by
automobile
Operating costs of inter-district, intra-district, and all buses
Automobile operating costs that would be incurred if bus passengers
traveled by car
The following outputs are provided for the entire service day:
Size of bus fleet
Bus operating cost
Bus capital cost
Cost of inter-district stations
Cost of yards and shops for buses
Total bus cost
-------
-52-
Automobile operating costs that would be incurred if bus passengers
traveled by car
Automobile capital cost that would be incurred if bus passengers traveled
by car
Total automobile cost that would be incurred if bus passengers traveled
by car
Bus trips
Average door-to-door travel time for bus passengers
Average door-to-door travel time for bus passengers if they travel by
automobile
Listing of districts in which intra-district service is provided
Listing of districts between which inter-district service is provided.
The cost outputs are expressed both as daily totals and as average values
per trip.
-------
-53-
APPENDIX C
Additional Los Angeles Results
-------
-54-
Figure C 1 - REDUCTION IN 6AM - 8PM AUTOMOBILE VMT AS FUNCTION OF
FRACTION OF 6AM - 8PM TRIPS USING TRANSIT
100
80
a.
CO
g
o
D
a
60
40
20
LEGEND
1. T= 15, C = 0
2. T = 17, C =0
3. T = 20, C = 0
4. T= 15, C = 0.10
5. T= 17, C = 0.10
I
I
20 40 60 80
FRACTION OF 6AM 8PM TRIPS USING TRANSIT (%)
100
T = DIFFERENCE BETWEEN BUS AND AUTOMOBILE TRAVEL TIMES (minutes)
C = DIFFERENCE BETWEEN BUS AND AUTOMOBILE COSTS ( $ PER TRIP)
-------
-55-
Figure C 2 - COMPONENTS OF BUS TRAVEL TIME AND COST
c
1
LU
60 r
40
20
I
WAIT
& TRANSFER
WALK
IN - VEHICLE
I
20 40
BUS TRAVEL TIME (minutes)
60
3.00
Q.
cc
I-
cc
LU
a.
V)
V)
O
o
2.00
1.00
1.00 2.00
BUS COST ( $ PER TRIP)
3.00
-------
-56-
Figure C 3 - SIZE OF TRANSIT SERVICE AREA AS FUNCTION
OF THRESHHOLD TRIP VOLUME
4000
3000
CM
UJ
tr
2000
1000
500
1000
1500
2000
2500
THRESHHOLD (TRIPS/HR.)
-------
-57-
Maps of the Transit Service Areas
for Three Threshold Trip Volumes
-------
-58-
Figurs C 4 - TRANSIT SERVICE AREA FOR 500 TRIP PER HOUR THRESHHOLD
SAN BERNARDINO
-------
-59-
Figure C 5 - TRANSIT SERVICE AREA FOR 1500 TRIP PER HOUR THRESHHOLD
SAN BERNARDINO
-------
-60-
Figure C 6 - TRANSIT SERVICE AREA FOR 2400 TRIP PER HOUR THRESHHOLD
SAN BERNARDINO
-------
-61-
Relatiohships Between Travel Time, Travel
Cost and Transit Mode Split for Three Threshold
Trip Volumes
-------
-62-
In the following figures, transit mode split, travel times, and travel
costs have been averaged over a range of ratios of work trip to non-
work trip mode split.
-------
-63-
Figure C 7 - BUS TRAVEL TIME - AUTOMOBILE TRAVEL TIME VS.
BUS TRAVEL COST - AUTOMOBILE TRAVEL COST
60
UJ
LU
-J
02
O
O
CO
D
CO
50
40
30
20
ms = 10%
ms = 25%
THRESHHOLD TRIP VOLUME - 500 TRIPS/HR.
ms = TRANSIT MODE SPLIT IN TRANSIT SERVICE AREA
10
-0.40
-0.20
0.20
0.40
0.60
0.80
1.00
BUS COST - AUTOMOBILE COST ($/TRIP)
-------
-64-
Figure C8 - BUS TRAVEL TIME - AUTOMOBILE TRAVEL TIME
VS. TRANSIT MODE SPLIT
60
THRESHHOLD TRIP VOLUME = 500 TRIPS/HR.
C = BUS COST - AUTOMOBILE COST
I
c
5
I-
DC
I-
UJ
CO
O
50
LU
LU
<
tr
i-
w
CD
40
30
20
10
C = 0
C = $0.10
0
20
40
60
80
100
TRANSIT MODE SPLIT IN TRANSIT SERVICE AREA (%)
-------
Q.
cc
CO
o
o
LJJ
00
o
<
I
CO
o
o
CO
OQ
-65-
Figure C 9 - BUS COST - AUTOMOBILE COST
VS. TRANSIT MODE SPLIT
2.00
1.50
THRESHHOLD TRIP VOLUME = 500 TRIPS/HR.
T = BUS TRAVEL TIME - AUTOMBILE TRAVEL TIME
1.00
0.50
= 15 MIN.
MIIM.
T = 20 MIIM.
-0.50
0
20
40
60
80
100
TRANSIT MODE SPLIT IN TRANSIT SERVICE AREA (%)
-------
-66-
Figure C 10 - BUS TRAVEL TIME - AUTOMOBILE TRAVEL TIME VS.
BUS TRAVEL COST - AUTOMOBILE TRAVEL COST
QJ
+rf
3
C
LLJ
S
I-
o
D
<
CO
m
60
50
40
30
20
10
ms = 10%
ms = 25%
ms = 50%
ms = 75%
ms = 100%
THRESHHOLD TRIP VOLUME = 1500 TRIPS/HR.
ms = TRANSIT MODE SPLIT IN TRANSIT SERVICE AREA
-0.04 - 0.20
0.20
0.40
0.60
0.80
1.00
BUS COST - AUTO COST ( $/TRIP)
-------
50
I
c
UJ
LLJ
-J
00
o
O
<
I
LU
cc
I-
oo
m
-67-
Figure C 11 - BUS TRAVEL TIME - AUTOMOBILE TRAVEL TIME
VS. TRANSIT MODE SPLIT
THRESHHOLD TRIP VOLUME = 1500 TRIPS/HR.
C = BUS COST - AUTOMOBILE COST
40
30
20
10
20
40
60
80
100
TRANSIT MODE SPLIT IN TRANSIT SERVICE AREA (%)
-------
2.00
1.501
1.00'
0.50!
-68-
Figure C 12 - BUS COST - AUTOMOBILE COST
VS. TRANSIT MODE SPLIT
THRESHHOLD TRIP VOLUME = 1500 TRIPS/HR.
T = BUS TRAVEL TIME - AUTOMOBILE TRAVEL TIME
T = 15 min.
T = 17 min.
T = 20 min.
-0.50
20
40
60
80
100
TRANSIT MODE SPLIT IN TRANSIT SERVICE AREA (%)
-------
-69-
Figure C 13 - BUS TRAVEL TIME - AUTOMOBILE TRAVEL TIME VS.
BUS TRAVEL COST - AUTOMOBILE TRAVEL COST
60
ms = 10%
c
LLI
UJ
_l
E
o
o
I
LLJ
GO
D
00
50
THRESHHOLD TRIP VOLUME = 2400 TRIPS/HR
ms = TRANSIT MODE SPLIT IN TRANSIT SERVICE AREA
40
30
ms = 25%
20
ms = 50%
ms = 75%
ms = 100%
10
-0.40
-0.20
0.20 0.40 0.60
BUS COST - AUTOMOBILE COST ( $/TRIP)
0.80
1.00
-------
-70-
ta
-------
-71-
Figure C 15 - BUS COST AUTOMOBILE COST VS. TRANSIT MODE SPLIT
2.50 r
2.00
Q-
cc
I-
o
o
111
_l
E
o
o
D
O
O
C/3
CQ
1.50
1.00
0.50
-0.50
THRESHHOLD TRIP VOLUME = 2400 TRIPS/HR.
T = BUS TRAVEL TIME AUTOMOBILE TRAVEL TIME
T = 15 min.
20
40
60
80
100
TRANSIT MODE SPLIT IN TRANSIT SERVICE AREA (%)
------- |