Total Delay Impact Study
A Comprehensive Assessment of the Costs and Impacts of Flight Delay in the United States
Final Report — October, 2010
Prepared by:
Michael Ball, Cynthia Barnhart, Martin Dresner, Mark Hansen, Kevin Neels, Amedeo Odoni, Everett Peterson, Lance Sherry, Antonio Trani, Bo Zou
With Assistance from:
Rodrigo Britto, Doug Fearing, Prem Swaroop, Nitish Uman, Vikrant Vaze, Augusto Voltes
i
Acknowledgments
The research documented in this report was sponsored by the Federal Aviation Administration Air Traffic Organization Strategy and Performance Business Unit, through its National Center of Excellence for Aviation Operations Research ( NEXTOR). The authors would like to thank David Chin for conceiving of this project and Thea Graham for skillfully managing it. Mike Wells and Dan Murphy, among others, provided valuable feedback on earlier drafts. Any errors or shortcomings that remain are, of course, our own.
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Table of Contents
Acknowledgments ............................................................................................................................ i
Table of Contents ........................................................................................................................... iii
List of Figures ............................................................................................................................... . v
List of Tables ............................................................................................................................... .. vi
Executive Summary ...................................................................................................................... vii
1 Introduction ............................................................................................................................. 1
2 Delays and Their Impact ......................................................................................................... 5
2.1 The Airline Perspective and Airline Costs ...................................................................... 6
2.2 The Passenger Perspective and Passenger Costs ............................................................. 7
2.3 Cost of Lost Demand ..................................................................................................... 12
2.4 Indirect Impact on US Economy ................................................................................... 13
2.5 Summary ....................................................................................................................... 14
3 Underlying Models and Justification ..................................................................................... 17
3.1 Impact of Delay on Airlines .......................................................................................... 17
3.1.1 Cost Model Set- up ................................................................................................. 17
3.1.2 Delay- based Model ................................................................................................ 18
3.1.3 Time- based Model ................................................................................................. 22
3.1.4 Cost Impact of Delay and Buffer on Airlines ........................................................ 25
3.2 Passenger Delay Cost .................................................................................................... 26
3.2.1 Passenger Trip Delay Causes ................................................................................ 27
3.2.2 Overview of Algorithm and Data Sources ............................................................ 29
3.2.3 Description of Algorithm ...................................................................................... 31
3.2.4 Results for 2007 ..................................................................................................... 32
3.2.5 Passenger Buffer .................................................................................................... 35
3.2.6 Monetary Value of Passenger Delays .................................................................... 35
3.3 Estimate of Costs of Voluntary Passenger Schedule Adjustments Due to Anticipated Schedule Delays ........................................................................................................................ 36
3.3.1 Data Sources .......................................................................................................... 36
3.3.2 Structural Model Specification .............................................................................. 37
3.3.3 Results ................................................................................................................... 38 iv
3.3.4 Calculation of VDTA Costs .................................................................................. 39
3.4 Capacity Induced Schedule Delay ( CSD) ..................................................................... 43
3.5 Value of Demand Lost Due to Delays ........................................................................... 49
3.5.1 Value of Demand to Travelers............................................................................... 49
3.5.2 Traffic Diversion Impacts ...................................................................................... 53
3.6 Estimating the Indirect Impact on the US Economy ..................................................... 58
3.6.1 USAGE Model Description ................................................................................... 59
3.6.2 Disaggregation of Air Transportation in USAGE Database .................................. 59
3.6.3 Incorporating Delay into the USAGE Model ........................................................ 60
3.6.4 USAGE Model Simulation .................................................................................... 61
3.6.5 Simulation Results ................................................................................................. 61
3.6.6 Sensitivity analysis ................................................................................................ 64
4 Individual Perspectives on Passenger Delay ......................................................................... 67
4.1 Qualitative Reports Confirm Study Findings ................................................................ 67
4.1.1 Avoiding the Most Delay Prone Parts of the System ............................................ 67
4.1.2 Personal Schedule Padding .................................................................................... 69
4.2 Delays and Unpredictability are Changing the Experience of Air Travel ..................... 69
4.2.1 Substitution of Electronic Communications for Travel ......................................... 70
4.2.2 Information Strategies ........................................................................................... 71
4.2.3 Productivity Strategies ........................................................................................... 71
4.3 Implications for Future Policy and Research ................................................................ 74
5 Public Policy Implications ..................................................................................................... 75
References ............................................................................................................................... ..... 79
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List of Figures
Figure 1- 1: Illustration of the relationship between delay, demand and system capacity ............... 1
Figure 2- 1: Ideal flight ................................................................................................................... 5
Figure 2- 2: Schedule buffer ( SB) ................................................................................................... 5
Figure 2- 3: Flight delay against schedule ( FDS) ............................................................................. 6
Figure 2- 4: Preferred passenger trip ............................................................................................... 8
Figure 2- 5: Illustration of passenger delay to schedule ( PDS) for the case where the passenger is booked on a flight ( F1) that is cancelled and is accommodated on another flight ( F1’) ................ 9
Figure 2- 6: Passenger delay to schedule ( PDS) for the case where the passenger has two leg itinerary and the first flight ( F1) is delayed inducing a missed connection. The passenger is accommodated to his or her final destination on a third flight ( F2’) ............................................... 9
Figure 2- 7: Illustration of delays related to difference between actual and desired departure time ............................................................................................................................... ....................... 11
Figure 3- 1: Identification of time components in the six possible situations ................................ 23
Figure 3- 2: Time- space diagram for Scenarios 1- 3 ....................................................................... 28
Figure 3- 3: Time- space diagram for Scenario 4 ............................................................................ 29
Figure 3- 4: Overview of the algorithm .......................................................................................... 30
Figure 3- 5: CVAR Scheduled Departures for CVG and LGA ..................................................... 44
Figure 3- 6: Capacity ( AAR) utilization for LGA .......................................................................... 45
Figure 3- 7: Capacity ( AAR) utilization for CVG .......................................................................... 45
Figure 3- 8: Schedule adjustment algorithm driven by parameter γ .............................................. 47
Figure 3- 9: Result of schedule adjustment algorithm applied to ORD departures data for August, 2007. Actual ( constrained) schedule had CVAR= 0.3940; projected schedule had CVAR= 0.8056, which was the value estimated by the regression model. .............................................................. 47
Figure 3- 10: Welfare changes from elimination of delays ............................................................ 51
Figure 3- 11: Cumulative density function of flight times between LGA and BOS by Airbus A319/ 320 aircraft .......................................................................................................................... 56
Figure 3- 12: Estimated padding times for 1294 origin- destination pairs in the national airspace system ............................................................................................................................... ............ 57
Figure 3- 13: Change in real GDP from reduction in flight delay: mean value and one standard deviation ............................................................................................................................... ........ 66
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List of Tables
Table 0- 1: Direct cost of air transportation delay in 2007 ............................................................. vii
Table 1- 1: Comparison of TDI and JEC delay cost estimates ($ billions) ...................................... 3
Table 2- 1: Airline cost estimates for 2007 ($ billions) .................................................................... 7
Table 2- 2: Passenger delay cost estimates for 2007 ($ billions) .................................................. 12
Table 2- 3: Cost of lost air transport demand for 2007 ($ billions) ................................................ 13
Table 2- 4: Overall cost of US air transportation delays for 2007 ($ billions) .............................. 14
Table 3- 1: Descriptive statistics of key variables .......................................................................... 19
Table 3- 2: Estimation results of delay- based Translog cost functions .......................................... 20
Table 3- 3: Estimation results of delay- based Translog cost functions with insignificant delay terms removed ............................................................................................................................... 22
Table 3- 4: Estimation results of time- based Translog cost functions............................................ 24
Table 3- 5: Airline cost estimates ($ billions), for 2007 ................................................................. 26
Table 3- 6: Passenger delay estimates for calendar year 2007 ....................................................... 32
Table 3- 7: Monthly passenger delay estimates for the 1st and 2nd calendar quarters of 2007 ....... 33
Table 3- 8: Monthly passenger delay estimates for the 3rd and 4th calendar quarters of 2007 ..... 34
Table 3- 9: Passenger cost estimates ( in $ millions), for 2007 ....................................................... 35
Table 3- 10: Conditional logit regression results........................................................................... 39
Table 3- 11: Predicted schedule adjustments between departure windows without delay ............ 40
Table 3- 12: Departures by quarter and departure window, 2006- 2008 ........................................ 41
Table 3- 13: Value of time lost to voluntary departure time adjustment ........................................ 41
Table 3- 14: Mean departure time, 2006- 2008 ............................................................................... 42
Table 3- 15: Estimates of cost of voluntary time adjustment ........................................................ 43
Table 3- 16: Regression results for departure model ...................................................................... 46
Table 3- 17: Summary of schedule delay results ........................................................................... 48
Table 3- 18: Estimation of fares and passengers – using three measures of delay ........................ 52
Table 3- 19: Estimation of welfare gains per passenger from eliminating delays from the three model specifications ...................................................................................................................... 53
Table 3- 20: TSAM model calibrated coefficients ......................................................................... 55
Table 3- 21: Changes in 2007 nationwide intercity passenger demand ( minimum feasible block times vs baseline system) .............................................................................................................. 58
Table 3- 22: Changes in 2007 nationwide safety impacts ( minimum feasible block times – baseline system) ............................................................................................................................ 58
Table 3- 23: USAGE model results using base values of the delay parameters ............................. 65
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Executive Summary
Flight delay is a serious and widespread problem in the United States. Increasing flight delays place a significant strain on the US air travel system and cost airlines, passengers, and society at many billions of dollars each year. While a number of previous studies have attempted to estimate the total economic impact of delays, scientific knowledge about the cost of delay is still limited. The Federal Aviation Administration sponsored the five NEXTOR universities and the Brattle Group to conduct a comprehensive study on the total delay impact ( TDI) in the United States.
This report analyzes a variety of cost components caused by flight delays, including cost to airlines, cost to passengers, cost of lost demand, as well as the indirect impact of delay on the US economy. This study offers a broader consideration of relevant costs than conventional cost- of- delay estimates, and employs several innovative methodologies for assessing the magnitudes of these costs. Of particular note are the passenger delay cost estimates, which recognize that flight cancellations and missed connections can lead to substantial passenger delays not revealed in traditional flight delay statistics.
The TDI project team estimates that the total cost of all US air transportation delays in 2007 was $ 32.9 billion. The $ 8.3 billion airline component consists of increased expenses for crew, fuel, and maintenance, among others. The $ 16.7 billion passenger component is based on the passenger time lost due to schedule buffer, delayed flights, flight cancellations, and missed connections. The $ 3.9 billion cost from lost demand is an estimate of the welfare loss incurred by passengers who avoid air travel as the result of delays.
In addition to these direct costs imposed on the airline industry and its customers, flight delays have indirect effects on the US economy. Specifically, inefficiency in the air transportation sector increases the cost of doing business for other sectors, making the associated businesses less productive. The impact here is subtle, however. For example, the airline industry would actually employ fewer people as it becomes more efficient. The overall impact, of course, would be positive. The TDI team estimates that air transportation delays reduced the 2007 US GDP by $ 4 billion.
Table 0- 1: Direct cost of air transportation delay in 2007
Cost Component
Cost ($ billions)
Costs to Airlines
8.3
Costs to Passengers
16.7
Costs from Lost Demand
3.9
Total Direct Cost
28.9
Impact on GDP
4.0
Total Cost
32.9
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Certainly, some flight delays are unavoidable and are not the result of airspace congestion. For example, delays could be caused by mechanical problems or problems boarding passengers. Even if ample aviation infrastructure is provided, operational uncertainty still exists and flights can be delayed if safety issues arise due to severe weather or other causes. Absent major policy changes, most decisions about how capacity is used are made by users, not the Air Navigation Service Provider ( ANSP). Not all delays can or should be eliminated. Nonetheless, this study provides a frame of reference for decision makers to assess the magnitude of the flight delay problem and the need for initiatives to address it. In this regard, it similar to other studies that attempt to measure the size of a problem, such as air pollution, motor accidents, or crime, while recognizing that the problem cannot be entirely eliminated.
One can certainly expect that new aviation technologies and procedures, including those associated with the Next Generation Air Transportation System ( NextGen), coupled with appropriate government policies and infrastructure investments, have the potential to reduce the identified costs by a very large percentage. One should also keep in mind that the air transportation system seeks a new equilibrium any time new capacity is provided. A very large capacity increase could reduce the majority of the delays identified in this report assuming the demand ( in terms of number of operations) placed on the system remained constant. However, the flight operators would no doubt react to such capacity increases and change their service offerings. The new equilibrium the system would reach is very difficult to predict. The gains from NEXTGEN and other aviation infrastructure investments will be greatest is they are combined with policy innovations, such as pricing NAS resources and services to encourage their more efficient use, setting realistic caps at airports, and so on. This will ensure the most effective use of new capacity in order to reduce flight delay and its associated cost, by reducing problems that arise from the externalization of delay costs in the present system. Assuming the new capacity is efficiently allocated, the cost of the delays that NAS investments would eliminate provides a lower bound on their benefits to society. The results of this study suggest that policies and mechanisms that discourage overscheduling should be considered in concert with capacity enhancements to insure effective use of new capacity in order to reduce flight delay and its associated costs.
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1 Introduction
Flight delay is a serious and widespread problem in the United States. In 2007, nearly one in four airline flights arrived at its destination over 15 minutes late ( BTS, 2009). About a third of these late arrivals were a direct result of the inability of the aviation system to handle the traffic demands that were placed upon it, while another third resulted from airline internal problems. Most of the remainder was caused by an aircraft arriving late and thus having to depart late on its next flight ( BTS, 2009).
Between 2002 and 2007, as the air transport system recovered from the 9/ 11 attacks, scheduled airline flights increased about 22 per cent, but the number of late- arriving flights more than doubled. Since 2007, traffic and delays have declined somewhat because of the recession, but the FAA expects growth to resume, with air carrier flight traffic reaching 2007 levels by 2012, and growing an additional 30 per cent by 2025. It is widely recognized that delay increases nonlinearly as demand approaches the capacity in the system ( Figure 1- 1). If current demand in the system is D1 with delay at delay1 level, it is likely that, without substantial upgrades to aviation infrastructure, such growth ( for example, to D2) would result in flight delays far in excess of any we have heretofore experienced ( delay2).
Figure 1- 1: Illustration of the relationship between delay, demand and system capacity
Growing delays threaten the competitiveness of the US in the world economy, by limiting the ability of the air transport system to serve the needs of the US economy. The growth in gross domestic product and air travel demand are closely linked; a recent multi- national study found a strong correlation between growth in economic productivity and growth in business travel ( Oxford Economics, 2009). Business travel accounts for about half the dollars spent on domestic air transport ( BEA, 2009), and with good reason— a recent study estimates that a dollar spent on business travel earns a return of about $ 12 in increased revenue to the traveler’s employer ( Oxford Economics, 2009). In addition to improving business performance generally, air transport impacts the economy through the jobs and revenue it directly creates in air transport-
Future SystemCapacity with UpgradeDemandDelayCurrent SystemCapacitydelay2delay1delay3D1D2D3 2
related industries, the expenditures of air travelers on auxiliary goods and services, and the secondary impacts that result as these dollars recycle throughout the economy. FAA estimates the total economic impact from civil aviation at $ 1.3 trillion in economic output, nearly $ 396 billion in earnings, and 12 million jobs in 2007 ( FAA ATO, 2009).
Ironically, the airline industry itself has realized very little return from these economic contributions. Most US airlines have operated in the red for most of this decade. US passenger airlines lost over $ 60 billion between 2000 and 2008, on revenues of just over $ 1 trillion ( ATA, 2009a). Large losses following the 9/ 11 attacks were followed by a recovery foreshortened by skyrocketing oil prices and a recession, which led to even larger losses. As of December 2009, the total market capitalization of major US carriers was about $ 26 billion, a drop of 65 per cent from early 2007, when the prospects for recovery appeared brightest. Flight delays, by increasing airline costs and reducing demand for air travel, compound these financial challenges.
Building on a strong domestic market, aerospace manufacturing had the highest net exports— some $ 60 billion – of any U. S. industry in 2008 ( FAA ATO, 2009). The four largest airlines in the world are all U. S. carriers, as are five of the world’s top ten busiest airports. The FAA Air Traffic Organization is the largest, busiest, and ( arguably) most efficient provider of air navigation services in the world. It may be difficult to maintain such competitive strength if future growth is stifled by high delays.
Substantial investments are required in order to modernize and expand our aviation infrastructure so that it can accommodate anticipated growth without large increases in delay. The Next Generation Air Transportation System ( NextGen) will deploy improved systems for communications, surveillance, navigation, and air traffic management and also require flight operators to invest in new on- board equipment. Substantial improvements in air transportation capacity also require airport infrastructure enhancement. Estimates of these combined investments reach well into the 10’ s of billions of dollars ( GAO, 2008; ACI, 2009).
The Federal Government together with the air transportation industry must decide on a level of investment to make in future system capacity. Other approaches to reducing delay, such as reducing incentives to over scheduling flights, might also be considered. To help inform decision making on such issues, the FAA has sponsored this study of the total economic impact of flight delay in the United States. Focusing on the year 2007— the worst on record in terms of flight delays— the study attempts a comprehensive accounting of the economic cost of flight delays to airlines, air travelers, and the rest of society. The analysis assesses the cost to society of all air transportation system delays. To be sure it would be impossible to eliminate all of these delays and their costs, and even unwise to seek to do so. In this regard, the TDI study is similar to others that attempt to measure the size— i. e. the social cost-- of a problem, such as air pollution ( e. g. Muller et al, 2007), motor accidents ( e. g. Cambridge Systematics, 2008), or crime ( e. g. Anderson, 1999), while recognizing that the problem cannot be entirely eliminated. At the same time, it is quite reasonable to seek to eliminate— through policy innovation, research and development, and capital investment-- a substantial portion of these delays and the magnitude of the costs involved suggests that doing so could benefit society significantly. The calculation of the cost of delays is one way to estimate the potential benefits of capacity increases. The air transportation system will react to any capacity increases by altering service patterns. For example, if future capacity is increased, the system might move to D3 and delay3 in Figure 1- 1, instead of D2 and delay2. Thus, the benefits of such capacity increases could manifest themselves as both delay decreases and better service offerings. Nonetheless, assuming capacity is used efficiently, the cost of the delays the capacity could eliminate provides a lower bound on the benefits the capacity increases provide to society.
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Table 1- 1: Comparison of TDI and JEC delay cost estimates ($ billions)
TDI
JEC
Costs to Airlines
8.3
19.1
Costs to Passengers
16.7
12.1
Indirect Impact on Economy
4.0
9.6
Costs from Lost Demand
3.9
N/ A
Total Cost
32.9
40.7
Other studies have examined the total cost of delay. According to a report prepared for the Senate Joint Economic Committee, the total cost, to airlines, passengers, and the rest of the economy, is estimated to be as high as $ 41 billion in 2007, including $ 31 billion in direct costs and $ 10 billion in spillovers ( JEC 2008). The Air Transport Association, using a different methodology, estimates costs ( for the year 2008) to be $ 14 billion, not including spillovers ( ATA, 2009b).
Part of the motivation for the present study is the disparity of the above estimates. In addition, the JEC and ATA results, as well as several earlier studies on the same subject, overlook factors whose importance has become increasingly recognized within the aviation research community. They do not, for example, recognize the rather complex relationship between flight delay and passenger delay, or consider how degraded service quality affects the demand for air travel. This suggests the need for a more comprehensive and careful look. Table 1- 1 provides a comparison of the TDI aggregate numbers, presented in the executive summary, and the JEC aggregate numbers. Note several significant discrepancies. The TDI airline cost estimate and the TDI indirect cost estimate are both substantially smaller than the corresponding JEC numbers. The TDI and JEC estimation approaches differed substantially. In both cases, we employed economic models calibrated on historical data. The JEC work relied on a simple allocation of costs based on total flight time for the airline cost estimate and a generic macroeconomic impact multiplier for the indirect economic impact estimate. On the other hand, the TDI passenger cost estimates are higher. This is principally due to our inclusion of estimates of the passenger costs due to flight cancellations and missed connections. The JEC report did not calculate an estimate of the costs associated with lost demand.
This report summarizes the findings from our cost assessment. Section 2 provides an overview of the flight delay phenomenon, the types of costs that are incurred from delay, and our final estimates of the magnitudes of such costs in 2007. Section 3 provides a more detailed description of the methodologies employed to obtain the cost estimates. It covers relevant components such as delay and buffer cost to airlines ( section 3.1), to passengers ( section 3.2), cost of voluntary passenger schedule adjustment ( section 3.3), capacity induced schedule delay cost ( section 3.4), value of demand lost due to delays ( section 3.5), and indirect impact of delays on US economy ( section 3.6). Section 4 provides additional perspectives on the results by relating them to practical experiences of air travelers and industry trends. It also suggests areas where further investigation may be warranted and discusses related costs and delays not covered. Finally, Section 5 suggests some possible policy implications of the results.
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5
2 Delays and Their Impact
To understand the impact of congestion and delays on the air transportation system, we start with a stylized view of how the system would operate in their absence. An airline might start the process of scheduling a flight by determining an ideal flight departure time ( IDT). The IDT would take into account not only preferred passenger travel times, but also internal airline constraints, such as those necessary to create efficient crew schedules and fleet plans. As part of this process, the airline would then choose the most appropriate aircraft type from its fleet for the flight. Using the characteristics of that aircraft and assuming it could fly the optimal, unimpeded origin- to- destination trajectory, an ideal arrival time could be computed as illustrated in Figure 2- 1. This unimpeded flight time is a key quantity in our analysis whose estimation will be discussed later in this document.
Figure 2- 1: Ideal flight
Now let us consider how congestion and delays alter this situation. As illustrated in Figure 2- 2, the airlines will typically increase scheduled flight times over unimpeded ones in order to account for delays resulting from flight restrictions imposed to organize traffic, congestion, and a variety of other factors. We call this added time, the schedule buffer ( SB). Once an unimpeded flight time has been determined the schedule buffer can be computed from historical data.
Figure 2- 2: Schedule buffer ( SB)
Of course, the type of delay most typically discussed occurs when the arrival is later than scheduled. This is illustrated in Figure 2- 3. Such flight delay against schedule ( FDS), like SB, reflects excess travel time much of which is related to congestion in the air transportation system. However, while SB is known in advance for a particular flight, FDS is not. FDS varies
Schedule Buffer ( SB)
IDT
IAT
scheduled flight arrival time ( SAT)
ideal arrival time ( IAT)
unimpeded flight time
ideal departure time ( IDT) 6
unpredictably from day to day and flight to flight; it can even be negative because the SB may exceed the delays incurred for a particular flight. This gives FDS a very different character when compared to SB.
Figure 2- 3: Flight delay against schedule ( FDS)
Congestion and delays affect both airlines and passengers, albeit in different ways. These phenomena have a definite impact on airline costs, which we assess. Passengers see increases in the time required for travel, experience inconvenience and stress, and may face additional expenses for food and lodging. The costs to airlines and passengers— some in the form of added expense and lost revenue, and others in the form of decreased convenience and additional misery— are the direct costs of flight congestion and delay. We note that infrastructure congestion, e. g. at an airport, can actually benefit an individual airline by limiting access by competitors and allowing that airline to charge higher prices. This effect is not captured in our work.
This discussion has implicitly assumed that the number of passengers remains fixed as system delays change. In fact, if air transportation delays were eliminated or reduced then air travel would become more attractive and the demand for it would increase. This increase in demand will provide benefits that are apportioned in some way between airlines and passengers. In fact, it can be difficult to isolate one benefit from the other so we calculate and discuss this effect in the section on passenger delay costs ( see 3.5.1). Of course, such demand increases could in turn spur additional flight traffic and restore some delays in the system. We do not consider this feedback effect here.
These direct congestion costs propagate through the rest of the economy, creating a third cost category. Any phenomenon that makes one industry segment, e. g. air transportation, more expensive leads to higher costs and lower efficiency in other segments, e. g. manufacturing, retail, etc. The added costs and reduced profits of any industry that depends on air travel, and the resulting impact on its customers, constitute the indirect impact of flight congestion and delay. Accordingly, we break down our discussion of costs into three categories: airlines ( Section 2.1), passengers ( Section 2.2) and indirect impact on US economy ( Section 2.3). We develop an estimate of the cost impact for each category.
2.1 The Airline Perspective and Airline Costs
As discussed we will estimate the impact of delays on airline costs in terms of two measurable quantities: schedule buffer ( SB) and flight delay against schedule ( FDS). To illustrate the impact of SB on airline costs, we note that the typical pilot contract specifies that pilots are paid based on
IDT
IAT
Flight delay against schedule ( FDS)
actual flight arrival time
SAT 7
the maximum of scheduled block time and actual block time. Thus, the SB directly increases pilot ( and airline) costs. Further, airlines create their fleet plans based on the scheduled flight arrival and departure times so that increasing SB leads to changes in schedules and eventually to poorer aircraft utilization and larger fleets. The high degree of uncertainty associated with FDS gives it a very different character. Since airline fleet and crew schedules are based largely on the scheduled times, excessive or even moderate amounts of flight delays can be highly disruptive causing extra crew costs, various costs associated with accommodating disrupted passengers and even aircraft repositioning.
We employ translog models, which incorporate both delay against schedule and schedule buffer to estimate airline cost functions. Our estimation results support the view that poorer operational performance ( i. e. more FDS and SB) leads to more expensive operations. Such airline cost models establish an empirical basis for translating delay and buffer into monetary terms. Using these models, the potential cost savings that could result from reducing FDS and SB are estimated. Table 2- 1 gives a summary of our estimates for 2007. Note that our cost model includes 7 major U. S. airlines whose service dominates in the entire air transportation system. An estimate covering the entire industry is also calculated. We investigated the relevant airline cost under two scenarios. In the first scenario, FDS is entirely eliminated; in the second scenario, we further reduce SB to zero. Section 3.1 provides more detail. We also tried alternative approach to modeling the relationship between airline cost and operational performance. This second approach yields somewhat higher costs estimates— as much as $ 13 billion industry wide. This is also discussed in Section 3.1. We report the lower value here because it is based on a more standard approach for characterizing flight delay and buffer.
Table 2- 1: Airline cost estimates for 2007 ($ billions)
Delay Against
Schedule
Buffer
Total
7 major airlines
3.3
2.6
5.9
Industry wide*
4.6
3.7
8.3
* Includes airlines with $ 20 million annual operating revenue only.
Of the $ 8.3 billion total, $ 4.6 billion is attributed to the most common notion of delay, FDS. The contribution of SB, $ 3.7 billion, is of comparable magnitude. These figures, like those in the presented elsewhere in this report, reflect cost savings that would result from an unattainable ideal case in which all schedule buffer and delay against schedule were eliminated. They are intended to establish an upper bound for the airline cost savings that could result from improving the operational performance of the air transportation system. The question of how much of these savings is actually attainable is addressed in Section 5 of this report.
2.2 The Passenger Perspective and Passenger Costs
It is common to view flight delay statistics as representative of passenger delays. In fact, NEXTOR research over the past several years has demonstrated that there can be very dramatic differences between flight delays and passenger delays.
To see the differences and also to understand passenger costs let us take a simple view of how a passenger approaches air travel in an ideal environment. A passenger might start with a preferred arrival time ( PAT). Based on the travel times offered by a chosen airline this could be converted 8
into a preferred departure time ( PDT) as illustrated in Figure 2- 4. We note that this time is a bit different from the unimpeded flight time described earlier. First, it could be that the scheduled itinerary time involves multiple flights. Of course, a passenger in most cases would prefer a single nonstop flight. However, multi- flight- leg itineraries are a way in which the airlines provide cost effective service to passengers. Passengers also benefit from this by enjoying more frequent services. Thus, while the extra time associated with such itineraries might be viewed as a type of delay, it is not caused by congestion or deficiencies in air traffic management but rather by mechanisms used by airlines to provide cost effective service. On the other hand, the schedule buffer included within each constituent flight is a result of congestion as discussed above and certainly represents extra passenger travel time and thus a cost to passengers.
Figure 2- 4: Preferred passenger trip
It is frequently assumed that flight delay statistics provide an accurate depiction of passenger delay. However, the quantity analogous to FDS, passenger delay against schedule ( PDS), can be very different from FDS. If a passenger books a direct flight to his or her destination and is able to take that flight, then the delay of that flight corresponds to the delay of the passenger. However, average flight delay statistics do not capture the delays associated with disrupted passengers. A passenger’s trip is disrupted if that passenger is not able to take one or more of his or her booked flights. The two most typical cases for trip disruptions are:
• a passenger arrives at the airport and, subsequently, the booked flight is canceled;
• a passenger misses a connection on a multi- leg trip.
Figures 2- 5 and 2- 6 illustrate these phenomena. Note from Figure 2- 6, the rather complex relationship between the delay on the first leg of a two leg trip and the passenger’s final delay. If the passenger makes his or her connection then the final delay depends only on the delay on the second flight leg. Thus, small delays on the first flight leg have no impact on the final delay. On the other hand, larger delays on the first leg can have the very dramatic effect of causing a missed connection and subsequent, sometimes extreme, delays. This illustrates the fact that average PDS depends on the distribution of flight delays ( as well as other factors), not just average FDS. Thus, while there are readily available statistics that allow direct compilation of total FDS, it is more difficult to compute ( or estimate) total PDS. In the past, NEXTOR has obtained proprietary airline data and has calculated passenger delays for individual airlines over limited time periods. For this study, new models in section 3.2 have been developed that allow more accurate estimation of passenger delays for an entire year on a NAS- wide basis. We note that passenger delays depend on flight delays but also on flight cancellation rates and load factors. The relationship to cancellation rates is easy to see based on Figure 2- 5. Note from both Figures 2- 5 and 2- 6 that both a flight cancellation and a missed connection require that passengers be accommodated on flights for which they were not originally ticketed. Doing this requires
preferred arrival time ( PAT)
scheduled itinerary time
preferred departure time ( PDT) 9
available space on the flights in question. As load factors become higher such space is harder to find, increasing delays for disrupted passengers.
Figure 2- 5: Illustration of passenger delay to schedule ( PDS) for the case where the passenger is booked on a flight ( F1) that is cancelled and is accommodated on another flight ( F1’)
Figure 2- 6: Passenger delay to schedule ( PDS) for the case where the passenger has two leg itinerary and the first flight ( F1) is delayed inducing a missed connection. The passenger is accommodated to his or her final destination on a third flight ( F2’)
To summarize the above discussion, passenger delay costs can be related to a combination of SB and PDS. While statistics on SB can be readily derived from historical data, PDS statistics must be estimated based on sophisticated models that depend of flight delays, cancellation rates and load factors.
F1
PDT
PAT
F2’
Passenger Delay to Schedule ( PDS)
F2
F1
F2
F1 ( cancelled)
PDT
PAT
F1’
Passenger Delay to Schedule ( PDS) 10
Just as airlines add buffers to flight schedules to increase schedule reliability in light of uncertain flight delays, passengers often plan their departure times taking into account the possibility of arrival delays. If a passenger absolutely needs to be at a destination by 10: 00 AM he or she typically would not take a flight scheduled to arrive at 10: 00 AM. Rather the passenger would take a flight scheduled to arrive earlier to ensure arrival by 10: 00 AM even in the case of significant flight delays. In fact, it is not uncommon for a traveler to fly in the night before, only to ensure timely arrival at a morning meeting. As illustrated in Figure 2- 7, we call this phenomenon and the associated adjustment in departure time voluntary departure time adjustment ( VDA)
While passengers and airlines might adjust departure times for specific reasons, it is also the case that there are many factors that influence scheduled flight times. Flights are rarely available at exactly the time when a given passenger would like to fly. For example, a passenger might wish to arrive at a destination at 9: 00 AM via a one hour flight. Thus, ideally the passenger would book an 8: 00 AM flight. However, it could be that the only flight offered before 9: 00 was a 7: 00 AM flight. Thus, the passenger would be “ forced” to take the 7: 00 AM flight and we would say the passenger suffered one hour of schedule delay. Generally, schedule delay is the result of airline scheduling practices, which depend on a wide range of factors the airlines must take into account in order to produce cost effective schedules. Thus, most schedule delay cannot be “ blamed” on NAS capacity constraints. However, at highly constrained airports, it could be that the airlines are forced to flatten their schedules and offer flights at inconvenient times when they otherwise would seek to provide better service to their passengers. Using techniques specifically developed for this project, we are able to estimate the schedule delay resulting from scarce capacity, isolating it from the schedule delay resulting from normal airline scheduling practices. Figure 2- 7 also illustrates this case; we call this phenomenon and the associated added time capacity induced schedule delay ( CSD). Clearly the delays just discussed are different from more traditional notions of delay. However, they would not occur in a system with ample capacity that and much less congestion.
PDT
PAT
desired arrival time
actual departure time
capacity induced schedule delay ( CSD) or voluntary early departure time adjustment ( VDA)
possible late arrival time 11
Figure 2- 7: Illustration of delays related to difference between actual and desired departure time
Before presenting our statistics on passenger costs and delay, it may be worthwhile to consider all of the cases we have discussed and their potential interaction. One can view the passenger decision- making process sequentially, as starting with a preferred arrival time, then calculating a preferred departure time. Associated with this hypothetical flight is the potential for an unknown passenger delay ( PDS). Based on the expected PDS, the passenger might further adjust the departure time by VDA to add certainty to the arrival time. Finally, schedule constraints could impose a further change by CSD. Our explanation has assumed a passenger begins with a preferred arrival time; however, a similar sequence could have been created assuming the passenger began with a preferred departure time. Clearly, these delays and schedule adjustments are inter- related but when one considers a particular passenger trip they are largely independent phenomena. VDA and CSD represent adjustments to the passenger’s chosen departure time due to generally independent mechanisms. SB is an expansion of the passenger’s scheduled ( and actual) flight time. This expansion is known in advance and anticipated by the passenger. PDS is highly stochastic and can be extremely disruptive. In the calculations that follow, we independently estimate each of these and associate a cost with each one. These costs are then added together. One might argue that there is a degree of “ double counting” in this approach. For example, if a passenger chooses to leave the night before to insure getting to a morning meeting on time, then the passenger has already adjusted for, and paid the price for, possible PDS. However, such a passenger may plan to have a leisurely dinner and/ or get to bed at a convenient time. If that passenger arrives three hours late, then these planned activities would be disrupted and further costs would be incurred. Thus, we argue that, once a passenger has planned a trip, with or without substantial departure time perturbations, the SB and PDS costs of the associated flight are still real and can be added to any costs related to the adjusted departure time.
Table 2- 2 provides the overall passenger delay costs. These are obtained by first deriving a cost estimate ( or a lower bound on the cost) of each delay component: TC[ SB], TC[ PDS], TC[ CSD], TC[ VDA]. The notation TC[] refers to the total cost of the respective component over all domestic passengers during 2007. Calculations of SB, PDS, CSD, and VDA are discussed in
PDT
PAT
desired arrival time
actual departure time
capacity induced schedule delay ( CSD) or voluntary early departure time adjustment ( VDA)
possible late arrival time 12
detail in sections 3.2 – 3.4. Based on the above discussion the various components are combined via a simple addition, i. e
Total Passenger Cost = TC[ SB] + TC[ PDS] + TC[ CSD] + TC[ VDA].
The preceding analysis discussed the estimation of the increased value of air travel assuming that the existing passenger made the same trips before and after delays were eliminated ( and implicitly that they paid the same price). In general, passengers are willing to pay a higher price for less delayed flights and airline costs are reduced as delay decreases. Thus, delay reductions would lead to a new equilibrium in the supply/ demand relationship between the airlines and their passengers with both the airlines and passengers accruing a portion of the overall welfare gain. Rather than trying to apportion the benefit of the reduced delay between the airlines and passengers, this analysis implicitly allocates the entire benefit to the passengers, i. e. passenger delay is reduced and passengers pay the same price. This accounts for the entire welfare gain while not attempting to accurately determine how the gain is apportioned between airlines and passengers. For similar reasons, the elimination or reduction of delays would also increase the demand for air travel. These new passengers would also incur a benefit. That benefit is the difference in the value of their travel over the value of travel on the alternative transportation mode they use today. To estimate this effect we take a social welfare approach and estimate that increase in social welfare accrued by these new trips using the air transportation system. This work is summarized in the next section.
Table 2- 2: Passenger delay cost estimates for 2007 ($ billions)
Delay Category
Delay Cost
1. SB ( schedule buffer)
6.0
2. PDS ( passenger delay against schedule)
2a. Delay due to delayed flights
2b. Delay due to flight cancellations
2c. Delay due to missed connections
Total estimated PDS ( 2a+ 2b+ 2c)
4.7
3.2 1.5
9.4
3. CSD ( capacity induced schedule delay)
0.7
4. VDA ( voluntary early departure time adjustment)
0.6
Total cost of passenger delay
16.7
* In calculating the delay cost for category 1 and 2, a standard cost per unit time ($ 37.6/ hr) is assumed ( DOT, 2003; inflated to 2007 value). Cost of CSD and VDA are based on the respective estimates.
2.3 Cost of Lost Demand
Flight delay degrades the quality of the airline product. While many air travelers choose to “ grin and bear it” others respond by switching to alternative transportation modes, or simply not traveling at all. Such travelers do not bear the costs of air travel delay discussed in Section 2.2, 13
but still incur a loss in welfare. In the air transportation market, both passengers’ decision on traveling and airlines’ pricing behavior are influenced by flight delays. We explicitly model passenger demand and fare to be functions of flight delays ( see Section 3.5.1). By simultaneously estimating the demand and fare functions, the demand and supply interactions on the route level are investigated. The model results indicate that delays have an upward impact on fares, while at the same time decreasing people’s willingness to pay for travel by air. Using a discrete choice model, we find some of the trips are shifted to automobile, and the additional road traffic generates congestion costs on other road users and environmental costs on society at large. Table 2- 3 summarizes these results. The first component is an estimate of the difference in the value ( or welfare) that certain air travelers would have achieved using air transportation in a delay- free ( or low delay) environment and the value they did achieve having chosen to shift to another mode because of air transport delays. There is an additional externality due to the switch to automobile. Specifically, car travel is less safe than air travel so that this switch from air to car will cause additional fatalities ( see Section 3.5.2). An estimate of this cost is also provided in Table 2- 3.
Table 2- 3: Cost of lost air transport demand for 2007 ($ billions)
Cost Component
Cost
1. Welfare loss due to switch from air to automobile
3.7
2. Externality cost from increased road traffic
0.2
Total cost of Lost Air Transport Demand
3.9
2.4 Indirect Impact on US Economy
The impacts of flight delays are not confined to airlines and their passengers. Other segments of the economy are also affected. Increases in airline costs caused by delay and schedule padding cause passengers to pay higher fares. These higher fares affect not just the demand for leisure travel but also lead to increases in the cost of production for industries that rely on air transportation to conduct business. Demand for the output of such industries in turn decreases. Schedule padding and flight delays also add to the time required for business trips, leaving business travelers with less time to do their work. As a result, delays cause employers to experience a loss in productivity.
Tracing out these various effects requires an integrated model of the national economy. For this purpose, we utilized a single- region Computable General Equilibrium ( CGE) model. 1
1 Specifically, we employed the USAGE model ( see Section 3.6). This model was modified to reflect our findings on the direct costs of delay. We explicitly modeled the increases in airline costs caused by delay, and the loss in productivity for business travelers. The CGE framework then traced the effects of these changes in cost as they rippled through the economy. The model traced the effects of cost increases on the growth of the U. S. economy over the period from 2005 through 2013. 14
Two sets of simulations were performed to assess the macroeconomic impact of flight delays. A baseline simulation projected the effects of changes in income, consumer tastes, and technology on the demand for air transportation and the amount of flight delay over the period from 2005 and 2013, assuming no policies or actions are taken to reduce flight delays. The second set of simulations assumed the elimination of delays ( actually reduction by 90%) for a given level of industry output. In this way we calculate that in 2007 U. S. GDP was approximately $ 4 billion lower than it would otherwise have been in the absence of delays. Of course, the investments and expenditures required to reduce delays would also generate economic impacts, but these are not considered here. We note that this estimate is lower than others that have previously been published ( see, for example, the JEC study -- JEC 2008). Many of these prior studies focus solely on delay- induced changes in cost, and fail to account fully for how these cost changes affect the growth of the economy. In contrast, our analysis took into account the fact that increases in the efficiency of air transportation would actually decrease certain direct economic activities associated with this sector since fewer pilots, flight crews, etc would be required to carry out the same business functions. On the other hand, there would be an increase in the economic activity of other businesses due to the reduction in the cost of a component of their production ( air transportation). The net effect is certainly a positive increase in economic activity but perhaps not as great as some earlier studies have estimated.
2.5 Summary
Table 2- 4 provides a compilation of all cost components. Certainly by any objective standards these costs are large and indicate that appropriate mitigation actions should be considered. At the same time, one should keep in mind that total elimination of all delays is neither practical nor desirable. Perspective on this issue as well as possible policy implication is discussed in Section 5.
It is instructive to compare these results with the results provided in the JEC report ( JEC, 2008). Our estimate of airline cost is smaller ( JEC: $ 19.1 B, TDI: $ 8.3 B). The difference may be due to the use of completely different approaches. This JEC number, as pointed out by the report itself, “ may overstate the relevant costs” ( JEC, 2008). In fact, the JEC study also reported their cost estimates using an alternative approach which produced much lower airline cost estimates ($ 3.6- 6.1 B). Our results just lie between their high and low ends of estimates. On the passenger side, our estimated costs are somewhat larger in magnitude ( JEC: $ 12.0 B, TDI: $ 16.7 B). One reason for the passenger cost discrepancy is the inclusion in the TDI analysis of delays due to flight cancellations, missed connections and other factors. The JEC study did not estimate the cost of lost demand.
Table 2- 4: Overall cost of US air transportation delays for 2007 ($ billions)
Cost Component
Cost
Cost to Airlines
8.3
Costs to Passengers
16.7
Cost from Lost Demand
3.9
Total Direct Cost
28.9
Impact on GDP
4.0 15
The two studies did diverge somewhat significantly in their estimate of the impact on the GDP ( JEC: $ 9.6 B, TDI: $ 4.0 B). As discussed earlier, the TDI modeling approach sought to capture both positive and negative impacts on GDP; this perhaps could explain this difference.
16
17
3 Underlying Models and Justification
3.1 Impact of Delay on Airlines
The research team employs a statistical cost estimation methodology to estimate how delays affect airline costs. This method differs from most previous research on this subject, which used cost factors to estimate airline delay costs. The cost factor approach involves decomposition of delay into different types and multiplying the quantity of each type by a cost factor. While simple and useful, this approach is problematic because it is difficult to know how to properly categorize delay, quantify delay by category, and determine the appropriate cost factors. In addition, most studies of this kind only account for delay against schedule, but ignore the fact that airlines routinely build buffer into schedule, in order to enhance their on- time performance record and preserve operational integrity. On the other hand, the cost impact of schedule buffer is more difficult than delay against schedule for airline managers to directly observe or account for.
We take an alternative approach based upon developing airline cost functions. The cost function approach investigates the statistical relationship between airline cost and its various influencing factors. The formulation is built upon production theory in economics. The cost function is derived assuming that each airline minimizes its cost of producing a certain output, given the costs of its input factors for production such as labor and fuel, as well as other factors that influence its production process. One factor among the latter can be delay. The statistical cost estimation approach provides an empirical basis for translating delay into monetary terms, which, unlike the cost factor approach, involves a minimum of assumptions about the delay– cost interaction mechanisms.
3.1.1 Cost Model Set- up
The cost function of a firm is defined as the lowest cost at which it can produce a given amount of outputitY, provided the input prices itW  it faces: ),( ititWYfC  =. Subscript i denotes a particular firm ( airline), and t identifies the time period. A typical output measure can be airlines’ revenue ton- miles. Inputs include labor, fuel, capital, and materials. The functional form represents the cost of acquiring the optimal set of inputs, given the output and input prices ( Hansen et al, 2001). In reality, however, capital inputs cannot be adjusted to the optimal level instantaneously ( Caves et al., 1984; Gillen et al., 1990). We therefore relax the assumption of optimal capital stock by treating capital input, denoted by S, as quasi- fixed and employing a variable cost function to reflect the short- run cost minimization process. The airline variable cost function can then be written as a function of its outputitY, the price of the three variable inputs ( fuel, labor, and materials) itW  , and capital inputitS, i. e. ),,( ititititSWYfVC  =.
In the airline cost literature, it has long been recognized that costs depend on the nature and quality of airlines’ output as well as the quantity. Because the nature and quality of output also vary over time and across carriers, the specification of the airline cost function above needs to take these into account. A set of additional variables itZ  describing the nature of the output are introduced. Variables of this kind that often appear in literature include a measure of the size of the airline’s network ( often measured as the number of points served) and the average flight distance ( stage length). We hypothesize that airlines’ operational performance also affects cost, and add a new variable ( or vector of variables) itN. The cost function then becomes),,,,( ititititititNSZWYfVC   =. As we will see in the ensuing sub- sections, we estimated two versions of this model with different characterizations of operational performance. 18
3.1.2 Delay- based Model
The first version of the airline cost model employs the concepts of delay against schedule ( FDS) and schedule buffer ( SB) explained in Section 2.1. As discussed in Section 2.1, delay against schedule and schedule buffer are both manifestations of limitations in the NAS that prevent airlines from adhering to schedules built on unimpeded flight times, although the former is more readily observable than the latter. Both delay against schedule and schedule buffer need to be considered in order to assess the full cost impact of delay in the NAS. Exclusion of the schedule buffer could result in an underestimate of the true cost impact.
To measure delay against schedule, we use average positive arrival delay, a widely accepted metric. The positive delay against schedule for a given flight is the difference between its actual and scheduled gate arrival times, truncated so that delays of early flights are counted as zero. The quantification of schedule buffer is less straightforward, because less attention has been paid to this phenomenon and no consensus has been achieved on its measurement. In this study two schedule buffer metrics are developed and investigated. The two metrics differ from each other in terms of defining the unimpeded flight time. For each flight segment and quarter, the unimpeded flight times under the two metrics are the 10th and 20th percentiles of the observed block time over all flights. Not choosing the minimum travel time makes the calculation more robust to measurement error, and reduces the influence of unusually favorable conditions, such as strong tailwinds. Then for each flight, the schedule buffer is defined as the difference between its scheduled block time and the unimpeded flight time. The average schedule buffer is obtained by averaging the schedule buffer across all flights for each airline and quarter.
The models presented here use the sum of the average positive arrival delay and the average schedule buffer as the measure of operational performance. We also estimated models in which these variables were included individually, but results suggested that the single combined measure was adequate.
Delay against schedule and schedule buffer are constructed using the Bureau of Transportation Statistics ( BTS) Airline On- Time Performance database. The database contains scheduled and actual arrival and departure times, as well as wheels- off and wheels- on times, for every domestic flight operated by major carriers that account for at least one percent of domestic scheduled passenger revenues in the US. The airline- quarter panel consists of nine US major airlines ( American, Alaska, Continental, Delta, American West, Northwestern, United, US Airways, and Southwest) spanning from the first quarter of 1995 to the fourth quarter of 2007. These nine airlines provide the majority of passenger transportation service in the U. S. airline industry, and are particularly dominant at airports with high delays. As a consequence, we expect that these airlines will absorb the majority of the increased costs resulting from delay.
For other variables in the cost model, data are extracted from the airline balance sheet, traffic, and expenditure information published in the BTS Form 41 database. We focus on domestic data, since airline on- time performance records are only for domestic flights. In our study, the selected airlines are all passenger service focused, with only a small portion of their traffic undertaking cargo, mail, and other types of business. For this reason we use total revenue- ton- miles ( RTM) to represent the aggregate output. Fuel and labor input prices are calculated using fuel expense per gallon and labor expense per employee per quarter. To account for the difference brought by full- and part- time employees, we use a weighted sum of employment based on the hours paid to employees. As a proxy for materials price, we choose the producer price index ( PPI), which varies by quarter but not by airline. Index data are collected from the US Bureau of Labor Statistics. Capital input is obtained by multiplying the capital stock with the utilization rate, for which load factor is used as a proxy. Our measure of capital stock consists of the asset values plus investment for each airline- quarter. Four types of assets are included: flight equipment, ground 19
property and equipment, capital leases, and land. Among the variables in vectoritZ  , we divide the total distance flown by the total number of departures performed to obtain the average stage length. The number of points served is extracted from the BTS Airline On- Time Performance database. Table 3- 1 presents the summary statistics of the variables in the sample. Overall, our data set is larger than the ones used in many previous airline cost studies, and thus provides richer information and greater variation of relevant variables, contributing to better estimates of the cost functions.
Table 3- 1: Descriptive statistics of key variables
Mean
Std. Dev.
Min.
Max.
Revenue- ton- miles ( million)
1266.5
662.5
176.6
2541.9
Fuel price ($/ gallon)
0.94
0.52
0.36
2.68
Labor price ($/ employee)
17800.7
4111.1
8688.8
30729.4
Materials price ( PPI)
147.9
22.3
109.3
187.9
Capital stock ( million $)
11314.7
8524.8
589.4
29127.7
Load factor (%)
72.0
5.7
55.3
87.4
Stage length ( miles)
815.9
187.2
396.5
1167.9
Number of points served
80.4
26.0
34.0
130.0
Variable cost ( million $)
1548.3
864.3
183.2
3513.6
Delay against schedule ( min)
12.2
3.2
5.5
28.8
Delay against 10th percentile feasible flight time ( min)
25.4
4.2
14.8
39.9
Delay against 20th percentile feasible flight time ( min)
22.2
3.8
13.1
36.7
We choose a translog model as the specific cost functional form for estimation. A translog cost model is in general an extension of the classic Cobb- Douglas cost model form, by introducing quadratic and interaction terms. 2 Compared to the Cobb- Douglas cost model, a translog model adds more flexibility and does not assume constant elasticities. In our study, we keep the delay variable in level form instead of taking its log value. This allows delay to be reduced to zero in the cost impact analysis. All continuous variables are normalized by removing their sample means. Therefore, the translog model can be regarded as a second- order Taylor expansion of a general function about the mean values of the data. The model also includes a time trend variable to capture the evolution of productivity over time, 3
2 For illustration purpose, suppose cost C is only a function of output Y and one input W, i. e. C= f ( Y, W). A Cobb- Douglas cost function has the form: logC= â0+ â1logY+ â2logW. â0+ â1logY+ â2logW. In a general translog cost set- up, logC= â0+ â1logY+ â2logW+ â11â0+ â1logY+ â2logW+ â11( logY) 2+ â22â22( logW) 2+ 0.5 â12â12( logY)( logW). and a set of airline fixed effects to account for
3 A time trend variable takes the value 1 in the first quarter in the dataset, and 2 in the second quarter, etc. 20
systematic differences between carriers in efficiency and other factors that influence cost but not captured by the included variables.
The translog cost function is jointly estimated with cost share functions and additional constraints, in order to conform to the underlying economic theory ( e. g. Shephard’s Lemma and homogeneity of input prices) and increase estimation efficiency. The seemingly unrelated regression ( SUR) technique is used to account for the contemporaneous correlation across equations. For further details regarding the estimation process, please refer to Caves et al. ( 1984), Gillen et al. ( 1990), and Oum and Yu ( 1998). Estimation results appear in Table 3- 2. We have two versions of translog cost models, which differ only with regard to the two delay variables constructed. To conserve space, only coefficients for first order variables are reported here. Coefficients for dummies and higher order variables are provided in the technical support document.
Table 3- 2: Estimation results of delay- based Translog cost functions
Model 1
Model 2
Est.
Std. Err.
Est.
Std. Err.
Output ( RTM)
0.4798***
0.0339
0.4743***
0.0342
Fuel price
0.2011***
0.0016
0.2009***
0.0016
Labor price
0.3861***
0.0022
0.3859***
0.0022
Materials price
0.4128***
0.0032
0.4132***
0.0032
Capital service
- 0.0542***
0.0009
- 0.0541***
0.0009
Stage length
- 0.1749**
0.0775
- 0.1571**
0.0776
Points served
0.6596***
0.0556
0.6658***
0.0558
Delay against 10th percentile feasible flight time
0.0065***
0.0014
Delay against 20th percentile feasible flight time
0.0061***
0.0015
R2
0.9900
0.9899
Adjusted R2
0.9889
0.9888
Notes: *** p< 0.01, ** p< 0.05, * p< 0.1
The first- order coefficients in Table 3- 2 suggest the sensitivity of cost to changes in relevant variables, at the sample mean. The first- order coefficients for input prices indicate that at the sample mean, fuel and labor inputs account for about 20% and 38%, respectively, in the total variable cost. This leaves the materials input to account for 41% of the total variable cost. The first- order coefficient for capital input is negative, implying a positive shadow value of capital input. The coefficient for average stage length indicates that a 1 percent increase in average stage length, output held constant, causes a decrease in variable cost of about 0.16~ 0.17 percent. This should be interpreted as the effect on cost of flying fewer passengers over a longer distance each 21
to obtain the same level of output. The coefficients for points served, about 0.66, suggest a 1 percent increase in network size leads to an increase in total variable cost of 0.66 percent. Of particular interest to this study are the delay variables, the estimates of which support our hypothesis that excessive flight time affects airline cost. The coefficient estimates are significant and rather consistent between these two models. The coefficients suggest that, at the sample mean, one minute increase in delay would cause around 0.6% increase in variable cost. The first order effect is, by construction, non- linear, since each additional minute of delay has the same percentage impact on cost. As discussed below, the quadratic delay term is insignificant, suggesting that the first order relationship is a reasonable approximation of the overall one.
Overall, the two models have very high goodness- of- fit ( as indicated by their R2’ s which are close to 1). In order to be consistent with the economic theory, the curvature conditions are further checked. The curvature conditions are derived by requiring the concavity of a cost function in its input prices, which is expected as a result of adjusting inputs quantities to their prices in the production process. Our results show that, about 67.6 percent of the data points in the sample satisfy the curvature conditions, which compares favorably to the other airline cost studies in which such a statistic is reported.
Before proceeding to delay cost estimation, we notice that the coefficients for some higher order terms involving the delay variable are not significant in the above two models. Keeping these variables in the model will certainly jeopardize the robustness of our subsequent cost estimates. As a consequence we removed insignificant delay terms ( in our models these are delay* delay and delay* stage length) and re- estimated the two models. The estimates for the remaining coefficients are almost unchanged. The percentage of data points satisfying curvature conditions is slightly higher ( 68.3 percent). Moreover, all the terms involving the delay variable now have coefficients that are statistically significant. Table 3- 3 documents the first- order coefficient estimates for these new models.
22
Table 3- 3: Estimation results of delay- based Translog cost functions with insignificant delay terms removed
Model 3
Model 4
Est.
Std. Err.
Est.
Std. Err.
Output ( RTM)
0.4840***
0.0339
0.4793***
0.0342
Fuel price
0.2012***
0.0016
0.2010***
0.0016
Labor price
0.3861***
0.0022
0.3859***
0.0022
Materials price
0.4127***
0.0032
0.4131***
0.0032
Capital service
- 0.0542***
0.0009
- 0.0541***
0.0009
Stage length
- 0.1753**
0.0771
- 0.1603**
0.0771
Points served
0.6628***
0.0558
0.6672***
0.0559
Delay against 10th percentile feasible flight time
0.0061***
0.0013
Delay against 20th percentile feasible flight time
0.0058***
0.0013
R2
0.9899
0.9898
Adjusted R2
0.9888
0.9887
Notes: *** p< 0.01, ** p< 0.05, * p< 0.1
3.1.3 Time- based Model
In this section, we consider a model with an alternative set of operational performance variables, itN  , that characterize the relationship between the times when a given flight is scheduled to be, and actually is, active. Three new time measures are introduced: total absorbed time, scheduled time, and actual flight time. The total absorbed time ( TAT) of a flight is defined as the time interval between the earlier of scheduled and actual departure times, and the later of the scheduled and actual arrival times. Scheduled time ( S) is a subset of TAT, defined as the time between the scheduled departure and scheduled arrival. Actual flight time ( A) denotes the time from the actual departure to the actual arrival; it is thus also a subset of TAT.
Using these three measures, the TAT for any flight can be categorized into the following subsets: scheduled- active time ( S∩ A), scheduled- non- active time ( S∩~ A), active- non- scheduled time (~ S∩ A) time, and non- scheduled- non- active time (~ S∩~ A). S∩ A denotes the time falling into both the scheduled flight time and actual flight time intervals. S∩~ A is the time within the scheduled flight time but outside the actual flight time. It can be caused by either late departures or early arrivals. ~ S∩ A represents the converse, which results from early departures and late arrivals. In the ( rare) events of extremely early or late departures, time between the actual arrival and scheduled departure, or between the scheduled arrival and actual departure, is ~ S∩~ A. Theoretically there are six possible situations, as illustrated in Figure 3- 1. For each situation, the solid and dashed arrow lines represent the scheduled and actual flight time respectively. For example, if the scheduled departure time of a flight is 7: 00am and it actually left the gate at 23
7: 30am, then | S∩~ A| = 30 min. At the arrival end, the scheduled arrival time is 9: 00am but the flight pulled up to the gate at 9: 20am. In this case |~ S∩ A| is just the arrival delay, equal to 20min. The time between the actual departure and the scheduled arrival is S∩ A, amounting to 90min. This corresponds to the top- left situation, i. e. late- departure- late- arrival. The other five situations can be described as: early- departure- early- arrival ( top right), late- departure- early- arrival ( middle left), early- departure- late- arrival ( middle right), extremely- late- departure ( bottom left), and extremely- early- departure ( bottom right). Note that, however, it is quite rare for the last two situations to take place.
Based on the above time categorization, we employ three new operational performance variables: the duration of TAT, denoted Ttot, the fraction of this time in S∩~ A ( i. e. | S∩~ A|/ Ttot), which we denote PS~ A, and the fraction that is in ~ S∩ A ( i. e. |~ S∩ A|/ Ttot), denoted P~ SA. These variables replace the delay variable that was used in the delay- based model. Ttot measures the total amount of time the aircraft and crews of an airline are dedicated, in either plan or execution, to performing flights. The other two variables quantify the deviations between realized and scheduled flight activity. Ttot is integral to airline production and we therefore keep this variable in logarithmic form. The other two variables are included in level form since they can, in principle, be eliminated under ideal operating conditions.
Figure 3- 1: Identification of time components in the six possible situations
Table 3- 4 provides the coefficient estimates for the first- order terms ( Model 5). Comparing with Models 1- 4, the factor price coefficients remain largely unchanged. The RTM coefficient is substantially lower, due to the inclusion of the total relevant time variable. Stage length is no longer significant and has a seemingly counter- intuitive sign, its effect captured by the total absorbed time variable, since longer average stage length allows the same output to be produced with less flight time.
S∩~ A S∩ A ~ S∩ A S∩~ A S∩~ A S∩~ A S∩~ A S∩~ A S∩ A S∩ A S∩ A ~ S∩ A ~ S∩ A ~ S∩ A ~ S∩ A ~ S∩ A ~ S∩~ A ~ S∩~ A 24
Turning to the operational performance variables, the coefficient for Ttot has the expected positive coefficient and is highly significant. The P~ SA variable has a significantly positive coefficient, suggesting everything else held equal, flight activity outside the schedule window results in additional cost. The PS~ A variable does not seem to have a significant impact on cost. This suggests that flight inactivity during the schedule window— either because of departing late or arriving early— does not significantly reduce costs.
Similar to the previous cost models, the time- based model also has very high goodness- of- fit. Checking the curvature condition reveals that an even higher 77.6 percent of the data points satisfy the concavity requirement using this model. To make the subsequent cost estimate more robust, we check with the higher- order time variable terms in Model 5. We find that the majority of such terms not involving input prices are statistically insignificant. 4
Considering that these variables are not subject to homogeneity restrictions, we re- estimate a simplified version of Model 5. In the simplified model ( Model 6), higher- order time variables not involving input prices are dropped out. Estimation results are reported in the 3rd and 4th columns of Table 3- 4. The sign and significance of the first- order coefficients are largely unchanged, as does the percentage of data points satisfying the curvature conditions. The coefficient for PS~ A remains insignificant and is now much smaller. The P~ SA coefficient is also somewhat smaller ( but still significant), apparently as a result of absorbing the effect of higher- order terms in the original model.
Table 3- 4: Estimation results of time- based Translog cost functions
Model 5
Model 6
Est.
Std. Err.
Est.
Std. Err.
Output ( RTM)
0.2102***
0.0561
0.2424***
0.0531
Fuel price
0.1997***
0.0016
0.1995***
0.0016
Labor price
0.3860***
0.0021
0.3858***
0.0021
Materials price
0.4143***
0.0031
0.4147***
0.0031
Capital service
- 0.0537***
0.0009
- 0.0536***
0.0009
Stage length
0.0918
0.0880
0.0979
0.0783
Points served
0.5111***
0.0718
0.4901***
0.0590
Ttot
0.4368***
0.0725
0.4424***
0.0687
PS~ A
- 0.4211
0.5167
- 0.0492
0.4383
P~ SA
1.0875***
0.3740
0.7111**
0.3201
R2
0.9901
0.9896
Adjusted R2
0.9885
0.9884
Notes: *** p< 0.01, ** p< 0.05, * p< 0.1
4 Only one among the 15 such variables has a coefficient estimate that is significant at 5% level. 25
3.1.4 Cost Impact of Delay and Buffer on Airlines
In this sub- section, the previously estimated cost models are used to gauge the potential cost impact of delay and buffer on airlines, assuming these estimated models still apply to the improved operational scenarios described below. We choose the more robust Models 3, 4, and 6. Using Models 3 and 4, two scenarios are considered. In the first scenario delay against schedule is entirely eliminated, without changing the buffer, and in the second one we further reduce schedule buffer to the zero level. The new operating costs for each airline- quarter are predicted under the two scenarios, and compared to predicted costs at 2007 values for delay and schedule buffer. The difference between these new operating costs and baseline predicted values gives the cost of delay against schedule and the total cost of delay respectively. The difference between the cost of delay against schedule and the total cost of delay corresponds to the schedule buffer cost. Estimates for these costs for 2007 appear in the first three rows of Table 3- 5.
We also use Model 6 to investigate the airline cost under two scenarios. In the first, Ttot is set to be the sum of SchAct and SchNonAct time over all flights, and the values P~ SA and PS~ A are reduced to zero. Under this scenario, aircraft’s departure and arrival times exactly coincide with the current schedule, which contains some schedule buffer. In the second scenario, we also reduce Ttot to the unimpeded flight time, the calculation of which is described in section 3.1.2. Therefore, under this scenario all flights fly not only strictly following the schedule, but also take an optimal, unimpeded amount of time. As before, airline costs are predicted under these two scenarios, and compared to cost predictions using 2007 operational performance levels. We consider the difference between the original cost and the cost in the first scenario as the cost of delay against schedule, and the difference between the original cost and the cost of the second scenario as the total cost of delay. Their difference is the cost of schedule buffer. Estimates are reported in Table 3- 5. We obtain somewhat larger estimates of delay- against- schedule and total cost from using the time- based model than from using the delay- based model. This may be because the counterfactual considered for the time- based model entails perfect adherence to both arrival and departure time schedules, whereas the delay- based model only considers arrivals. In any case, the similar magnitude of the cost estimates obtained from the two models provides some cross- validation of the basic approach. Also buffer cost estimates from the two models are very similar—$ 2- 2.5 billion for the seven major airlines.
As a first- order industry- wide estimate, we extrapolate the above cost to the entire system based on the portion of available seat miles ( ASM) provided by the major airlines in all carriers reporting data to BTS. Results are also reported in Table 3- 5. Although this leaves out some regional and commuter airlines ( those whose annual operating revenue is below $ 20 million), such airlines account for a very small fraction of the total ASM, so excluding them will have little effect on the system- wide result.
In our cost summary, we have elected to emphasize estimates derived from the delay- based model. This model features a simpler and more conventional representation of operational performance, has a slightly higher R2, and has lower standard errors for the relevant coefficients. The higher estimate derived from the time- based model is also quite plausible however, making the choice largely as matter of judgment.
26
Table 3- 5: Airline cost estimates ($ billions), for 2007
Cost category
Delay against 10 percentile feasible flight time
Delay against 20 percentile feasible flight time
7 major airlines*
Delay- based model
Delay against schedule
3.3
3.1
Buffer
2.6
1.9
Total
5.9
5.0
Time- based model
Delay against schedule
6.7
6.7
Buffer
2.4
1.8
Total
9.1
8.5
Industry wide**
Delay- based model
Delay against schedule
4.6
4.4
Buffer
3.7
2.7
Total
8.3
7.1
Time- based model
Delay against schedule
9.4
9.4
Buffer
3.4
2.7
Total
12.8
12.1
* US Airways and American West are excluded due to merger.
** Includes airlines with annual operating revenue greater than $ 20 million.
As a final remark, we reiterate that a delay- free NAS is a limiting— and unreachable— case. As long as there are winds and storms, aircraft parts fail, and people make mistakes, there will be delays. As long as there are delays, airlines will seek to mitigate their impacts through schedule buffer. As a consequence, the cost estimates presented here— and elsewhere in this report-- should be regarded as an upper bound on the cost savings that could be obtained from improving the capacity and operational efficiency of the NAS at 2007 activity levels.
3.2 Passenger Delay Cost
The primary mission of the national air transportation system is the rapid, affordable, and safe transportation of passengers and cargo between geographically distant and/ or remote destinations. Flight delay impairs this mission by increasing passenger trip times and reducing schedule reliability. In this section, we estimate the resulting costs to passengers in 2007. Most of the effort went to estimating passenger arrival delay against the ticketed schedule, which we term Passenger Trip Delay. We also consider the additional passenger travel time resulting from schedule padding. The final step was to monetize these passenger time costs. Section 3.2.1 describes ways in which passenger trip delays can occur. Section 3.2.2 provides an overview of the algorithm used to compute the passenger trip delay metrics and identifies the associated data sources. Section 3.2.3 briefly describes the workings of the algorithm and identifies some of the methodological contributions made by this study. Section 3.2.4 provides the results generated by 27
using publicly available data sources and our algorithm to compute passenger trip delay performance for 2007. Section 3.2.5 presents estimates of additional passenger travel time from schedule padding, while Section 3.2.6 estimates the monetary value of the passenger delays computed in the previous sections.
3.2.1 Passenger Trip Delay Causes
Passenger Trip Delay is defined as the positive difference between the actual time of arrival of the passenger and the scheduled time of arrival on the ticket purchased by the passenger. It is analogous to flight delay against schedule; we consider the effect of schedule buffer on passenger delay cost later on.
Passenger Trip Delay = max ( Actual Time of Arrival – Scheduled Time of Arrival, 0)
Passenger Trip Delay can occur as a result of one of the following scenarios:
1. Passenger arrives late on the last ticketed flight of an itinerary.
2. Passenger arrives late because a ticketed flight was diverted to another airport.
3. Passenger arrives late after being re- booked on a later itinerary when a ticketed flight is cancelled.
4. Passenger arrives late when the passenger misses a connection and is re- booked on a later itinerary.
Scenarios 1, 2, and 3 are illustrated in the Time- Space diagrams in the Figure 3- 2. Scenario 4 is illustrated in Figure 3- 3, in which the term “ hub” refers to airports where a connection is made.
The trip delays experienced by passengers on late flights and on diverted flights ( Scenarios 1 & 2) are proportional to the magnitude of the delay of these flights. The trip delays experienced by passengers that have to be rebooked due to a cancelled flight or missed connection ( Scenarios 3 & 4) are a function of the frequency and load factors ( i. e. the percentage of seats filled) on other flights to the desired destination. As the frequency of the flights diminishes and/ or the load factor of candidate rebooked flights increases, the trip delay experienced by these passengers typically increases non- linearly – and at a very high rates when load factors are high and/ or the frequency of flights is low. 28
Figure 3- 2: Time- space diagram for Scenarios 1- 3
Total Pax Delay1 refers to the total passenger delay experienced by the passengers on Flight 1. 29
Figure 3- 3: Time- space diagram for Scenario 4
3.2.2 Overview of Algorithm and Data Sources
Figure 3- 4 provides an overview of the computation of Passenger Trip Delay for each of the scenarios described in Section 3.2.1. The algorithm is based on the work of Bratu and Barnhart ( 2005), Wang and Sherry ( 2007), Sherry and Calderon- Mesa ( 2008), and Zhu ( 2009) at MIT and GMU. This body of work has been extensively refined and enhanced in research performed specifically for this study.
The algorithm is summarized in Figure 3- 4 below, which also indicates at its top part the three sets of data that are required. These are:
1) Airline Flight Performance Data
Airline flight performance information is required to determine flight delays for each individual flight, as well as diversions and cancellations of individual flights. This information is derived from the BTS Airline On- Time Performance database, which is reported by US certified air carriers that account for at least one percent of domestic scheduled passenger revenues.
2) Aircraft Seat Capacity and Load Factor Data
Aircraft seat capacity and load factors for each flight are required by the algorithm for rebooking passengers on cancelled flights and/ or missed connections. This data is derived from the BTS T- 100 data- base.
The scenario for passengers who miss connections: inbound flight is delayed, connecting flight is cancelled, or inbound flight is cancelled. 30
Figure 3- 4: Overview of the algorithm
3) Passenger Itinerary and Flight Load Factors
Passenger Itineraries are estimated using aggregated, average monthly load factors from the BTS T- 100 data- base. The algorithm for estimating passenger itineraries and load factors is described in section 3.2.3 below.
The specific databases used to provide the 2007 estimates reported in Section 3.2.4 are:
• T- 100 Domestic Segments Data ( U. S. Carriers) – domestic segment data aggregated by month
• DB1B Coupons Data – a 10% sample of domestic itinerary data aggregated by quarter
• Flight On- Time Performance Data ( ASQP) – daily on- time arrival data for domestic flights operated by major U. S. carriers
• Innovata Flight Offerings Data – expected flight offerings for 2007 as of January 1st, 2007
• Proprietary Passenger Bookings Data – proprietary legacy carrier bookings data for Q4 2007 ( used for the purpose of validating the proposed approach)
• Other Data – FAA Aircraft Registry, which includes seating capacities by carrier and aircraft type
Data- sources and Algorithm used to compute Passenger Trip Delays.
For each flightFlight CancelledFlight DivertedPassengers Denied BoardingCycle through next single- segment flights and connecting flightsfor same O/ D pair re- booking passengers, until all passengers re- booked. Max 15 hour delay. Estimate additional delays for Diverted PassengersFlight DelayedCompute PaxDelay based on LF and Flight DelayPaxTrip DelayCompute PaxDelay based on Scheduled arrival TimeCompute PaxDelay based on Scheduled Arrival TimeYNPassengers with Missed ConnectionsFlight Performance DataPassenger Itinerary DataLoad Factor DataFor Data 31
3.2.3 Description of Algorithm
This section provides a brief description of the algorithm utilized to calculate passenger delays. A more detailed description can be found in a technical support document for the passenger delay calculation algorithm. The algorithm proceeds in three steps:
1. Generation of potential passenger itineraries.
2. Estimation of passenger demand allocation to each potential itinerary.
3. Determination and rebooking of disrupted passenger itineraries.
In the first step, we generate all potential itineraries that passengers may take based on the flight schedule data in ASQP and the sampled passenger itinerary data in the DB1B Coupon database. For the purposes of our analysis, we only include non- stop and one stop itineraries, as itineraries with more than one stop account for only 2.5% of the one- way trips in DB1B. A non- stop itinerary is generated for every flight in ASQP, whereas a one- stop itinerary is generated only for valid flight pairs. Using the 2007 ASQP and DB1B data sets, this procedure leads to the generation of some 270 million itineraries, of which about 7.5 million are non- stop.
In the second step, we utilize a statistical approach to estimate the passenger demand associated with each of the potential itineraries. To do so, we use one quarter of proprietary booking data from a large legacy carrier to estimate the passenger utility associated with itinerary features such as local time of departure, day of week, and connection time. Next, we use these estimated utilities to calculate the probability that each itinerary would be selected. Finally, we use the estimated probabilities to sample an itinerary that matches each passenger’s route. We determine the number of monthly passengers traveling on each route by combining the passenger demand data available in T- 100 and DB1B databases. The results of these three steps can then be fed into the Passenger Trip Delay Algorithm of GMU ( or alternatively the Passenger Delay Calculator of MIT) to estimate total passenger delays.
Computing these estimates of passenger bookings is necessary in order to estimate the passenger delays due to missed connections and to refine the estimates of delays due to cancellations and diversions. Historical information on passenger bookings is considered proprietary and highly sensitive by the airlines. Absent such proprietary data, a good estimate of bookings based on approaches that utilize published data is the best that can be realistically achieved. The approach described above estimates two intermediate sets of data that are then utilized to estimate passenger delays: ( a) load factors and aircraft size for all scheduled flights on a day- of- week and time- of- day basis, and ( b) itineraries for all passengers including connections at transfer airports.
In the last step, the algorithm processes each individual flight, starting with the first flight in the period under investigation and terminating with the last flight of the period. If the flight was cancelled or diverted, all the corresponding passengers are rebooked to their final destinations. For the purpose of our analysis, we treat diversions as cancellations, because the ASQP database does not provide the destination of the diversion. Diversions represent approximately 0.2% of total flights, so we do not expect their treatment in this approximate manner to significantly impact the results. Passengers that miss connections are treated in the same manner as passengers on cancelled flights and are rebooked from the connecting airport to their final destination. The generation of estimates of delays due to missed connections had not been possible until this study due to the unavailability ( in the public domain) of passenger itinerary data. In today’s air transportation system, missed connections are a very important cause of passenger delays.
The results described in this report include both re- booking on direct ( i. e. single segment) flights, as well as connecting ( i. e. two segment) flights. Because all flight options are not available in the ASQP database ( e. g., non- reporting carriers) and to ensure that our overall estimates are conservative, we limit the amount of rebooking- incurred delay. For passengers disrupted during 32
the day ( e. g., between 5: 00am and 5: 00pm) we limit the rebooking delay to a maximum of 8 hours, whereas for passengers disrupted during the evening ( e. g., between 5: 00pm and 5: 00am), we limit the rebooking delay to 16 hours. Thus, if passengers cannot be rebooked to their final destination, we assume their trip delay equals the maximum allowed in their case ( i. e. either 8 hours or 16 hours). Prior to assigning to a passenger the maximum rebooking delay, we also attempt to rebook the passenger on carriers other than the ticketed carrier or its subcontracted carriers.
Finally, delay for passengers whose itineraries are not disrupted is computed based on the publicly available data reporting flight delays for all scheduled commercial flights in the US.
3.2.4 Results for 2007
This section provides estimates of Passenger Trip Delay for January – December 2007. The analysis is based on data provided by BTS for the airlines with more than 1% of enplanements per annum and the MIT algorithm for estimated passenger itineraries and flight load factor.
In 2007, 7.45 million flights provided transportation for 487.2 million passengers on 4437 direct routes between 267 airports. The average number of flights between O/ D pairs in 2007 was 4.57. The total estimated delay accrued by passengers due to delayed flights, cancelled flights, and missed connections was 28,539 years. The monthly differences, as reported in Tables 3- 7 and 3- 8, are due to seasonal weather and traffic factors. Despite these influences, results are fairly consistent throughout the year. The average delay experienced, computed for all the passengers in 2007, was 31 minutes per passenger.
Table 3- 6: Passenger delay estimates for calendar year 2007
2007
Number of Flights Operated
7,455,458
Number of Passengers Boarded
487,197,014
Percentage of Flights Delayed 15+ Minutes
24.2%
Percentage of Flights Cancelled
2.2%
Average Delay for Operated Flights
15.0
Average Delay for all Passengers
30.8
Number of Disrupted Passengers
16,419,439
Percentage of Passengers Disrupted
3.4%
- Disrupted due to Cancellations
69.7%
- Disrupted due to Missed Connections
30.3%
Average Delay for Non- disrupted Passengers
15.9
Average Delay of Disrupted Passengers
456.9
- Due to cancellations
68.5%
- Due to missed connections
31.5%
33
Table 3- 7: Monthly passenger delay estimates for the 1st and 2nd calendar quarters of 2007
January
February
March
April
May
June
Number of Flights Operated
621,559
565,604
639,209
614,648
631,609
629,280
Number of Passengers Boarded
36,351,929
34,397,205
42,640,307
41,407,749
42,679,424
43,924,679
Percentage of Flights Delayed 15+ Minutes
24.2%
28.0%
23.9%
22.3%
20.8%
28.8%
Percentage of Flights Cancelled
2.5%
4.5%
2.6%
1.8%
1.1%
2.7%
Average Delay for Operated Flights
14.1
17.2
14.9
13.5
12.3
19.6
Average Delay for all Passengers
28.4
43.0
34.6
27.3
22.6
43.0
Number of Disrupted Passengers
1,318,378
1,948,863
1,675,589
1,201,043
946,770
1,931,463
Percentage of Passengers Disrupted
3.6%
5.7%
3.9%
2.9%
2.2%
4.4%
- Disrupted due to Cancellations
72.5%
79.1%
74.9%
69.1%
62.5%
70.8%
- Disrupted due to Missed Connections
27.5%
20.9%
25.1%
30.9%
37.5%
29.2%
Average Delay for Non- disrupted Passengers
14.3
18.0
15.8
14.6
13.1
21.6
Average Delay of Disrupted Passengers
402.9
459.3
493.8
453.5
439.6
508.5
- Due to cancellations
70.7%
79.6%
75.9%
68.1%
59.5%
70.2%
- Due to missed connections
29.3%
20.4%
24.1%
31.9%
40.5%
29.8%
34
Table 3- 8: Monthly passenger delay estimates for the 3rd and 4th calendar quarters of 2007
July
August
September
October
November
December
Number of Flights Operated
648,560
653,279
600,187
629,992
605,149
616,382
Number of Passengers Boarded
45,613,812
44,915,170
37,400,161
40,784,536
39,087,925
37,994,117
Percentage of Flights Delayed 15+ Minutes
27.8%
26.2%
17.1%
20.5%
18.8%
31.9%
Percentage of Flights Cancelled
2.1%
1.9%
1.1%
1.2%
1.0%
3.5%
Average Delay for Operated Flights
18.1
16.8
10.1
12.0
10.9
19.8
Average Delay for all Passengers
37.0
33.6
18.5
21.1
18.6
41.0
Number of Disrupted Passengers
1,664,301
1,501,007
777,976
868,813
750,117
1,835,119
Percentage of Passengers Disrupted
3.6%
3.3%
2.1%
2.1%
1.9%
4.8%
- Disrupted due to Cancellations
67.2%
66.0%
63.4%
60.5%
60.8%
71.7%
- Disrupted due to Missed Connections
32.8%
34.0%
36.6%
39.5%
39.2%
28.3%
Average Delay for Non- disrupted Passengers
19.8
18.2
10.6
12.8
11.4
20.2
Average Delay of Disrupted Passengers
491.8
478.1
391.7
402
387.2
449.4
- Due to cancellations
65.5%
64.5%
57.1%
55.1%
55.8%
71.3%
- Due to missed connections
34.5%
35.5%
42.9%
44.9%
44.2%
28.7% 35
3.2.5 Passenger Buffer
We employ an aggregate approach to quantify passenger buffer. As discussed in section 3.1, airlines routinely build buffer into flight schedules. Once a flight is flown, each passenger on that flight will have to bear this extra amount of time. In order to be consistent with the airline cost model, we employ the same “ Avg. buffer10” measure. The same airline- quarter data as in section 3.1 are used. For each airline- quarter observation, the average buffer time per flight is multiplied by the average number of seats per flight and the load factor, and then by the total number of flights flown. Values are summed up across all airlines and quarters. For 2007 the total passenger buffer amounts to 9,526 million minutes, or an equivalent 159 million hours.
3.2.6 Monetary Value of Passenger Delays
There exist numerous studies about how travelers value their time during the trip. One way to obtain the value of travel time is by using wage rates. Economic theories postulate that individuals will adjust the amount of time they devote to work and leisure such that an additional small increment of either may be valued at the wage rate. More sophisticated models recognize that constraints on the ability of workers to alter work schedules or the conditions under which time is devoted to either work or leisure can cause the value people place on an incremental gain or loss of time to deviate, perhaps significantly, from the wage rate ( GRA, 2004, Small, 1992). Alternative approaches have been adopted to infer passenger value of travel time. One intensively utilized method is based upon random utility theory and mode/ itinerary choice models, where most popular are the multinomial logit model and its variants. A few studies explicitly investigate how passengers value air travel delays, prominent among which are Adler et al. ( 2005) and Forbes ( 2008).
The Department of Transportation provides recommended values of travel time in their departmental guidance ( DOT, 2003). The values are based on a survey conducted by the Air Transportation Association in 1998 and updated it with changes in median annual income from 1998 to 2000. Certain percentage rates are factored in to generate the value of time for different travel purposes. The TDI team follows this guidance and uses weighted average across business and leisure travelers, inflated to 2007 U. S. dollars. The number used here is the same as the one adopted in JEC ( 2008), valued at $ 37.6/ hour.
The above value of travel time is then applied to passenger buffer and delay against schedule. The TDI team finds that the total passenger delay cost amounts to $ 15.4 billion, with breakdown detailed in Table 3- 9.
Table 3- 9: Passenger cost estimates ( in $ millions), for 2007
Delay Category
Delay Cost
( million dollars)
1. SB ( schedule buffer)
5,969
2. PDS ( passenger delay against schedule)
2a. Delay due to delayed flights
2b. Delay due to flight cancellations
2c. Delay due to missed connections
Total estimated PDS ( 2a+ 2b+ 2c+ 2d)
4,699
3,221
1,480
9,400
Total
15,369 36
3.3 Estimate of Costs of Voluntary Passenger Schedule Adjustments Due to Anticipated Schedule Delays
3.3.1 Data Sources
In order to measure the extent to which delay and unpredictability cause travelers to leave the night before their scheduled meetings we need information on the timing of their departures. The aim of this piece of the project is to understand how delay and other variables such as cancellations and arrival time influence passengers’ decision of what time to fly. In order to undertake this analysis we require flight- level data describing arrival and departure times.
We focus on simple round trips. We sample itineraries that are contained entirely within the confines of a single work week, which we define as the period from midnight Monday morning through midnight Friday evening.
We categorized the outbound departure window as follows:
• Early ( Midnight to 8am)
• AM Peak ( 8am to 10am)
• Midday ( 10am to 4pm)
• PM Peak ( 4pm to 7pm)
• Evening ( 7pm to Midnight)
Information on the timing of departures cannot be obtained from publicly available data sources. The on- time arrival database maintained by the FAA provides a wealth of information about aircraft arrivals, but no information about the itineraries of the passengers traveling on those aircraft. The OD1A and OD1B databases provide a wealth of information about passenger itineraries, but virtually no information about the timing of passenger travel ( other than the quarter in which the trip took place). In order to carry out an empirical study of the effects of delays on departure timing, therefore, we needed to identify a new source of data.
That source of data turned out to be the Sabre system. Sabre is the oldest and the largest of the original airline computerized reservation systems. 5
Sabre covers a large but not necessarily representative fraction of the total universe of air travel. Missing from Sabre are tickets purchased from other GDS systems, from dedicated airline websites, or from certain new electronic distribution channels such as Priceline. As a result, Sabre tends to under- represent low cost carriers and low cost fares. It tends to over- represent travel booked through travel agencies, and corporate travel. The distinctive footprint of Sabre complicates the task of generalizing results based upon Sabre data. At the same time, however, that distinctive footprint makes Sabre a well- equipped and suitable laboratory for investigating hypotheses about business travel behavior.
Sabre contains data on passenger itineraries as booked. Changes made prior to departure are captured as long as they are made through Sabre, which generally requires that they be made by the travel agency that originally booked the flight. Changes made at the airport or directly through the airline may not be reflected in the Sabre data. Sabre records contain complete information on dates and times of departures and arrivals of all flights within a passenger’s itinerary. The system also captures the carrier, the fare, and
5 These systems are now referred to as Global Distribution Systems, or GDS. 37
the airport endpoints of each flight segments. Sabre retains the full detail on each booking for a period of three years. Confidentiality provisions in Sabre’s agreements with participating airlines restrict the information it is allowed to release to third parties. For the most part, it is prohibited from releasing individual itinerary data. It can however, provide aggregated summaries that contain a considerable amount of detail.
3.3.2 Structural Model Specification
We model choice of departure window as a standard discrete choice problem. We assume that a passenger, having selected an airport pair, seeks to maximize utility across departure windows. We model utility as being a function of the time at which the passenger can expect to arrive at his or her destination and of the delay the passenger can expect to experience.
Let j be an index of departure windows. At a high level, we can characterize the utility associated with choosing departure window j as follows:
Uj = Dj + Aj + Lj + ε ( Equation 3- 1)
where:
Dj is the disutility associated with schedule delay.
Aj is the disutility associated with the arrival time dictated by choosing departure window j.
Lj is the disutility associated with arriving late.
ε is a random variable.
3.3.2.1 Schedule Delay
The more departures there are, the greater the chances are of finding a departure at a convenient time. The schedule density, defined as the number of flights per unit of time, varies over the course of the day. All else equal, a passenger will desire a higher schedule density. However, the value of an additional flight declines as the number of flights increases and the schedule becomes saturated. Thus, a reasonable specification for schedule delay is be given by:
jjNDλ= ( Equation 3- 2)
Where Nj is the number of scheduled departures per minute6
3.3.2.2 Arrival Time Disutility for that route and quarter and λ is an estimated coefficient. For each cell, we record the number of flights found in the On Time Performance dataset.
Travelers will generally prefer to arrive at some point during the business day. We will assume that there is some disutility associated with arriving during each hour interval of the destination day. Call these πi. Let the set of dummy variables dji equal 1 if a departure during window j implies an arrival in hour i, and 0 otherwise. We can calculate dji from Tj, the scheduled flight time, and the time required to exit the airport.
6 It is important to scale Nj by the length of the departure category in order to make the Dj’s comparable across departure categories. This could be accomplished by dividing the number of flights by the number of hours in the departure category; we divide by the number of minutes simply to produce regression coefficients of a magnitude similar to those on our other variables. Because this is a mere scaling, it has no impact on other regression coefficients or on the measured significance of any of our results. 38
We can then express the arrival time disutility as:
Σ= ijiijdAπ ( Equation 3- 3)
where the πi are estimated coefficients.
For each cell, we calculate arrival probabilities for each of seven time windows, measured in local time for the destination airport: the two- hour increments from 6am- 8am, 8am – 10am, 10am – 12pm, 12pm – 2pm, 2pm – 4pm, and 4pm – 6pm, and the six hour increment from 6pm – 12am. These probabilities are calculated from the scheduled arrival times from the On Time Performance dataset for each cell. That is, if, for a given quarter, route and departure window there are 100 flights in the On Time Performance dataset, and 25 of them arrive between 10am and 12pm, then we simply assign a 25% probability of arrival within that time window for that cell; if 27 of them arrive between 12pm and 2pm we assign a 27% probability of arrival within that time window; etc.
3.3.2.3 Late arrival disutility
To account for late arrival disutility we will need to divide the time period around the scheduled arrival time into a series of time intervals. Let k be an index of these intervals. In our analysis, we use:
k = 1 implies early or on- time,
k = 2 implies arrival more than half an hour late
We measure the probability with which a traveler experiences delay by calculating the fraction of flights in each year, quarter, route, and departure category that fall into each delay interval. Define the set of variables gjk to equal the probability of arriving within delay interval k for passengers in departure category j.
The late arrival disutility, then, is then given by:
Σ= kjkkjgLγ ( Equation 3- 4)
where the γk’s are estimated coefficients.
We represent lateness as the probabilities of being late by various amounts, based on the empirical distribution of delay observed in the On Time Performance Dataset. Thus, we calculate the percentage of flights that arrived early and the percentage that arrived more than half an hour late. We employ the four- quarter lag of observed delay, specific to the relevant year, quarter, and O- D pair.
We estimate this model as a standard conditional logit model, in which the probability of selecting a given departure window is a function of its characteristics and those of the other departure windows available to a passenger traveling in a given year, quarter, and origin- destination pair.
3.3.3 Results
We present our econometric results in Table 3- 10.
We observe an appropriately negative sign on the inverse of flights per hour. The pattern of coefficients observed on our arrival time windows suggests that passengers prefer to arrive early in the morning or late in the workday. The coefficients on early and late arrival are measured relative to the implicit 39
coefficient of zero on the excluded category of lateness, from on time arrival to half an hour late. The implication is that passengers experience a small amount of disutility for early arrival ( which can cause them to have to wait for rides or to meet business contacts), and a substantially larger level of disutility for arrival more than half an hour late.
Table 3- 10: Conditional logit regression results
3.3.4 Calculation of VDTA Costs
To calculate the number of passengers who make Voluntary Schedule Time Adjustments made in response to delay we set all delay probabilities to zero and use the results shown in Table 3- 11 to recalculate departure window shares.
Left- Hand Variable is Choice of Departure WindowObservations ( Trips)= 4,258,827 VariableInverse of Flights per Hour- 0.376*** ( 0.002) Arrival 6am- 8am2.044*** ( 0.021) Arrival 8am- 10am2.020*** ( 0.020) Arrival 10am- 12pm1.556*** ( 0.020) Arrival 12pm- 2pm1.455*** ( 0.021) Arrival 2pm- 4pm1.836*** ( 0.020) Arrival 4pm- 6pm2.311*** ( 0.020) Arrival 6pm- 12am0.839*** ( 0.020) Cell- Specific Lateness: Early, Lag 4 qtrs- 0.0641*** ( 0.009) Cell- Specific Lateness: Greater than 30 Minutes Late, Lag 4 qtrs- 0.204*** ( 0.014) Notes: Arrival and Lateness variables are probabilities expressed in decimal terms, i. e. 5% = 0.05. Arrival prior to 6am and lateness between 0 and 30 minutes are excluded. *** p< 0.01, ** p< 0.05, * p< 0.1 40
Table 3- 11: Predicted schedule adjustments between departure windows without delay
We calculate the extent of schedule shifting one departure window at a time. 7
In order to translate these adjustments into hours ( and ultimately, dollars) lost, we must make an assumption concerning the departure window from which these passengers are switching. We assume that they are switching from preceding departure window – e. g., from Early to AMPeak, from AMPeak to Midday, and so on. Thus, we assume that the net change in each departure window under the assumption of no delay is equal to the gross increase for that departure window less the gross increase for the following departure window. For each departure window, we calculate the number of trips predicted in our regression sample with observed delay. We then calculate the number predicted for each departure window if the probability of delay greater than half an hour is set to zero for that departure window only. The difference between these two is the predicted gross increase for the departure window.
The first two columns of Table 3- 11 present the results of this exercise. The second column is the net predicted number of trips in the departure window with no delay. The third column is the predicted gross increase for the departure window. Of course, in each case, with delay set to zero, the gross increase for each departure window is positive. The right- most column of Table 3- 11 expresses the predicted gross increase in demand for each departure window as a percentage of the preceding window ( from which, we continue to assume, the gross increase is pulled).
We next apply these estimates to the universe of passenger air travel represented by the DB1B 10 percent ticket sample. Table 3- 12 presents the total number of passengers represented in this dataset in each quarter of 2006- 2008, and the number departing in each departure window calculated from the distribution observed in our Sabre dataset.
7 We carry out the calculation one departure window at a time in order to be able to observe the gross number of shifts. If we were to recalculate all windows simultaneously we would observe the net results of people shifting out of one departure window to the next, and shifting into that same departure window from the previous window.
Voluntary Time AdjustmentDeparture CategoryPredicted Trips in SamplePredicted Trips in Sample - No Delay in Departure WindowPredicted Gross IncreaseDifference as Percent of Predicted Trips in Previous Departure WindowEarly848,661 843,745 58063.03% AMPeak900,058 883,949 107221.26% Midday1,666,114 1,669,603 268322.98% PMPeak652,072 666,937 233431.40% Evening191,922 194,594 84781.30% Total4,258,827 4,258,827 NotesThe increase in the predicted number of trips without delay is equal to the predicted number of trips with delay plus the predicted gross increase less the predicted gross increase of the following period - i. e., itmeasures the net change, so that the total number of trips predicted remains constant 41
Table 3- 12: Departures by quarter and departure window, 2006- 2008
We were able to identify an empirical study presenting estimates of how traveler value of time varies over the course of the day. 8 See Table 3- 13. We rely on these estimates in our calculation, so that the value of time we express is in terms of the hourly wage of a ‘ representative passenger’. 9
Table 3- 13: Value of time lost to voluntary departure time adjustment
We assume that the time saved by a passenger switching departure category is the difference between the mean departure times of the relevant windows, as measured by the flights in the On Time Performance dataset. We treat passengers that switch from an evening departure to an early departure the next morning
8 Mehndiratta, Shomik Raj, 1996, “ Time- of- Day Effects in Inter- City Business Travel,” Institute of Transportation Studies at UC Berkeley Dissertation Series.
9 The hourly wage we employ is that measured for private sector production workers in the Bureau of Labor Statistics’ Consumer Expenditures Survey, which averages $ 17.42 over 2006- 2008.
[ 1][ 2][ 3][ 4][ 5][ 6] YearQuarterDB1B PassengersEarly DeparturesAMPeak DeparturesMidday DeparturesPMPeak DeparturesEvening Departures2006147,442,47512,637,89711,773,99315,361,2025,506,5292,162,8532006253,492,82414,249,61113,275,53317,320,2206,208,778 ,438,6822006350,879,89413,553,56912,627,07216,474,1905,905,5022,319,5612006451,289,44413,662,66612,728,71116,606,7975,953,0372, 38,2322007149,055,67213,067,62612,174,34715,883,5335,693,7692,236,3972007255,655,45514,825,70013,812,24218,020,4496,459,7892,53 ,2742007353,250,92614,185,17313,215,50017,241,8976,180,7022,427,6542007452,523,82013,991,48413,035,05217,006,4706,096,3082,394, 062008150,282,91613,394,54412,478,91716,280,8975,836,2122,292,3462008254,944,88214,636,41513,635,89617,790,3766,377,3152,504,88 2008350,415,90813,429,97112,511,92216,323,9585,851,6482,298,4092008447,863,45212,750,03811,878,46915,497,5095,555,3912,182,045T tal617,097,668164,384,693153,147,656199,807,49871,624,98228,132,838[ 1] = DB1B 10% Ticket sample multiplied by 10 to obtain total population estimate; see also Table 5[ 2] = [ 1]* 26.6%, percent of Sabre Bookings with Early Departures, from Table 8[ 3] = [ 1]* 24.8%, percent of Sabre Bookings with AMPeak Departures, from Table 8[ 4] = [ 1]* 32.4%, percent of Sabre Bookings with Midday Departures, from Table 8[ 5] = [ 1]* 11.6%, percent of Sabre Bookings with PMPeak Departures, from Table 8[ 6] = [ 1]* 4.6%, percent of Sabre Bookings with Evening Departures, from Table 8ActivityValue of Time as Multiple of Average Hourly WageLeisure0.93 Work1.86 Sleep5.67 42
somewhat differently, reducing the difference between these two departures by eight hours to allow for time spent sleeping. 10
Table 3- 14 shows the average departure time associated with each departure window across our three year sample.
Table 3- 14: Mean departure time, 2006- 2008
We assume that a passenger that adjusts from an AMPeak departure to an Early departure loses sleep time, and that a passenger that adjusts from an early departure time to a departure the night before loses leisure time. All others lose work time. Based on these assumptions, we estimate of the cost to passengers of voluntary departure time adjustment. These are presented in Table 3- 15.
In columns 1- 5 of Table 3- 15, we apply our estimates of the percentage of passengers in each departure window that would adjust their schedule in the absence of delay to the passenger counts in Table 3- 12. In column six we translate these passenger counts into hours lost to voluntary departure time adjustment. Column 7 further translates these estimates of time lost to delay into the dollar value of that time. Finally, in column 10, we present our estimates of passenger costs assuming that, in addition to the value of the time lost to voluntary departure time adjustment, passengers who travel the night before their preferred departure also incur the cost of a one- night stay in a hotel and a meal on the road.
10 This implicitly assumes that the passenger is indifferent between sleeping in his or her own bed and one on the road.
Departure CategoryMean Departure TimeEarly6: 47 AMAMPeak8: 54 AMMidday12: 57 PMPMPeak5: 26 PMEvening8: 23 PM 43
Table 3- 15: Estimates of cost of voluntary time adjustment
3.4 Capacity Induced Schedule Delay ( CSD)
In following their business models, airlines tend to generate “ peaked” schedules. The two reasons that stand out most clearly are:
i) to support a large number of low delay passenger connections as part of a banking operation;
ii) to satisfy the natural hourly peaks in customer demand over the course of a day ( especially for business customers).
As the number of scheduled flights gets closer to the runway capacity constraints, airlines may have to change their schedule, by moving flights to a less congested time of day. That is, capacity constraints may force a “ flattening” of schedules. De facto flattening can also arise in other ways. For example even if flight schedule is peaked, actual times may be flattened as a result of delays. Here, however, our focus here is on flattening of the actual schedule. Thus, we hypothesize that there is a negative relationship between the degree to which airline schedules are peaked and the capacity utilization of an airport. To test this hypothesis and quantify this relationship we first need to develop metrics for both “ peakedness” ( or schedule variability) and airport capacity utilization. We quantify the relationship between them using a regression model. We then use this model to address the problem of estimating the cost impact of capacity constraints on schedule delay. Specifically, this regression model allows us to estimate what the peakedness measure would be in the absence of a capacity constraint for the airports analyzed. We then estimate the decrease in schedule delay that passengers would experience when a schedule with the higher
[ 1][ 2][ 3][ 4][ 5][ 6][ 7][ 8][ 9][ 10] YearQuarterEarly to AMPeak SwitchesAMPeak to Midday SwitchesMidday to PMPeak SwitchesPMPeak to Evening SwitchesEvening to Next- Day Early SwitchesHours SavedPassenger Time CostsAverage Hotel CostMeal CostTotal Passenger CostsEstimated Percent Switching1.26% 2.98% 1.40% 1.30% 3.03% 20061159,674350,997215,21971,59265,4343,082,220111,961,779$ 125$ 40$ 122,758,433$ 20062180,037395,759242,66680,72373,7793,492,743127,624,505$ 125$ 40$ 139,798,059$ 20063171,243376,428230,81376,78070,1753,320,008122,416,630$ 125$ 40$ 133,995,551$ 20064172,621379,458232,67077,39870,7403,371,151126,451,345$ 125$ 40$ 138,123,469$ 20071165,103362,932222,53774,02767,6593,197,441122,352,409$ 132$ 40$ 133,989,800$ 20072187,315411,759252,47683,98676,7623,626,193141,219,140$ 132$ 40$ 154,422,185$ 20073179,223393,970241,56980,35873,4453,457,039137,555,107$ 132$ 40$ 150,187,731$ 20074176,775388,590238,27079,26072,4433,435,208137,956,074$ 132$ 40$ 150,416,208$ 20081169,233372,011228,10475,87969,3523,271,544131,917,892$ 129$ 40$ 143,638,364$ 20082184,924406,502249,25382,91475,7823,582,831144,457,866$ 129$ 40$ 157,264,998$ 20083169,681372,995228,70876,07969,5353,294,334133,877,181$ 129$ 40$ 145,628,652$ 20084161,090354,111217,12972,22866,0153,112,303127,038,268$ 129$ 40$ 138,194,785$ Total2,076,9194,565,5142,799,414931,223851,12240,243,0161,564,828,196$ 1,708,418,237$ [ 1] = Early Departures ( Table 11)* 1.26%, percent switching from Early to AMPeak with no AMPeak delay[ 2] = AMPeak Departures ( Table 11)* 2.98%, percent switching from AMPeak to Midday with no Midday delay[ 3] = Midday Departures ( Table 11)* 1.4%, percent switching from Midday to PMPeak with no PMPeak delay[ 4] = PMPeak Departures ( Table 11)* 1.3%, percent switching from PMPeak to Evening with no Evening delay[ 5] = Evening Departures ( Table 11)* 3.03%, percent switching from Evening to Next- Day Early with no Early delay[ 6] = Total hours saved, assuming the mean departure time within each year, quarter, and departure window. Hours saved for switching from Evening to Next- Day Early are equal to the difference in mean departure time less eight hours sleep time. [ 7] = Total Passenger Time Costs saved, assuming Mehndiratta values for value of timeSwitches from AMPeak to Midday, Midday to PMPeak, and PMPeak to Evening departures are assumed to save ' Work' time. Switches from Evening to Next- Day Early departures are assumed to save ' Leisure' time. Switches from Early to AMPeak departures are assumed to save ' Sleep' time. [ 8] = Average Hotel Cost. Sour