Francis M Vanek
Working Paper
Department of Systems Engineering
University of Pennsylvania
293 Towne Building
Philadelphia, PA, USA 19104-6315
May 5, 1995
ABSTRACT
In
response to the need to both improve public transit in low density residential
areas and to better accommodate transit riders with disabilities, we analyzed
the breakeven ridership levels for introduction of minibus service in areas
previously served by regular bus.In
the first part of this paper, a general analysis of breakeven levels was
performed, based on typical cost of vehicles and labor faced by medium-
to large-sized transit agencies in the United States.The
results were then applied to the conversion of a specific route from regular
bus to minibus in a suburban area between Philadelphia and Paoli, PA.Analyses
in both parts of the paper suggested that in areas where regular buses
currently operate with low levels of ridership, agencies can use conversion
to minibus to either reduce costs with same headways or improve service
with reduced headways.Our findings
also show that operators can improve the economics of the minibus service
by carrying some passengers previously carried by paratransit service,
for example those passengers who have limited mobility but are not confined
to a wheelchair.
In this paper I will cover all three of these possible applications in general terms, and then focus more specifically on the last one. Accordingly, there are two parts:
a. General Model: Uses a hypothetical route without specific geographic features to measure the effect of varying minimum headway, demand peaking, and hourly rates of demand to compare regular bus to minibus service.
b. Route 105 Case Study: Takes an existing SEPTA route where introducing minibuses seems promising to study the implications of incorporating former paratransit riders into the service.
1. Regular bus only: Situation in which agencies meet demand along fixed transit routes using only regular full-sized buses. Does not take into account the requirements of riders with disabilities.
2.
Minibus only: Same as 1, but agencies substitute minibuses for regular
buses. When such minibuses are outfitted with AVMC (Advanced Vehicle Monitoring
and Control) Systems or are capable of route deviation for pickup and dropoff,
they can be referred to as AMB (Advanced Minibus) service.
3. Regular bus for transit, minibus for paratransit: Regular buses provide service along fixed routes, with the possibility of serving the disabled using wheelchair lifts built into rear stairwells. Minibuses of various sizes (and some passenger cars) provide for all other specialized service to the disabled and elderly. This is the scenario which describes most U. S. cities.
4. Multipurpose minibus: Specialized minibuses (e.g. with wheelchair fifts) continue to provide service to existing paratransit ridership, but another n-dnibus service with fixed route but ability to deviate from the route for pickup and dropoff carries both the regular transit ridership and the more mobile portion of the former paratransit ridership (i.e. those not confined to wheelchairs).
For purposes of this paper 1 will refer to the process of meeting some of the demand for specialized transit with minibuses that also carry regular passengers, as in scenario 4, as "paratransit switching."
The first focus of my search yielded some interesting comments about the challenges associated with implementing n-dnibuses in North America, including the following cautionary note [3,293]:
That unsubsidized, privately supplied minibuses work in Buenos Aires, Hong Kong, and Bangkok, however, does not mean that they would work in the United States, Canada, or Western Europe. DifFerences in factor prices -- particularly the wage rates of bus operators and the values actual and potential riders attach to their travel time -- are substantial between Minneapolis and Buenos Aires let alone between Minneapolis and Bangkok.
Even in the case where some level of subsidy is assumed, implementing minibus service will require innovative pricing and cost-saving measures in order to be competitive.
The second search located the 1981 cost model [8] developed at the Illinois University at Chicago Circle which will be used later in this study.(Hereafter 1 refer to this as the "I.U. Model.") Talley and Anderson published a multi-service transit agency model in 1986 which they claimed was the first model to combine various services such as regular bus and paratransit, suggesting that unlike regular bus service, the modelling of paratransit and other specialized services has not developed very far up to recent times [5, 365]. (See the extended annotated bibliography and Appendix 2 for a complete review of documents consulted.)
passenger demand. The standard minibuses and regular buses for the route seat 15 and 50 passengers, average 15 MPH and 12 MPH, and cost $40,000 and $200,000, respectively. Cost models for both minibus and regular bus are the same as used in earlier calculations in the ongoing Advanced Minibus Concept project [1, p.42 and p.56, respectively].
1. short minimum headway: A minimum headway of 20 minutes is required on the route for level of service reasons. Costs therefore start at the minimum fleet and level of activity to have either three buses or three minibuses pass each stop in an hour, and increase after demand exceeds the minimum capacity provided due to the minimum headway. This type of service compares to a main suburb-to-city bus link, but without peaking during rush hours. As seen in the graph, breakeven occurs at approximately 75 passengers/hour, or half of the seat capacity provided by the regular bus at the given frequency.
Figure
IA. Breakeven for 20 mnin. headway
Annual
cost as a function of output (Psgrsihr)
$3,500,000.00
$3,000,000.00-
$2,500,000.00-
$2,000,000.00-Minibus
$1,500,000.00Regularbus
$1,000,0C)0.00
$500,000.00 $0.00
050100150200
2. Long minimum headway: Same as #1 but with a minimum headway of 1 hour, and no peaking. Again, the graph shows that breakeven occurs at approximately 25 psgr/hr, or roughly half of the capacity provided by the regular bus.
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Annual cost as a function of
output (psgrsibr)1 br headway
$3,500,000.00
$3,000,000.00
$2,500,000.00
$2,000,000.00Minibus
$1,500,000.00--&-Regularbus $1,000,000.00
$500,000'00
$0.00
mCDLDC:)LOC:)
U"3CD LOr@.C3cl@jWr..CD
3. Short headway w/ peaking effects: Same as #1, but assumes that the passenger demand doubles during 4 hour peaks in the morning and evening -- note that even though passenger demand on x- axis is demand during off-peak hours, peaking effects are built into overall cost calculation. Because the regular bus service provides a minimum of capacity of 150 psgr/hr due to the minimum frequency requirement, I am assuming that it will accommodate all of the peak (up to 75 psgs/hr) or part of the peak (75 to 150 psg/hr base) without putting additional buses into service on the line. However, since minibus must add an additional vehicle for each added 1 5 passengers, this slack does not exist up front, so that accommodating peaks with a low base demand incurs a higher cost on minibus than on regular bus for an equal rate of passengers per hour in the off peak. Hence the lower breakeven point for this situation:
Figure IC: Breakeven for 20 min. Headway w peaking
Annual cost as a function of base output -
output doubled during peaks (psgrs/hr)
$6,000,000.00
$5,000,000.00
$4,000,000.00
Minibus $3,000,000.00 . .....
egularbus
R
$2,000,000.00
$1,000,0C)0.00
$0.00
-1
C:)LDC3U')CDLOWLOCD
c@'iLOr@-CDclirl-CD
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B. The routes in the minibus network, are 1.25 times longer than the regular bus routes, and both bus services run at the same headway. This scenario prioritizes area coverage over seat-trips provided.
The chart below compares scenarios A & B with regular bus for various measures of performance (See Appendix 5 for further details of calculation):
MeasureRegular
BusScn.AScn.B
RT runs in day486048
No. Routes served466
Seat miles prov'd334081879218749
OW seat-trips prov'd960054004320
1
Area coverage [mi'213.875.817.10
Figure 2 RB v AMB comparison using
step functions here
Fig 3 Breakeven analysis w and wo
adjustment of paratransit costs here
A. Each route in the minibus network is the same length as the routes in the regular bus network, and the minibuses run at a shorter headway due to their higher average speed. This scenario prioritizes seat-trips provided over area coverage.
B. The routes in the minibus network, are 1.25 times longer than the regular bus routes, and both bus services run at the same headway. This scenario prioritizes area coverage over seat-trips provided.
The chart below compares scenarios A & B with regular bus for various measures of performance (See Appendix 5 for further details of calculation):
MeasureRegular
BusScn.AScn.B
RT runs in day486048
No. Routes served466
Seat miles prov'd334081879218749
OW seat-trips prov'd960054004320
1
Area coverage [mi'213.875.817.10
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AlternativeNo.Vehicles req'dAnnual Cost
Regular
Bus1 hr3$580,283
Mnibus 1 hr3$381,249
Minibus 1/2 hr5$655,812
Especially in the case where minibus service costs slightly more than regular bus, an agency will be interested in reducing the total annual cost by using the minibus to reduce their expenditures on paratransit. As a first estimate of how much could be saved, 1 have assumed that each paratransit trip saved reduces costs by 1 average cost unit, while the additional cost to the minibus is negligible, as shown:
NetAnnCost = MBAnnCost - NumPTDailySwitch*PTCostPerTrip*365
After calculating new costs with two estimates of paratransit switching potential, 1 found that with the low estimate, the minibus service would still exceed the regular bus cost by 10%, but with the high estimate, the minibus achieved a 1% reduction compared to regular bus (See Appendix 6 for both the direct comparison of the two bus services and also the effect of paratransit switching on costs). Figure 3 shows the net cost for minibus as a function of number of paratransit switching passengers per day.
CostPerTrip = Sum [ Coeff.(lnput)*lnput ]
As it was the only model I have uncovered thus far which allows the variation of ridership density and percentage with disability, I incorporated it into the breakeven analysis for the rt. 105 service.
A model which fits estimated unit costs calculated from Section 15 data or other agency accounting can be used to estimate the effects of changing a service with more confidence. For example, if the value derived in practice for average cost per trip is 515 but model's output unit cost is only $5 based on the agency's inputs, the model will likely underestimate the effect on cost of making changes (vice versa for a model whose output is $25/trip for the same situation). Therefore, before estimating the change in cost for remaining paratransit ridership, I needed to validate the model for the existing SEPTA paratransit cost structure.
I located or estimated inputs for the 9 categories required in the IU model as follows:
1. Service Area: since 1983, the entire area of the City of Philadelphia, or 138 sq. mi.
2. Rider Density: Based on a rides/year count of 367,100 as estimated in the Section 15 data for 1991. Dividing this figure by #1 gives an approximate value of 2660 rides/sq.mi.
3. Average Trip Distance: Section 15 data gives a total passenger miles delivered of 2,921,800. Dividing this number by the rides per year gives an average of 7.96 miles/trip.
4. Proportion wheelchair: This statistic captures the effect on costs of time and resources needed to carry individuals with disabilities; 1 have interpreted it to include all disabled riders with some type of special service requirement, such as door-to-door service or use of a lift, and strictly those in wheelchairs. According to an earlier interview with John Roth of SEPTA (November 1993) this number is approximately 40%.
5. Driver wages: The private carriers and not SEPTA set wages for drivers, so they vary over a range from $5/hr. to $7/hr. 1 have used the median value of $6/hr. in the model validation.
6. Government agency? (dummy variable): Although SEPTA itself is a public agency, it subcontracts minibus service to private carders, so 1 have set this variable to 0. Since the coefficient for this variable is negative, cost-per-trip increases. However, this resulting higher cost concurs with SEPTAs comparison to a range of cost-per-trip numbers from Ohio paratransit services [41.
7. Proportion government subsidy: SEPTA paratransit is known to receive government funding from the Pennsylvania state lottery and other sources; the fare for eligible senior citizens and people with disables is only a small portion of the current average cost-per-trip. 1 have somewhat arbitrarily set this number at 80% subsidy, although the actual value might lie anywhere in the 70%-95% range.
8. Individual volunteers (dummy variable): The I.U. model has shown that the use of individual volunteers who commit to single trips without possibility of multiple occupancy increases agency costs. SEPTA does not make use of such variables so this variable is set to 0
9. Percentage over 65 years: From the same interview as in #4, this value is set at approximately 60% for SEPTA.
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$1
in 1978
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$1.43
in in 1982
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$1
in 1992
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$0.82
in 1982
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The multiplier for changing the coefficients can then be calculated as
ConvFactor = PPI(1978 to 1982)/PPI(1992 to 1982) = 1.74
I then multiplied all of the coefficients by the resulting inflator of 1.74 before recalculating the model.
The land area for assigning paratransit ridership to the route is based on the ADA standard shed width of 3/4 mile on either side of the route [7, 5-2]. Appendix 7 provides two cost per trip estimates not including overhead using two values for ridership density:
Sparse: Ridership assigned to the route 105 shed based on fraction of SEPTA’s total revenue- rides carried by this route (200 rides per year per square mile).
Dense: Ridership assigned assuming same density of rides per square mile as within the city of Philadelphia (2660 rides per year per square mile).
The true value for ridership density is probably somewhere between these two. The new calculation with the inflated coefficients gave a value of $13.75 or $14.21 per trip ($20.55 or $21.01 with overhead) depending on density estimate, or roughly 7-10% lower than the empirical cost. At this point I was satisfied that the adjusted coefficients could be used to model the effects of changing the nature of the ridership. While a model output closer to $15.42 might be achievable by further refining the coefficients or empirically calculating an inflator that would exactly fit the change in costs between $7.89 and $15.42, 1 decided against this for the following reasons:
-- Fitting the model exactly to the two data points loses sight of the aggregate way in which the model was calculated from many different paratransit providers, using various characteristics.
-- The cost-per-trip measured by SEPTA is itself only approximate since many of its components are costs shared among different operations or spread out arbitrarily over the course of many years. It therefore should not be treated as an exact benchmark.
-- The only valid way to create a more accurate model would be to go out in the present year, gather data from numerous agencies for the 9 characteristics mentioned, and recalculate the coefficients using regression analysis. Short of that, the coefficients can be adjusted by a uniform inflator or any one of a myriad individual inflators and still give a plausible explanation for a given value, in our case $13.75. In other words, it is impossible given the data at hand to calculate the single best set of coefficients for the model, so instead I propose that one should seek adequacy rather than optimality -- the PPI inflator can be assumed adequate for the task at hand. At the limit, it can safely be assumed to more accurately measure the effect of changing inputs than if we used the original coefficients without any inflator. (Other calculations from the model which illustrate the effect of changing status wrt government, wage levels, and coefficients are included in Appendix S.)
After validating the I.U. model with the appropriate coefficients I recalculated the effect of paratransit switching on the net annual cost of the minibus service and on the cost for the remaining paratransit ridership. Appendix 9 shows the calculation of the new cost per trip value using the model; the values are:
Sparse model:$27.21
Dense model:$27.48
Once we have these costs we can calculate the new net annual cost value as a function of amount of paratransit switching:
NetAnnCost -= (CPTold - (CPTnew - CPTold))*NumPTSwitchDaily*365
where
CPTold = initial cost per tripCPTnew = cost per trip after paratransit switch
Figure 3 compares the breakeven point for the minibus service with the dense estimate of initial paratransit ridership with the breakeven point which disregards changes in paratransit cost. While the breakeven ridership increases from 8.9 psgs/day to 10.9 psgs/day, the goal of making up for the additional cost of the minibus service through paratransit switching is clearly feasible even taking into account the effects on paratransit cost per trip.
2. For less densely travelled suburban routes, especially those with low cost recovery, however, agencies could greatly reduce costs through substitution of minibuses at the same headway if the extra seating capacity of the regular bus is not needed. This substitution also improves level of service thanks to the shorter trip times on minibus. In other situations where minibus would improve level-of-service but cost more, passengers may well accept an extra fare for the minibus (i.e. raising the fare from $1.50 to $1.95 in the example).
3. Analysis of the route 105 suggests that in some suburban areas, agencies can substitute minibus for regular bus, double headways, and still save money by carrying some former paratransit riders on the minibus, especially if they allow route deviation for pickup and dropoff.
-- A more realistic study of peaking effect could be undertaken using average peaking data for the New York City bus system [21, rather than the arbitrary doubling of demand for 4 hours in each of the two peak periods.
-- In costing the minibus, we used a cost per vehicle-hour input of 70% that of regular bus, which translates roughly into a driver wage of $10.50 per hour, compared to $15 for regular bus drivers. On the other hand, SEPTA paratransit drivers are typically paid on a scale from $5 to $7 per hour. While this latter wage may lead to labor problems such as absenteeism, lack of professionalism, and high turnover (on the order of 200%/annum according to interviews), the group might investigate the effect on breakeven analysis of a driver wage in the range of $8-$9 hour, with accompanying cost per vehicle-hour structure.
-- I had hoped to get more precise data for the route 105, not only annual ridership and average trip length, but average occupancy at different times of day and at different points along the route. With this information 1 could better verify that the proposed minibus schedule for route 105 would provide sufficient capacity for the demand. I might be able to do this analysis using boarding and alighting data gathered from stops in the Villanova area as a proxy for overall hour- by-hour demand trends along the route.
-- With more accurate information from Septa for the inputs in the I.U. model, 1 could better validate the model in terms of the difference between the predicted and actual cost per trip.
-- While the route 105 may appear attractive for conversion to minibus by virtue of its long headway and low ridership, some of Septa's suburban/frontier routes have even lower cost recovery factors (as low as 15% of full cost recovery for the route 118). The minibus conversion analysis could be applied to a number of routes to better understand common features which make conversion particularly attractive.
1988
3. Mohring, H.; "Minibuses in Urban Transportation'; Journal of Urban Economics Vol. 14 293-317 (1983).
4. Ohio Department of Transportation; Status of Public Transit in Ohio. July 1993
5. W.K.Talley et al, "an urban transit firm providing transit, paratransit, and contracted-out services". Journal of Transportation Economics and Policy, September 1986, p.353-368.
6. U. S. Bureau of the Census; Statistical Abstract of the United States. Washington, 1994.
7. U. S.D.O.T., UMTA; ADA Paratransit Handbook. Washington (September 1991).
8. U.S.D.O.T., UMTA (Robins et al, Illinois University at Chicago Circle); Economies of Scale in Paratransit: Special Service Agencies and Taxicab Companies; Washington 1981.
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J. Berechman et al, "Analysis of the cost structure of an urban bus transit property", Transportation Research B V 18b N 415, pp273-287, 1984
Mathematical model of cost structure, including factor and price elasticities. Did not include any localized data or cost components useful to this study.
J. Berechman, "Costs, economics of scale, and factor demand in bus transit'; Journal of Transportation Economics and Policy, January 1983, p7-24.
Application of cost model to Israeli bus industry, with estimation of coefficients of parameters for two models. Not directly applicable to paratransit.
Cervero, Robert; "Making transit work in the suburbs"; Preprint for 73rd ann. TRB Meeting
Includes data for the growth of population, employment and transit in major US urban centers over the last 15 years.
Cervero, Robert; Transit Service Contracting: Cream-skimming or deficit-skimming?; Washington 1988 Contains cost information for several US transit agencies with a focus on the most profitable routes in these agencies in order to show that profitable routes are not the ones that have been or ought to be contracted out. No specific reference to paratransit or minibus.
Dougherty, J; "Paratransit: searching to find a balance"; Passenger Transport (Newsletter); March 6, 1995. Provides financial information for Albany, NY; Madison, Wl; Springfield, MA.
Information Management International; "Ride Tracking Project Newsletter"; March 1993-present: Provides numerical data on growth and costs in providing paratransit in U. S.
Institute of Transportation Engineers; Manual of Traffic & Transportation Engineering Studies; 1976 Contains chapter on "Public Transportation Studies", which includes statistical sample requirements for measuring ridership at different times of day. Sought relationship between peak and off-peak ridership, but focus mainly on meeting peak demand , not on variation between peak and off-peak.
Institute of Transportation Engineers; Traffic & Transportation Engineering Handbook; 1976
Again, focus mainly on peak demand.
Institute of Transportation Engineers; Traffic Engineering Handbook; 1962
No direct mention of public transit considerations.
J.0.Jansson; "A simple bus line model for optimisation of service frequency and bus size; Journal of Transportation Economics and Policy January 1980, p.53-30.
Discussion of optimal frequency by the "square-root formula", etc.
Koffinan, David; "Appropriate cost sharing for paratransit service"; Transportation Research Record 1463, p.61-71.
Addresses cost issues raised by large agencies making use of paratransit & their need to pay their marginal cost of adding to the paratransit agency load. Contains information & methodology for breaking down paratransit costs.
Levinson (USDOT), Characteristics of Urban Transportation Demand: an Update. Washington 1988: Contains a chart of average peaking in bus demand for NYC transit by hour of day. No data clearly pertinent to paratransit or minibus
Levinson & Weant, Urban Transportation: Perped v@es & ProM@2ts, Eno Foundation 1982
Contains profiles of dial-a-ride and disabled paratransit riders for representative US cities. No cost models for paratransit included.
Mahalel,David;"A dual-purpose paratransit taxi service"; Transportation Quarterly V38 pp.605-14, October 1984.
Study provided level-of-service comparison for paratransit alternatives in Israel, but not cost data.
J.J.McLary
et al, "Implementation of service routes in the United States"; Transportation
Research Record 1378;
Description of service routes as developed in Sweden and their application in the United States (i.e. Madison). Could serve as basis for minibus route w/diversion.
Mohring, H.; "Minibuses in Urban Transportation"; Journal of Urban Economics V. 14 293 -3 17 (1983) Possible economic justification of converting some bus routes in US to minibus in order to reduce subsidy level.
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Morlok,
E.K.; "Supply functions for public transport: initial concepts and models";
from Traffic Equilibrium Methods, M.A. Florian, ed; Springer-Veriag
(NewYork 1976); pp. 322-367
Discussion of basic components of engineering cost models for urban transit: cost per bus; cost per hour of wages, etc. Odutola, Adenaji; "Services and longevity of paratransit operations"; Transportation Quarterly, V.44 pp. 151-62, Jan. 1990 Statistical study of data from paratransit agencies to show correlations among trends. Did not use any cost data, so not directly relevant to this report. Odutola, Adenaji; "A Strategic marketing model for the paratransit operation"; V 42 pp. 447-55, July 1988 Marketing study which did not include any cost data so not relevant to report. Ohio Department of Transportation; Status of Public Transit in Ohio; July 1993 Cost and performance measures of transit and paratransit providers in Ohio (1991 data). Pratt
et al, Traveler Response to Transportation System Changes .1 S.N.Robinson; "Transit Operations for Individuals with disabilities"; Research Results Digest1994 |
W.K.Talley et al, "an urban transit firm providing transit, paratransit, and contracted-out services"; Journal of Transportation Economics and Policy September 1986, p.353-368
Authors claim to have first model of multi-service transit firm, which my search has not disproven. However, paratransit component not broken down into inputs so this model was not directly useful to the study.
U.S.D.O.T., LTMFA; ADA Paratransit Handbook., Washington (September 1991);
Reference for service requirements of fixed routes, timetable of implementation, etc. P.R.White et al;"Cost-benefit analysisof urban minibus operations”. Transportation V19, 59-74,1992
Models conversion from regular bus to minibus using elasticity of demand to measure increase in demand.
to be consulted later:
Ardilaga, B et al; "Demand, supply, and cost modelling framework for demand-responsive transportation systems"; Transportation Research Board, TRB Special Report No. 147 pp 32-47
Cost model may be useful; not available from Penn library system.
J.W.Billheimer et al, Paratransit Handbook: a Guide to Paratransit Implementation; Systan
May be available from Systan, although no copy available yet.
S.Rooney et al; "Developing a cost model and rate negotiating methodology..."; Public Transport Innovation Journal; V3 N4 pp.4-7
On order from PTI journal
U. S. Federal Ifighway Administration, FTA; Characteristics of Urban Transportation Systems: Revised Edition; September 1992; 147 pp.; NTIS No. PB93-178960ftM
Provides single source of planning data for urban transportation. Not yet ordered.