Ripple delay and its mitigation[^1]

James A. Rome\
Simon D. Rose\
Ronald W. Lee\
Oak Ridge National Laboratory, Oak Ridge, TN

James H. Cistone\
Lockheed Martin Air Traffic Management, Rockville, MD

George F. Bell\
GFB and Associates, Fayetteville, GA

William S.Leber\
Northwest Airlines, St. Paul, MN

Abstract

Arrival delays, especially those that occur early in the day, tend to
exponentiate with time unless the crew and equipment remain together
throughout the day's schedule. Consequently, to achieve optimum results,
the airline must account for these downline ripple delay effects when
managing its flights. In this study, which uses data from Northwest
Airlines, we attempt to minimize the costs of such delays by allowing
the airline to swap its landing slots within a ±10 minute window. The
study has three parts: (1) calculation of the incremental cost
(including affected later flights) as each flight's landing time is
moved within the ±10-minute window; (2) determining a near optimum
resequencing algorithm for making the swaps and applying it; and (3)
extrapolating the results to the industry as a whole. Annual
industry-wide savings for airlines at major hubs are over \$75 million
if airlines are restricted to using only their own slots, and over \$100
million if other (available) slots can be used.

# Background

Most airlines that use hub-and-spoke operations rely upon a bank of
planes arriving at the hub in as short a period as possible (less than
an hour). The passengers and crews transfer to their next flight leg and
again, all the planes take off and leave the hub as simultaneously as is
possible. This sort of operation makes the best use of equipment, gates,
and crews so long as everything is working well. However, when a
significant number of flights are late, connections will be missed,
passenger misconnection costs and ill will escalate, and ripple delays
start to build. In a previous study with American Airlines \[[^2]\], we
found that a minute of delay early in the day could cause up to 13
minutes of delay later in the day. This effect was called *ripple delay*
in that study.

Ripple delay is caused by the scheduling practices of the airlines. Turn
times between flight legs are minimized to fully utilize expensive
resources, so there is not much slack in the schedule to absorb delays.
In addition, crews are commonly split between flight legs to allow them
to live in different places. In addition to the active crew on a flight,
deadhead crew (crew being transported to or from their active flights)
must also be taken into account if they are assigned to later flights.
Because of the crew and equipment splits, one late flight can delay a
handful of other flights on the next leg. It is this splitting that
causes delays to get worse as the day progresses.

While minutes of delay give an indication of problems, not all minutes
are created equal---it is the dollar cost of a delay that ultimately
matters to the airline. For Northwest Airlines (NWA), most costs of
delay are associated with passenger misconnect costs and ill will, so
minimizing the airline costs is also best for the traveling public.
Furthermore, the costs of other flights affected by the ripple delay
must also be taken into account in determining how to handle the flights
in a landing queue; larger cost contributions could arise from later
flights.

During both normal and constrained operations, after an aircraft is
airborne the estimated time of arrival (ETA) can be accurately computed
and adjusted throughout the flight. Although the Federal Aviation
Administration (FAA) controls air traffic and assigns landing slots at
major airports, it has no knowledge of the economic value of each flight
to its customers, the airlines. Once the runway arrival time or landing
slots have been computed, it is believed that airlines could further
refine and improve their operating efficiency by having the ability to
establish the actual landing sequence for their flights at a given
airport. In addition to direct cost savings, resequencing could also
allow the airline to:

-   Control the order in which flights arrive into the terminal
    complexes thereby reducing taxi time and ramp congestion and
    improving gate utilization,

-   Prioritize arrivals to permit smoother passenger and cargo/mail
    connections: reducing miss-connections and disrupted passenger
    expenses, reducing departure delays and the downline effects of
    these delays and associated disruptions,

-   Prioritize arrival for aircraft and flight crew rotations based on
    next assignment

-   Avoid diversion in situations where longer-haul or load-limited
    flights may not have sufficient fuel to absorb airborne holding
    delays, by allowing these flights to have landing priority while
    other company flights, with higher fuel reserves, absorb additional
    holding delay, and

-   Maintain bank integrity. Hub-and-spoke systems work smoothly when
    all of the flights arrive and depart in groups. While the planes are
    at the gate, the passengers make their connections. Resequencing
    tends to reform the bank by delaying early flights and speeding up
    late ones.

To calculate and mitigate the costs from ripple delays, the first step
is to model the airline connectivity. This means integrating the crew,
equipment, passenger and flight schedules into a multiply linked list
that can be traversed forwards and backwards. The airline cost model and
the requirements for equipment and crew turn times must be integrated
into this data structure in order to calculate the "ready" time for each
flight leg, and the cost associated with moving it forward and backward
in time.

Next, the flights must be associated with the landing queue for a bank
at a hub airport. If these flights are allowed to swap landing slots
within the ±10 minute window, the ripple-delay cost (or savings)
associated with each swap must be calculated. Given these costs, a
method for selecting the best (or a very good) set of swaps must be
devised. Once the swaps are made, the resulting savings can be
calculated, and extrapolations can be made for the airline and the
industry.

Previous studies \[[^3], [^4], [^5] \] of arrival queue resequencing
have considered a different problem, namely how to increase the number
of landings at a given airport. When cost was introduced in the
optimization, only fuel, crew, and aircraft costs per minute were
considered; we find these costs to be insignificant compared to
passenger costs, especially when the ripple delay effects are included.

The National Aeronautics and Space Administration (NASA) Center Tracon
Automation System (CTAS) was designed to sequence an arrival queue so
that an airline could specify a preferential arrival order using only
their landing slots \[[^6]\]. This study was undertaken as part of the
CTAS effort to quantify the cost benefits that could be derived by an
airline from such resequencing. It was also recognized that the downline
effects needed to be accounted for in order to make the best use of this
resequencing capability.

As is usual, this is a "chicken and egg" problem. The FAA controllers do
not ordinarily allow swaps in the air. Planes are often sequenced from
takeoff to landing. Such actions require extra work, and there could be
safety issues that occur during the process. We have also ignored the
problem of aircraft size in the landing sequence separation as was
discussed in \[Error: Reference source not found\]. However, if the cost
savings that can be achieved by these swaps can be shown to be
significant, it might motivate the system and in particular Air Traffic
Service Providers (ATSPs) to devise safe ways to accommodate these
requests. In the meantime, an airline has some control over the landing
queue by changing pushback times and air speeds, and occasional requests
for queue resequencing can be honored.

Although Northwest Airlines participated in this work, it was not
performed for Northwest Airlines and hence the airline has not had any
reason to independently verify the results.

# Data and cost models

This study utilized NWA data from two periods, April 6--8, 1998, and
July 30--August 5, 1999. NWA provided us the following data:

-   Flight leg data for NWA and its two commuter airlines, Mesaba and
    Express. The commuters are collectively referred to as Airlink.

-   Flight delay causes.

-   Passenger ticket data for the three hub airports (incoming and
    outgoing).

-   Passenger connection times.

-   Crew patterns for pilots and flight attendants.

-   Aircraft schedule and minimum turn time data.

-   Flight leg load factors.

-   Aircraft tail number, type and model information and seat capacity.

-   Aircraft performance data.

-   Cost model for passengers, crew, equipment, and fuel.

In addition, we obtained Enhanced Traffic Management System (ETMS) data
for the period from Bruce Ware of the FAA's Airspace Redesign Office,
and airspace performance data from Carlton Wine's FAA Consolidated
Operations and Delay Analysis Systems (CODAS) Web site.

One of the challenges to real-time implementation of resequencing the
landing queue is the availability of all the data required to calculate
the ripple delay costs. In particular, at the time of our study, NWA had
difficulty in assembling the passenger data. In order to get the study
finished before our deadlines, we used passenger data from a similar
period a month earlier. The data were modified to accommodate schedule
changes and flight number changes, but a few flights added to the
schedule in the intervening month might have no passengers on them.

Not all data are hard and fast numbers. In particular, the turn times
for the crews are scheduled to be 45 minutes, but in fact, crews can
generally be ready in 35 minutes if they hustle. We used 35 minutes for
crew turn times in this study. The aircraft turn time is a function of
the aircraft type and the airport.

Passenger connection times are of course defined by the airline when
schedules are created, and are used to schedule connections. However,
the actual time needed to make a connection depends on many factors: the
agility of the passenger, the distance between gates, and the lateness
of the connecting flight. Overseas connections require extra time for
customs and immigration. To accommodate this situation, NWA has created
a proprietary probabilistic model for passenger connection times. If the
effective connection time (ECT = scheduled *out* time − actual *in*
time) is large, the chance of making a connecting flight is 100%, but
even if the connection time is negative, there is a finite chance of
making the connection because the connecting flight might be late or
held for connecting passengers or baggage. We used this model when
evaluating passenger misconnection costs. There are also costs for
passenger ill will, which begins when a flight is 15 minutes late; for
interrupted trip expenses, which begins when a flight is 95 minutes
late; and for baggage misconnection costs.

Because of the details of crew contracts, the only crew cost that occurs
is when the crew exceeds its scheduled block time (scheduled *in* −
scheduled *out*). Increased block times can arise from late arrivals and
from early departures. We observed some flights pushing off up to 10
minutes ahead of schedule. Although they arrived early, they still
incurred a block delay cost.

Ground operation overtime costs occur when a flight takes at least a
30-minute delay. However, by this time, passenger costs are much greater
than ground operations costs, so the latter were ignored.

Fuel cost can be broken into gate, taxi, and air delays. We assumed that
taxi times, gate costs, and air delays were unchanged by our
resequencing, but did calculate the fuel costs (or savings) for
resequencing. Fuel costs increase if the plane is speeded up to land
earlier and decrease if it slows down to land later.

NWA has maintenance contracts for A320 and DC-10-30 engines based on
hours flown. Minor changes in enroute time are assumed to have no impact
on either engines or airframes.

Except for baggage misconnection costs, all costs increase monotonically
with time. For baggage, the costs increase for a period, and then
decrease because the passenger was probably delayed along with his
baggage, and then they increase again because the baggage is probably
lost. However, when the baggage cost formula is combined with the
passenger costs, the result always increases with time. This will be an
important factor when determining how to resequence the flight-landing
queue.

# Scope of the study

Our study focused on NWA operations at three hubs, Minneapolis (MSP),
Detroit (DTW), and Memphis (MEM), over a three-day period (April 6--8)
in 1998, and a week period (July 30 --August 5) in 1999. These periods
covered a variety of weather and operational conditions. The airline
operations for both periods are summarized below in excerpts from the
NWA ATC Coordinator daily log highlights.

**1998\
**April 6 Thunderstorms directly impacting MSP terminal operations\
April 7 Rain showers at MSP much of the day reducing the Airport Arrival
Rate (AAR)\
April 8 Thunderstorms at MEM and in the Ohio Valley

**1999\
**July 30 Thunderstorms at MSP causing diversions and single runway ops
much of the day\
July 31 Thunderstorms across Florida\
August 1 Thunderstorms impacting the Washington DC. Metro airports\
August 2 Thunderstorms impacting central Florida\
August 3 Thunderstorms impacting MIA\
August 4 Thunderstorms impacting the southern Great Lakes & Florida.
Ground stops at DTW\
August 5 Thunderstorms impacting PA through New England in the afternoon

Airline performance for the period April 6 through April 8 was
influenced by the following operational factors:

-   Labor actions causing high numbers of cancellations on both April 7
    and 8

-   Runway constructions at MSP reducing the AAR from 60 to 52

-   Thunderstorms directly impacting the MSP terminal area causing 15
    MSP diversions

Airline Performance for the period July 30 through August 5 was
influenced by the following operational factors:

-   Runway construction at MSP and MEM

-   Runway closure at DTW

-   Taxiway construction at all three airports

-   Thunderstorms directly impacting MSP and DTW terminal areas

-   Thunderstorm outside the HUB airport, terminal areas causing
    reroutes and a lower AAR

-   Thunderstorms outside the DTW terminal area creating enroute
    congestion impacting DTW

-   Ground stops at DTW

-   Single Runway operations at MSP

-   High levels of enroute congestion and ground stops in the Northeast

The daily percentage of flights that arrive less than 15 minutes late
(excluding cancellations) is called the DOT A14%, and is a good metric
of performance. Table 1 shows the A14% for NWA for the 1998 and 1999
study periods. A0% is the percentage of flights that arrive on schedule,
and A30% is the percentage that arrives within 30 minutes.

Table 1. NWA Arrival Performance.

  ---------- ----------------- ---------- ----------- ------------- --------------
  **Date**   **Destination**   **A0%**    **A14%**    **A30%**      **Arrivals**

  4/6/98     DTW               71.9%      92.1%       96.7%         366

  4/6/98     MEM               84.2%      93.0%       98.2%         114

  4/6/98     MSP               50.6%      76.5%       86.6%         328

  4/7/98     DTW               61.3%      83.8%       93.8%         357

  4/7/98     MEM               58.4%      85.8%       92.0%         113

  4/7/98     MSP               55.8%      81.1%       90.2%         317

  4/8/98     DTW               37.7%      69.6%       84.1%         358

  4/8/98     MEM               35.7%      51.8%       74.1%         112

  4/8/98     MSP               53.3%      79.7%       88.3%         315

  7/30/99    DTW               61.4%      82.1%       89.5%         363

  7/30/99    MEM               67.0%      83.5%       89.9%         109

  7/30/99    MSP               40.4%      56.8%       68.6%         354

  7/31/99    DTW               44.0%      63.2%       70.2%         302

  7/31/99    MEM               53.8%      76.9%       80.8%         104

  7/31/99    MSP               56.9%      74.8%       83.1%         325

  8/1/99     DTW               63.7%      83.4%       92.1%         331

  8/1/99     MEM               69.4%      92.6%       96.3%         108

  8/1/99     MSP               68.5%      84.9%       93.2%         352

  8/2/99     DTW               66.6%      90.4%       95.9%         365

  8/2/99     MEM               67.3%      85.5%       95.5%         110

  8/2/99     MSP               73.0%      89.8%       95.3%         363

  8/3/99     DTW               73.9%      90.8%       96.5%         368

  8/3/99     MEM               64.9%      91.0%       98.2%         111

  8/3/99     MSP               60.7%      87.3%       94.2%         361

  8/4/99     DTW               43.4%      61.9%       73.4%         357

  8/4/99     MEM               63.6%      83.6%       88.2%         110

  8/4/99     MSP               61.6%      87.0%       93.9%         362

  8/5/99     DTW               62.9%      84.6%       91.9%         369

  8/5/99     MEM               49.1%      79.1%       90.0%         110

  8/5/99     MSP               68.9%      89.8%       93.7%         363
  ---------- ----------------- ---------- ----------- ------------- --------------

From NWA's point of view, August 2, 3, and 5 were good operational days.
We have similar data for the two NWA commuter airlines and for departure
performance.

# Airline connectivity

Efficient resequencing cannot be performed by only considering the
arriving flights independently of their connectivity to the remainder of
the airline schedule, because this connectivity causes downline delay
effects that may have more cost impact than the initiating flight. In
the delay model, the equipment and the crew cause this connectivity. In
order for a flight to take off, the crew and equipment must be available
and have had time for their required procedures. We also assumed, in our
connectivity calculations, that takeoff could not occur before the time
scheduled in the Official Airline Guide (OAG) (although this can happen
in practice).

#### Equipment

The Out-Off-On-In (OOOI) data contain the tail numbers for NWA flights
and commuter advanced regional jets (ARJs), but not for commuter
propeller planes. We sorted the NWA Excel spreadsheet data by tail
number, date, and *out* time to obtain the flight leg sequence for each
aircraft. We use a list of equipment turn times (a function of the
aircraft type and airport category) to determine how much turn time is
required before the equipment is ready for the next flight leg. Thus,
equipment availability time = actual *in* time + turn time.

#### Cockpit crew and flight attendants

We have the crew rotations for all NWA flights, both scheduled and
actual. We used the actual rotations to determine the sequence of flight
legs for each member of the crew. We treated deadhead legs just like
ordinary legs. Thirty five minutes was used as the minimum turn time for
all crew.

Crew availability time = actual *in* time + 35

In the 1998 version of the study, we assumed that the crew connect time
was 45 minutes. Reducing this by 10-minutes made a big difference in the
number of downline flights delayed due to late crew availability. The
delay chains were much shorter and less frequent using the 1999 value of
35 minutes.

#### Delay chains

It is important to understand how delays can propagate through the
airline\'s schedule. We developed a graphical representation of these
delay chains that helps to clarify several issues.

Figure 1 shows an example of a delay chain created using a 45-minute
crew connect time to enhance the effects. Three horizontal lines for the
*actual*, *scheduled*, and *model* block times represent each flight
leg. The lines connecting the flights show the elements that connect the
flight legs, equipment, crew, or flight attendants. For example, the
first flight (NW735) delays three other flights. The turn times
discussed above must be obeyed between flights. Because we should not
predict the future with our model, future block times used in the model
are always the same as the scheduled block time. The lower figure shows
the effect of moving the on time for NW735 forward by 9 minutes. The
number of delayed flights is dramatically reduced (from 2 to 17) and the
total number of delay minutes is cut from 578 to 405.

![](media/image1.wmf){width="5.9944444444444445in"
height="8.196527777777778in"}

Figure 1. Delay chain for NWA 735. Top figure is as flown which delays
21 flights. Bottom figure shows the effect of moving the initial landing
time up by 9 minutes. Only 17 flights are affected and the number of
minutes of delay is cut from 578 to 405. A 45-minute crew turn time was
used.

Using 35-minute turn times for the crew, we saw many fewer delay chains,
and they were of shorter duration. Changes in schedule are evident in
the delay chain plots when a leg in the chain is scheduled to depart
before its resources were scheduled to arrive. In such cases, there are
large delay costs associated with the rescheduled flight that are not
associated with the initiator of the delay chain. Nonetheless, moving
the head of the chain can still cause large changes to these costs.
These changes are calculated correctly and do arise from the
resequencing process.

Figure 1 shows that the delay chains can spread, affecting many more
flights as time goes on, and also that a given flight can be affected by
more than one resource. In this study, we examined resequencing one bank
at one hub at a time. It is easy to envision delay chains originating
from multiple flights intersecting in the future. If the heads of these
chains were not in the same bank at the same hub, we will miss this
interaction. Our current model treats resources originating from other
banks using their "as flown" times. However, our model does correctly
calculate which resource for each future flight leg is "controlling,"
and recursively traverses the multiply-linked list of flight legs to
determine the effects of the crew and equipment on the lateness of a
given future flight leg.

The cost model, correctly applied to the flights in each delay chain,
determines the cost changes when a flight in the arrival queue is moved
forward or backward. Most of the model is concerned with reading the
airline data, determining the connectivity of each flight leg, and
calculating the cost (including downline effects) for each flight in
each landing slot that it can access by reasonable (10-minute) speedup
or slowdown.

# Resequencing algorithm

Once the costs for landing each flight in each slot are determined, we
can try to optimize the landing queue. This optimization is a
computationally separate exercise, and depends upon the definition of
optimum. For the purposes of this study, "optimum" was defined as
minimum cost to the airline. There may be auxiliary constraints that
need to be applied. The only one we considered was to avoid swapping
flights if the savings were small (e.g., \<\$100). The effects of this
additional constraint will be discussed later.

The model allows us to calculate the ripple delay costs for each landing
slot that a flight could use (within ±10 minutes of the actual *on*
time). We use two different cost models. The first one we call the
*ripple delay cost*. It is the total cost of delay added up for all
affected downstream flights. The ripple delay cost represents the
potential impact to the airline for each flight in the arrival queue,
and we use this cost to make resequencing decisions. However, when we
calculate the savings to the airline, we only use the cost savings up to
and including the next arrival at an NWA hub. To go further downstream
would count cost savings for this flight more than once. We call this
the *delay cost*. We will give examples of the differences between these
costs in a later section.

#### Arrival queue

To clarify the algorithm, Figure 2 shows the situation at the end of the
first bank at Memphis on April 7, 1998. The left three columns show the
NWA slot number, local time, and the flight number that actually landed
in that slot. The other columns contain the cost of all flights that can
land in each available slot. Slots past the ±10 minute variation contain
an asterisk. The flight selected by the optimizing algorithm (see below)
for each slot is outlined, and because the algorithm works backwards in
time, the earlier slots for that flight are shaded to show they are
unavailable. Several slots may occur at the same time because multiple
runways are used (e.g., slots 45 and 46), or a given time may not
contain an NWA landing slot (8:04). For example, NW1741originally landed
at 8:09 in slot 54 for a cost of \$160. It could have landed in any slot
between 7:59 and 8:19, inclusive. If this flight were moved earlier
(left in Figure 2) to 8:06, the cost would be eliminated. If it were
delayed more, the cost would increase. Therefore, the task is to
determine which flight to land in each available slot to achieve the
minimum cost for the airline.

  -----------------------------------------------------------------------
  ![](media/image2.wmf)

  Figure 2. Queue data for NWA arrivals at the end of the first bank in
  Memphis on April 7, 1988. The outlined cells designate the flight
  selected for landing in each slot. The numbers in the cells are the
  incremental cost in dollars for landing each flight.
  -----------------------------------------------------------------------

#### The algorithm

The first task is to determine the start and end of an arrival bank. For
the purposes of our study, any gap of more than 10 minutes between
landing slots will delineate a bank because swaps cannot span a longer
time gap. At the start of a bank, a flight can only land in its assigned
slot or in later slots. At the end of a bank, the flight can only land
in earlier slots or in its assigned slot. In Figure 2, slot 60 is the
end of the first bank

The key to the resequencing algorithm is to start from the end of each
bank and to work forward. The "cost" to optimize is the cost in a slot
minus the cost in the first available slot for the flight. It may occur
that a flight incurs a cost no matter in which slot it lands. Only the
cost savings count when performing the resequencing. The rules of the
algorithm are as follows:

-   Don\'t do any resequencing unless the number of available slots
    exceeds the number of planes that must land before they run out of
    slot times on the early side. In slot 49, we must take flight 854
    because there are no earlier slots, later slots are already taken,
    and it must land. This situation also occurs for flight 1294 in
    slot 48. We discuss this in more detail in the section *Results of
    the Analysis*.

-   In each slot, select the minimum cost flight and land it in the slot
    (9E5130 in slot 60). In slot 58, the lowest cost flight is NW1831
    (\$334 -- \$207 = \$127). In slot 56 it is NW790 (\$249 --\$160 =
    \$89)

-   In case of a tie for minimum cost, land the flight with the latest
    original slot time, i.e., the bottom flight on the spreadsheet.
    (Pick NW1770 in slot 50)

-   Because we select the lowest cost flight in each slot, and costs
    increase with time, this algorithm yields results that are close to
    optimum. Unaccommodated flights cost less in an earlier time slot.

-   This resequencing algorithm has the ability to sacrifice one flight
    for the common good. NW635 was delayed, thus incurring an extra \$27
    in cost because landing any other flight in this slot would cost at
    least \$133.

You might think that the same results could be achieved by starting at
the beginning of a bank and working forward in time. Indeed, this method
was the first approach tried. In this case, you must look ahead to find
the flight that is going to yield the biggest cost and land it first.
Flights must be considered that would land more that 10 minutes ahead,
and so are not listed in the column of the slot being optimized. By
starting at the back and working backward in time, we obtain an easier
to code, and easier to understand algorithm that works better in all
cases.

It is not trivial to determine whether resequencing is allowed at a
given slot, because we must look backward in time for all the flights
that could land in this slot, and make sure that enough slots are
available to land them all. The algorithm for this is as follows:

-   Create a *needs* array of dimension at least as big is the maximum
    number of planes that could land in any slot, and set all elements
    to zero.

-   For each plane that could land in the slot (and has not already
    landed), find the number of available slots, *ns*, between the slot
    time and the earliest possible landing time for the flight. If there
    are multiple flights landing at this slot time, do not count slots
    with a higher slot number.

-   Add 1 to each element of the *needs* array from *ns* upward,
    indicating that a flight could need to land in that slot.

-   If any element of the array is equal to the index of that element,
    it means that there are just enough slots available to land the
    flights under consideration and hence, swapping is not allowed.

It may occur that a subgroup of *n* contiguous flights all must land in
the same range of slots. In that case, we determine the flights that can
swap among themselves and allow resequencing among these *n* flights.

In general, determining an optimum algorithm for resequencing is a very
complicated Operations Research problem. However, in our case, several
things make this easier. First, as discussed in the cost model section,
the cost of delaying a flight increases monotonically in time. So
landing a flight earlier will never cost more if fuel costs (for
speedup) are ignored. Second, all planes are subject to the same cost
model, so the change in costs between slots for one flight is generally
similar to the change in costs for another flight. Finally, the cost
slopes for later flights are usually higher because more costs start to
kick in. If the cost slope was the same for all flights, we could prove
that our resequencing algorithm was optimum. Because the cost slopes do
change from flight to flight, we can merely say that this algorithm is
easy and fast to apply and yields excellent results. A counter example
is shown in Figure 3. The figure caption explains why this case is
unusual.

  ---------------------------------------------------- -------------------------------------
  ![](media/image3.wmf){width="2.7472222222222222in"   Figure 3. A counter example for the
  height="2.0625in"}                                   resequencing algorithm. The algorithm
                                                       would select the two slots labeled
                                                       *A*, whereas the selection labeled
                                                       *B* would yield more cost savings.
                                                       (Remember it is the difference
                                                       between the current cost and the
                                                       earliest possible cost that counts.)
                                                       However, in practice, most cost
                                                       curves are concave up because the
                                                       cost rate increases as time goes on
                                                       (up to a maximum incurred cost). In
                                                       addition, the curve with the highest
                                                       cost usually has the greatest slope
                                                       because more passengers are affected
                                                       and additional costs arise as the
                                                       flight becomes later. In this case,
                                                       the curve with the higher slope would
                                                       be above the curve with the lower
                                                       slope and the algorithm is optimum.

  ---------------------------------------------------- -------------------------------------

# Assumptions of the Model

#### Costs increase with time

The resequencing algorithm assumes that costs increase monotonically
with increasing delay. This is true for everything except the fuel costs
for speedup or slowdown. Fuel costs generally decrease when a plane is
slowed down and increase when it is speeded up. Accordingly, we ignored
the fuel speedup costs (which are usually much smaller than the
passenger delay costs) when performing the optimization. Then, after the
resequencing, we adjusted the costs for the resequenced flights to
reflect the speedup fuel costs. As a result, some flights that were
speeded up to reduce passenger costs actually cost a little more due to
these increased fuel costs. On the other hand, some delayed flights
incurred a negative cost (savings) due to the slowdown. If flights with
small cost savings are not swapped, the increased fuel costs will become
negligible. We examine the effects of such actions in the analysis
section.

The cost of misconnected luggage is also non-monotonic. It increases
with time, then decreases because the owner is delayed also, and then
increases again. However, the increases in other passenger costs always
make the sum of the passenger costs increase monotonically.

#### Airplane Performance

Using Aircraft Operating Manual data provided by NWA Performance
Engineering a series of flight path computations were performed for each
of the Northwest Airlines turbo jet aircraft:

-   B747 (-200, -400)

-   DC10 (-40 -30)

-   B757 --200

-   DC9 (MD80, -30, -40, -50)

-   A310, A320

-   B727-200

-   ARJ

-   Turbo Props (SF series)

To simplify the model, aircraft fleet types were combined where the
performance and cost deltas were similar.

Flight profiles were computed over a wide range of speeds and altitudes,
and a cost model was built for the variance of time around the nominal
operating speed for each airplane type. Time-fuel-speed (Cost Index)
profiles were integrated to resolve the minimum cost for a given flight
time for each aircraft. The cost model included the price of fuel and an
allocation for the operating cost per minute for aircraft itself. The
strategic value for crew and airplane utilization costs was not included
because the crew block time is included in the main model. In general,
it is believed that resequencing will in fact keep airlines operating
closer to their published schedule and therefore within their business
allocations for aircraft and crew utilization costs.

The data in Table 2 for the B747-400 are typical of the cost delta for
flight time variance around nominal.

.

Table 2. B747-400 flight data.

  -------------- --------- ------------ ------------- ------------ --------------
  **Cost Index**           **Time       **Fuel Cost   **A/C Cost   **Cost Delta
                           Variance**   (\$)**        (\$)**       (\$)**

  300                      −12          351           \(104\)      247

  200                      −7           170           \(61\)       109

  107            Nominal   0            0             0            0

  100                      1            \(12\)        9            \(4\)

  0                        15           \(145\)       130          \(15\)
  -------------- --------- ------------ ------------- ------------ --------------

The descent profiles were based on Idle Thrust Descents from the Top of
Descent Point (TOD) to FL100, deceleration to KCAS250, continued descent
and deceleration to the final landing runway at Vth+10 knots. These data
produce a general view of airplane performance that can be applied to
all turbo jet aircraft.

Specific engineering data for the turbo prop aircraft was not available
so an assignment of cost was made using the basic turbo jet cost profile
and a best fit achieved for the turbo prop aircraft from knowledge of
their fuel consumption and operating costs.

The model was further adjusted in recognition that not all the speed
change would be achieved by changing the cruise profile for the
aircraft. Other techniques can be used to reduce or increase the time to
landing such as:

-   Reducing Distance to Landing (more direct routing to the airport)

-   Increasing Distance to Landing (such as extending the
    downwind-base-final)

-   Reducing time to touch down by utilizing drag devices to enable a
    steeper approach profile allowing for higher cruise speed to be held
    to a closer TOD point.

The airplane flight profile data demonstrated that for both turbo jet
and turboprop airplanes, a time window for speed up/slow down of --10
(earlier) to +10 (later) around the nominal landing time is practical
and achievable. As a result of these considerations, we arrived at the
fleet cost model for NWA equipment that was used to calculate fuel costs
for speedup or slowdown during the landing phase of the flight as shown
in Table 3.

Table 3. Fleet cost model. Costs are in Dollars.

  --------- ---------- ---------- ---------- ---------- --------- -------- ----------- --------------
  **Time    **B727**   **DC10**   **B747**   **B757**   **DC9**   **RJ**   **SB340**   **A319/320**
  ∆**                                                                                  

  **-10**   90         180        210        110        70        45       30          75

  **-9**    80         160        187        98         62        40       27          67

  **-8**    70         140        163        86         54        35       23          58

  **-7**    60         120        140        73         47        30       20          50

  **-6**    50         100        117        61         39        25       17          42

  **-5**    40         80         93         49         31        20       13          33

  **-4**    30         60         70         37         23        15       10          25

  **-3**    20         40         47         24         16        10       7           17

  **-2**    10         20         23         12         8         5        3           8

  **-1**    5          10         12         6          4         3        2           4

  **0**     0.0        0.0        0.0        0.0        0.0       0.0      0.0         0.0

  **1**     \(3\)      \(6\)      \(7\)      \(4\)      \(2\)     \(2\)    \(1\)       \(3\)

  **2**     \(5\)      \(10\)     \(12\)     \(6\)      \(4\)     \(3\)    \(2\)       \(4\)

  **3**     \(7\)      \(14\)     \(16\)     \(9\)      \(5\)     \(4\)    \(2\)       \(6\)

  **4**     \(9\)      \(18\)     \(21\)     \(11\)     \(7\)     \(5\)    \(3\)       \(8\)

  **5**     \(11\)     \(22\)     \(26\)     \(13\)     \(9\)     \(6\)    \(4\)       \(9\)

  **6**     \(13\)     \(26\)     \(30\)     \(16\)     \(10\)    \(7\)    \(4\)       \(11\)

  **7**     \(15\)     \(29\)     \(34\)     \(18\)     \(11\)    \(7\)    \(5\)       \(12\)

  **8**     \(16\)     \(32\)     \(37\)     \(20\)     \(12\)    \(8\)    \(5\)       \(13\)

  **9**     \(18\)     \(35\)     \(41\)     \(21\)     \(14\)    \(9\)    \(6\)       \(15\)

  **10**    \(19\)     \(38\)     \(44\)     \(23\)     \(15\)    \(10\)   \(6\)       \(16\)
  --------- ---------- ---------- ---------- ---------- --------- -------- ----------- --------------

#### Equipment connectivity

-   Flight leg data for NWA and its two commuter airlines were based on
    actual tail number utilization, (*actual* rather than *planned* tail
    number determined equipment connectivity).

-   There was no tail number information available for the two commuter
    airlines except for the ARJs in 1999.

#### Crew patterns for pilots and flight attendants

-   Patterns were based on actual flown rather than scheduled.

-   The deadhead crews (crews being transported to or from their active
    flights) were treated the same as regular crews for the connection
    matrix. But often they are not on a tight schedule to meet a flight.

-   Crew information for the two commuter airlines was not available.

#### Commuter flights are treated with prejudice

Aside from ARJs in 1999, there is no downline connectivity for the two
commuter carriers. Consequently, there are no downline delay costs. In
addition, commuters carry fewer passengers so that the ill-will costs
are always lower than on an NWA flight delayed by the same amount.
Because the cost of delaying commuter flights is small, the resequencing
algorithm will delay commuter flights and advance NWA flights, all
things being equal.

# Understanding the Model Output

A few words are in order to explain the assumptions and limitations of
the model, to show examples of the output data, and to explain where the
final numbers come from.

#### Internal Consistency

The primary "errors" in the model concern the quality of the input
data---its consistency and its correctness. The model reads, parses, and
stores hundreds of megabytes of data for a week\'s run. These data sets
are all preprocessed using Excel. The commuter data are not always in
the same format (or contain the same quantities) as the NWA data, so
these must be converted and reconciled. Most problems in this process
occur at date boundaries, conversions to and from Zulu (GMT), or in
associating a time with the correct date. However, the airline data are
collected on a daily basis, and we want the "daily" runs to be
associated with a local day, not a Zulu day. These issues lead to
problems when a flight crosses a date boundary between *out* and *off*
or between *on* and *in*. The code and the Excel preprocessing must look
for and correct these problems. The recursive nature of the delay
calculation and the complicated interconnectedness of the airline are
very efficient at pointing out any such problems. Nonetheless, a few
such cases remain, and the ones we have examined manually all have
faulty or inconsistent input data.

The code prints out numerous diagnostics for items such as large delay
times, large numbers of passengers, and passenger connections that
cannot be found.

#### Limitations of the Model

Given the duration of this study and the complexity of the data being
analyzed, it was not possible to build a model that could simulate the
total airline operation.

The current model does not deal with:

-   Determining if moving flights forward could reduce the number of
    overnight passengers.

-   Calculating if moving up the last flight of the day could avoid or
    reduce a crew rest delay before the next day\'s departure.

-   Costs associated with gate occupancy impacts for early flight
    arrivals or the delays and additional taxi in times caused by late
    departing flights.

-   Complete simulation of the resequencing of flights in the arrival
    stream for the entire airline.

The model calculates each delay chain separately. In general, delay
chains from multiple flights may intersect a few airports downstream,
and the downstream flight must await all its resources before departure.
The model has the capability of following all resequencing downline for
the entire day. However, to simulate the rest of the day we would have
to reorganize all of the data so that the entire NWA system was advanced
simultaneously rather than an airport at a time. There was insufficient
time to perform this effort. To resequence the whole airline schedule,
it would also be necessary to resolve the availability of landing slots
at the future times that the model decides they are needed. In an
extreme case, the demand for arrival slots could bunch up so that dozens
of flights might want to land at the same time.

The model currently gives a valid representation of the activities for
one bank. As was mentioned earlier, rescheduled equipment or crew can
lead to downline costs that may not be attributable (solely) to the
landing time of a given flight. Because of this, the "cost" of landings
at a hub on a given day must be taken as indicative rather than
absolute. However, the cost savings achieved by resequencing are
independent of these issues and are accurate.

#### The Landing Slot Viewpoint

Because we are resequencing the landing queue to save money for the
airline, one way of looking at the model output is on a slot-by-slot
basis. Unless extra slots are introduced (as will be discussed later),
NWA has *n* landing slots for *n* flights, so the optimization algorithm
is trying to find the rearrangement of these slots that will save the
most money. Other constraints can also be considered.

If a flight originally lands in a slot *s* at time *t*, it incurs a
certain cost to the airline. By speeding up or slowing the flight, it
could be possible land in earlier or later slots. For this study, we
chose a ±10-minute landing window from its actual landing time. This may
encompass a range of slots that depends upon the number of nearby NWA
flights. For example, a flight scheduled to land at the start of a bank
can only land in later slots, and one at the end of the bank can only
land in earlier slots. Given the available slots for a flight, the cost
model determines the cost of landing the flight in each slot. Then the
optimizer resequences all the flights

There are many costs associated with a given flight. For the purposes of
resequencing the landing queue, we use the costs for the incoming flight
plus the costs for all the downstream flights that will be affected by
this flight. We call this the *ripple delay* cost because it gives the
airline scheduler the best idea of the eventual impact of moving this
flight. However, after the flights from one bank are resequenced, we cut
off the downline costs the next time a flight returns to a hub when we
calculate the savings to the airline (to avoid double counting), and
call this the *delay cost*.

We have developed a three-dimensional plot that illustrates the day at a
hub from the slot viewpoint. We illustrate this in Figures 4 and 5 with
a plot of arrivals at MSP on 7/30/1999 --- a very bad day for NWA. The
*Original Slot* axis represents the slot for each flight. The time of
the slot is printed in the front, and the number of original flight that
landed in the slot is printed in the rear. Colored boxes are plotted for
each other slot that the flight could land in (the *∆ Slot* axis). In
fact, the horizontal plane is just Figure 2 replotted along the diagonal
axis. The color of the box represents the ripple delay cost if the
flight were to land in the slot. Earlier slots are in front and later
slots are behind the *∆ Slot* axis. Banks start and end when the number
of early or late slots for a flight goes to zero.

  -----------------------------------------------------------------------
  ![](media/image4.wmf){width="5.989583333333333in"
  height="5.261111111111111in"}

  Figure 4. An enlargement of Figure 5 to display the details. For
  example, NW1763 originally was to land in slot 53 at 7:55 AM for a
  ripple delay cost of \$4232. It was swapped with another flight to land
  10 minutes earlier, so that ripple delays cost \$2782, a potential
  savings of about \$1500. The outlined rectangles represent the
  resequenced landing slot. Before resequencing, all planes landed on the
  *∆ Slot* = 0 axis.
  -----------------------------------------------------------------------

A gray patch in a slot represents no cost to NWA for landing in that
slot. Colored patches in front of the ∆ Slot = 0 line represent
cost-savings opportunities for the airline. Gray slots behind the axis
represent flights that can be delayed without incurring a cost. In this
run, we did no resequencing if the cost for all flights that could land
in the slot was below \$100. Accordingly, the first flight that needs a
swap originally landed in the slot at 7:42 am.

The vertical bars represent the pre (red) and post (green) costs for the
flight that was originally in the slot. A bar that moves forward (∆ Slot
\< 0) represents a flight that was moved earlier, and a bar that moves
backward represents a flight that moves later. The vertical (Cost) axis
is a nonlinear scale that represents the cumulative *delay cost* savings
achieved by resequencing.

As the day progresses, things get steadily worse due to a thunderstorm
line that moved across the airport. On the last two plots, it is evident
that bank integrity has been destroyed; almost every flight arrived
late. The gray patches have almost vanished. The front-to-back extent of
the possible arrival patches gets smaller, indicating a reduced AAR.

Unfortunately, these 3-D plots get rather crowded when many flights are
delayed. It is then useful to examine the raw data by slot. In Table 4
we show the time corresponding to the slots from 293--320.

Table 4. Slot occupancy before and after resequencing.

> **Slot Slot Local Original Minutes Original Rescheduled Minutes
> Optimum Rescheduled\
> Number Time Time Flight Late Cost Flight Late Cost Cost**
>
> 293 15556165 16:25 NW1021 53 1280.22 XJ2767 20 45.98 39.65
>
> 294 15556172 16:32 NW725 32 15.08 XJ3611 31 219.83 236.5
>
> 295 15556175 16:35 XJ3611 34 232.25 NW751 39 1577.01 1600.34

296. 15556176 16:36 XJ2724 50 243.64 NW137 14 384.38 384.38

> 297 15556176 16:36 NW137 14 384.38 XJ2724 50 243.64 243.64
>
> 298 15556176 16:36 XJ2791 22 13.01 NW725 36 30.16 23.16
>
> 299 15556179 16:39 NW751 43 2307.44 NW861 37 6222.65 6320.43
>
> 300 15556184 16:44 NW1269 42 2403.92 XJ2791 30 21.6 16.27
>
> 301 15556188 16:48 NW861 46 9664.77 NW1269 46 2858.98 2851.98
>
> 302 15556190 16:50 NW44 -9 0 NW1056 67 4096.21 4106.21
>
> 303 15556192 16:52 NW1056 69 4339.71 XJ3128 71 1184.1 1184.1
>
> 304 15556192 16:52 XJ3128 71 1184.1 XJ3158 63 1460.85 1484.18
>
> 305 15556194 16:54 NW614 10 48.75 NW102 10 52.5 62.5
>
> 306 15556196 16:56 NW102 12 60 NW218 -11 5076.93 5126.93
>
> 307 15556200 17:00 XJ3095 7 0 NW614 16 145.83 132.83
>
> 308 15556200 17:00 XJ3158 71 1592.1 NW44 1 14.2 -23.8
>
> 309 15556203 17:03 NW316 13 113.6 NW316 13 113.6 113.6
>
> 310 15556203 17:03 NW218 -4 5931.45 NW678 34 628.63 668.63
>
> 311 15556205 17:05 NW1298 -7 0 NW1046 17 478.98 478.98
>
> 312 15556205 17:05 NW1046 17 478.98 NW960 16 233.53 256.86
>
> 313 15556208 17:08 NW678 39 876.34 NW714 3 20.96 33.18
>
> 314 15556209 17:09 NW960 20 248.61 XJ3095 16 16.74 10.91
>
> 315 15556210 17:10 NW714 5 31.44 NW1298 -2 8.28 -0.89
>
> 316 15556211 17:11 NW1842 -9 0 NW327 -2 1373.66 1420.33
>
> 317 15556215 17:15 XJ2877 15 0 NW1842 -5 15.08 8.08
>
> 318 15556217 17:17 NW114 2 20.56 NW1252 9 33.75 63.75
>
> 319 15556218 17:18 NW327 5 1906.05 NW114 3 24.7 22.2
>
> 320 15556220 17:20 XJ3166 70 777.14 NW860 -2 103.44 127.88

In this table, the Rescheduled Cost column includes the fuel cost for
speedup or slowdown. To help illustrate the swaps, we have inserted
lines that connect the flights before and after resequencing. Because we
display the start of a fractured bank, few slots are available. Thus, in
order to move up NW861 (from slot 301 to slot 299) to obtain a \$3300
savings, we must move several other flights. Because there are no extra
slots, it is not obvious how to do these swaps manually. Furthermore,
the aggregate of swaps involves almost all of the flights, although many
of the swaps are very small. NWA feels that the cost of a swap of less
than five minutes is in the noise level. There is no real penalty to
small moves, but unless the move produces significant savings, perhaps
it should be avoided. We discuss the effect of requiring a minimum
savings level in the *Results of the Analysis* section.

![](media/image5.wmf){width="5.118055555555555in"
height="8.990972222222222in"}

![](media/image6.wmf){width="5.778472222222222in"
height="7.084027777777778in"}

Figure 5. NWA arrival queue for Minneapolis on 7/30/1999 when the
airport was impacted by thunderstorms. Resequencing the arrival queue
could save over \$50,000 for the day.

#### Extra slots

It is an unnecessary (and usually inaccurate) constraint to restrict NWA
to only use its slots for swaps. Although there may be no extra slots
available in the middle of a bank, there are certainly many available
between banks at the NWA hubs. We decided to add extra slots to the
model to see how the optimizer would use them.

For DTW, we determined the weather conditions and hence the airport
acceptance and departure rates. We also obtained the OOOI data for all
other airlines landing at the airport, although there were some
discrepancies in this data, and unscheduled traffic is not included. We
also traded off departure and arrival slots when necessary to come up
with a list of times when extra landing slots would be available.

To insert these extra slots into the model, we created a fictitious
airline (JR) that carries no passengers, flies planes that have no fuel
charges, with crews that incur no block delay. Consequently, these
flights can be moved at will with no cost. We inserted these flights
into the input data and reran the DTW cases for three days. We can
illustrate some of the results with excerpts from the DTW run for
7/30/1999

Table 5. Slot usage when extra landing slots (JR flight numbers) are
added.

> **Slot Local Original Minutes Original Resched Minutes Optimum Resched
> Swap? Empty**
>
> **Number Time Late Cost Flight Late Cost Cost Slot?**
>
> Start of a bank
>
> [740 19:00 JR10259 -19 0.00 JR10259 -19 0.00 0.00 0 1]{.mark}
>
> [741 19:01 JR10260 -19 0.00 JR10260 -19 0.00 0.00 0 1]{.mark}
>
> [742 19:02 JR10261 -19 0.00 JR10261 -19 0.00 0.00 0 1]{.mark}
>
> [743 19:03 JR10262 -19 0.00 JR10262 -19 0.00 0.00 0 1]{.mark}
>
> [744 19:04 JR10263 -19 0.00 NW1192 -27 244.86 311.53 1 1]{.mark}
>
> [745 19:05 JR10264 -19 0.00 JR10263 -18 0.00 0.00 1 1]{.mark}
>
> [746 19:06 JR10265 -19 0.00 NW330 77 8,812.94 8,922.94 1 1]{.mark}
>
> [747 19:07 JR10266 -19 0.00 JR10264 -17 0.00 0.00 1 1]{.mark}
>
> [748 19:08 JR10267 -19 0.00 JR10265 -17 0.00 0.00 1 1]{.mark}
>
> [749 19:09 JR10268 -19 0.00 NW1417 87 5,290.45 5,360.45 1 1]{.mark}
>
> 750 19:10 NW268 -27 0.00 JR10266 -16 0.00 0.00 1 0
>
> [751 19:11 JR10269 -19 0.00 JR10267 -16 0.00 0.00 1 1]{.mark}
>
> 752 19:13 NW1192 -18 844.69 JR10268 -15 0.00 0.00 1 0
>
> 753 19:15 NW642 -14 648.00 NW268 -22 0.00 -22.00 1 0
>
> 754 19:15 XJ2975 -10 0.00 JR10269 -15 0.00 0.00 1 0
>
> 755 19:16 NW330 87 10,662.73 NW642 -13 648.00 645.67 1 0
>
> 756 19:17 NW696 -9 72.00 XJ2975 -8 0.00 -1.67 1 0
>
> 757 19:19 NW1417 97 6,383.39 NW696 -7 72.00 68.11 1 0
>
> 758 19:20 XJ3097 -10 0.00 XJ3097 -10 0.00 0.00 0 0
>
> 759 19:21 XJ3580 -9 0.00 XJ3580 -9 0.00 0.00 0 0
>
> End of a bank
>
> 916 21:50 XJ3326 -10 0.00 XJ3326 -10 0.00 0.00 0 0
>
> 917 21:50 XJ3362 -1 0.00 XJ3362 -1 0.00 0.00 0 0
>
> 918 21:50 NW749 2 72.00 NW749 2 72.00 72.00 0 0
>
> 919 21:53 NW1571 -2 288.00 NW1721 0 22.62 22.62 1 0
>
> 920 21:53 NW1721 0 22.62 XJ3561 4 24.84 58.17 1 0
>
> 921 21:54 NW443 -11 0.00 NW231 5 30.16 61.27 1 0
>
> 922 21:55 XJ3347 4 0.00 XJ3588 27 0.00 4.17 1 0
>
> 923 21:56 XJ3588 28 4.14 NW1571 1 288.00 282.56 1 0
>
> 924 21:58 XJ3561 9 45.54 NW443 -7 0.00 -7.00 1 0
>
> 925 21:59 NW231 10 193.01 XJ3347 8 0.00 -3.00 1 0
>
> [926 22:00 JR10338 -19 0.00 NW1441 20 59.06 121.28 1 1]{.mark}
>
> [927 22:01 JR10339 -19 0.00 NW990 6 0.00 40.00 1 1]{.mark}
>
> [928 22:02 JR10340 -19 0.00 NW1189 14 1,834.56 1,892.89 1 1]{.mark}
>
> [929 22:03 JR10341 -19 0.00 NW1754 123 5,409.07 5,471.29 1 1]{.mark}
>
> 930 22:06 NW990 11 14.00 NW339 13 0.00 73.33 1 0
>
> [931 22:07 JR10342 -19 0.00 NW1410 5 98.62 168.62 1 1]{.mark}
>
> [932 22:08 JR10343 -19 0.00 NW694 5 73.00 111.89 1 1]{.mark}
>
> 933 22:09 NW1441 29 247.88 JR10338 -10 0.00 0.00 1 0
>
> [934 22:10 JR10344 -19 0.00 JR10339 -10 0.00 0.00 1 1]{.mark}
>
> 935 22:10 NW1189 22 2,133.69 JR10340 -11 0.00 0.00 1 0
>
> [936 22:11 JR10345 -19 0.00 JR10341 -11 0.00 0.00 1 1]{.mark}
>
> 937 22:12 NW1754 132 5,945.72 JR10342 -14 0.00 0.00 1 0
>
> 938 22:13 NW339 20 120.26 JR10343 -14 0.00 0.00 1 0
>
> 939 22:14 NW694 11 82.00 JR10344 -15 0.00 0.00 1 0
>
> [940 22:15 JR10346 -19 0.00 JR10345 -15 0.00 0.00 1 1]{.mark}
>
> [941 22:16 JR10347 -19 0.00 JR10346 -18 0.00 0.00 1 1]{.mark}
>
> [942 22:17 JR10348 -19 0.00 JR10347 -18 0.00 0.00 1 1]{.mark}

The first set of flights is from the start of a bank. The empty slots
are shaded in gray and are originally occupied by JR flight numbers. The
usage of the extra slots is indicated in the last two columns of the
table. Without the extra slots, late flights at the start of a bank have
no earlier slots available. Adding these extra slots at the start of the
bank enabled a large savings for NW330 and NW1417 that were actually
scheduled to arrive in an earlier bank. At the end of a bank, late
flights "straggle in," and extra slots among these stragglers enable
flights such as NW1754 to move forward from slot 937to slot 929. Extra
slots at the end of a bank also enable early flights to move back
(beyond the bank end) to make earlier slots available for late NWA
flights.

#### The Flight Leg Viewpoint

The slot viewpoint displays *how* savings can occur by swapping slots,
but not *why*. To understand where costs and savings occur, we must
examine the effect of a swap upon the flight involved.

Consider NW560 landing at MSP at 9:40 am. Although it only lands 3
minutes late, it is 20 minutes late by the time it reaches the gate and
kicks off a delay chain:

> NW561 MSP to DEN uses equipment from NW560
>
> NW580 DEN to MSP uses equipment and crew from NW561
>
> (only "ripple delay" costs past here)
>
> NW580 MSP to MCO uses equipment from NW580
>
> NW577 from MCO to MSP uses equipment and flight attendants from NW580

This chain can be represented graphically in Figure 6. In this plot, the
actual, scheduled, and modeled block times for each leg are displayed.
It appears that NW561 was scheduled to depart before its equipment was
scheduled to arrive. This is an obvious indicator that there was a
change in the original equipment schedule. The equipment for NW561
didn\'t arrive and NW560\'s equipment was substituted. So, the whole
cost of delay for flight 561 is not attributable to 560\'s late arrival.
Nonetheless, if flight 560 were to arrive earlier, 561 could leave
earlier and save costs for the airline, so the savings due to a move up
will be correct. Figure 6 also shows the situation after NW560 was
allowed to land 9 minutes earlier. The four downline flights are each
delayed 9 minutes less for a time savings of 45 minutes.

In our model, landings at hubs are treated as independent events. In
this example for NW560, although NW580 from DEN to MSP was moved up 9
minutes because of the resequencing of NW560, when we resequence the
NW580 arrival bank later in the day, we treat NW580 as arriving at its
actual *on* time.

  -----------------------------------------------------------------------
  ![](media/image7.wmf){width="5.760416666666667in"
  height="3.6354166666666665in"}

  Figure 6. Delay chain before and after resequencing for flight NW560.
  -----------------------------------------------------------------------

Table 6. Costs accumulated in the NW560 delay chain.

+---------------------------------+-----------------+--------+---------+
| **Flight Leg**                  | **Cost item**   | **Orig | *       |
|                                 |                 | inal** | *Resequ |
|                                 |                 |        | enced** |
+---------------------------------+-----------------+--------+---------+
| *NW 561 from MSP to DEN*\       | Ill will        | 5      | 4726.54 |
| delayed by NW560 equipment      | terminating     | 328.62 |         |
| available 97 min. late          | passenger       |        |         |
+---------------------------------+-----------------+--------+---------+
| *NW 580 from DEN to MSP*\       | Ill will        | 2      | 2057.34 |
| delayed by NW561 equipment      | terminating     | 165.46 |         |
| available 88 min. late\         | passenger       |        | 5149.78 |
| NW561 cockpit available 93 min. |                 | 5      |         |
| late\                           | Passenger       | 385.84 |         |
| NW561 attendants available 93   | connect cost    |        |         |
| min. late                       |                 |        |         |
+---------------------------------+-----------------+--------+---------+
| \-\-\-\-\-\-\-- End of          |                 |        |         |
| non-ripple delay costs          |                 |        |         |
| \-\-\-\-\--                     |                 |        |         |
+---------------------------------+-----------------+--------+---------+
| *NW 580 from MSP to MCO*\       | Ill will        | 2      | 2408.34 |
| delayed by NW580 equipment      | terminating     | 959.38 |         |
| available 78 min. late          | passenger       |        |         |
+---------------------------------+-----------------+--------+---------+
| NW 577 from MCO to MSP          | Ill will        | 3      | 2259.04 |
|                                 | terminating     | 289.44 |         |
| Delayed by NW580 equipment      | passenger       |        | 236.16  |
| available 59 min. late          |                 | 233.76 |         |
|                                 | Passenger       |        |         |
|                                 | connect cost\   |        |         |
|                                 | (The connect    |        |         |
|                                 | cost went up    |        |         |
|                                 | because luggage |        |         |
|                                 | costs do not    |        |         |
|                                 | increase        |        |         |
|                                 | monotonically.) |        |         |
+---------------------------------+-----------------+--------+---------+

Table 6 shows the costs that were attributable to each of the legs in
this delay chain. The passenger connect costs have three components: an
interrupted trip expense cost (ITE) for long delays, a luggage
misconnect cost which increases, then decreases, and finally increases
again, and a passenger misconnection cost. In this model, we assume that
passengers on legs that leave a hub terminate. If they arrive late, they
incur an ill-will cost for terminating passengers. Because we apply
resequencing a bank at a time (rather than for the whole schedule), we
terminate cost benefits from the resequencing after the NW580 leg.
Terminating any cost savings when a plane arrives at the next hub should
prevent double counting of the cost benefits that we claim for
resequencing.

The downline costs are added to the costs for the passengers on flight
560 to obtain the total costs as follows:

Table 7. Summary for NW560.

  ------------------------------------ ----------------- ----------------
  **Item**                             **Pre Swap**      **Post Swap**

  Slot number                          101               94

  Local slot time                      9:50 am           9:41 am

  Flight number                        NW560             

  Passengers                           143               

  Scheduled *in* time                  9:52 am           

  Minutes late                         20                11

  Block delay \$                       45.54             8.28

  Passenger delay \$                   0.00              0.00

  Passenger ill will                   115.25            0.00

  *Downline effects*                                     

  Delay \$                             12,879.92         11,933.66

  Ripple delay \$                      19,362.50         16,837.20

  Fuel costs for resequencing          0.00              66.67

  Total cost                           13,040.71         12,008.61

  Savings                                                1,032.10

  Delay minutes                        182               164

  Ripple delay minutes                 309               273

  DOT A14%                             Late              On time
  ------------------------------------ ----------------- ----------------

For NW560, most of the savings were due to downline effects. The only
direct costs attributable to this flight were a block time overage for
the crew, and a small passenger ill-will cost. After resequencing, this
flight had the further advantage of being less than 15 minutes late and
therefore improved the DOT A14% (the percentage of flights arriving
within 15 minutes of scheduled in time) on-time performance. However,
without utilizing extra slots, other flights are delayed, so the overall
improvement in the DOT14 percentage is small.

# Results of the Analysis

The model was run to determine the baseline cost of operation for the
day, before any resequencing was applied. Then, our (close to)
optimum-resequencing algorithm was applied and an "optimum" arrival
sequence was determined. The savings in delay minutes and actual dollar
cost were computed for each flight and then summed for the day. In the
case of resequencing, the optimization algorithm was applied using only
NWA slots. In a separate run, NWA flights were permitted to swap with
added empty slots at DTW. Because it was not feasible to determine empty
slot availability for all days of the study, we extrapolated the results
from 3 days in DTW.

Based upon the rationale described in previous sections, the results of
the study were annualized for NWA operations at the three hubs studied.
Subsequently, the results were extrapolated to other airline hub
operations based upon DOT delay figures.

#### Financial summary of resequencing

We looked at the dependency of the savings achieved and the number of
flights that were resequenced as a function of the minimum resequencing
cost (MRC). The results are shown in Figure 7. The maximum savings seem
to be achieved for an MRC of \$100. The reason for this is that it does
not pay to swap flights with a small cost saving because of the fuel
costs for speedup and slowdown . On the other hand, the savings do not
decrease very much as the MRC is increased to \$300, but the number of
resequenced flights decrease by nearly a factor of two (from about 300
to 150 flights). For the purposes of this study, we picked an MRC of
\$100 to achieve the maximum cost savings, but it would be interesting
to repeat the extrapolations for the \$300 case.

  -----------------------------------------------------------------------
  ![](media/image8.wmf){width="5.652777777777778in" height="3.5in"}

  Figure 7. Minimum resequencing cost dependence averaged over all NWA
  hubs and all days.
  -----------------------------------------------------------------------

The model run for an MRC of \$100 produced the results shown in Table 8
for cases where only NWA and NWA commuter slots were used for
resequencing. The entries are ordered according to their pre-swap DOT
A14% .

Table 8. Resequencing savings for NWA and its commuters if no extra
slots are used.

  ----------------- -------------- ----------- ------------ -------- ------------- -------- ----------- -------------- -----------
  **Date**          **Total        **NWA       **Commuter   **Pre    **Savings**   **Post   **Reseq.    **Reseq.       **Savings
                    Passengers**   Flights**   Flights**    Swap                   Swap     Flights**   Passengers**   Per
                                                            A14%**                 A14%**                              Flight**

  **Detroit**                                                                                                          

  8/4/1999          30558          354         150          62.4     \$42,941.44   67.5     343         21157          \$85.20

  7/31/1999         33667          294         131          64.6     \$36,248.06   66.7     283         22270          \$85.29

  4/8/1998          33310          358         126          69.8     \$28,190.19   72.6     385         27384          \$58.24

  7/30/1999         42753          363         172          82.6     \$30,182.78   85.1     285         24981          \$56.42

  8/1/1999          42673          330         140          83       \$27,444.17   87       324         29084          \$58.39

  4/7/1998          31201          356         127          84.3     \$9,538.84    88.8     307         21063          \$19.75

  8/5/1999          30230          369         169          84.6     \$14,209.63   86.4     310         16904          \$26.41

  8/2/1999          45580          364         165          90.7     \$10,943.97   92.6     293         23476          \$20.69

  8/3/1999          31039          368         169          91       \$7,155.47    93.2     259         14274          \$13.32

  4/6/1998          33297          354         128          92.4     \$5,648.43    93.8     252         19506          \$11.72

  **Memphis**                                                                                                          

  4/8/1998          10620          110         98           56.3     \$13,995.20   57.2     140         7475           \$67.28

  7/31/1999         11558          104         87           79.1     \$2,652.16    81.2     67          4352           \$13.89

  8/5/1999          13684          110         92           80.2     \$6,430.75    81.7     108         8022           \$31.84

  7/30/1999         13923          109         96           86.8     \$2,629.61    87.8     61          4220           \$12.83

  8/4/1999          13029          110         92           88.6     \$1,584.50    87.6     59          3784           \$7.84

  8/2/1999          13996          110         95           88.8     \$1,631.73    91.2     52          3839           \$7.96

  4/7/1998          9459           112         98           90.5     \$1,269.85    91.4     107         5489           \$6.05

  8/3/1999          12324          111         94           91.2     \$930.48      92.7     62          4154           \$4.54

  8/1/1999          13615          108         85           94.3     \$533.69      92.2     20          1879           \$2.77

  4/6/1998          11011          114         98           94.3     \$497.83      94.8     45          2958           \$2.35

  **Minneapolis**                                                                                                      

  7/30/1999         41682          333         121          60.4     \$53,255.69   62.2     326         32480          \$117.30

  7/31/1999         35711          325         125          74.8     \$44,444.47   76.6     297         24514          \$98.77

  4/6/1998          29425          311         141          79.7     \$25,981.49   81       342         21683          \$57.48

  4/8/1998          33119          315         145          79.7     \$23,614.97   85.4     339         24552          \$51.34

  4/7/1998          28506          316         142          81.6     \$19,013.58   83.5     324         20662          \$41.51

  8/1/1999          42698          350         138          85.4     \$27,865.47   88.9     261         24388          \$57.10

  8/4/1999          46348          362         150          86.7     \$23,264.44   90.1     341         32361          \$45.44

  8/3/1999          40149          360         155          87.8     \$22,857.69   90.8     344         27950          \$44.38

  8/2/1999          44889          364         152          89.6     \$26,362.17   91.8     372         33899          \$51.09

  8/5/1999          47909          363         153          89.8     \$28,394.92   91.5     290         27953          \$55.03
  ----------------- -------------- ----------- ------------ -------- ------------- -------- ----------- -------------- -----------

Using CODAS data, the total number of operations at DTW was plotted
against the actual landing time for NWA and its commuter flights. The
total arrival rate was then compared with the weather conditions and the
AAR from the Air Traffic Control System Command Center (ATCSCC) logs to
identify where additional landing slots were available. The additional
landing slots were then injected into the model for use within the
resequencing algorithm as described previously. Open slots were added
into the model for the days of July 30, 31, and August 1, 1999 as shown
in Table 9.

Table 9. Savings when extra slots were used at DTW.

  ----------- -------------- ----------- ------------ ------- ------------- -------- ----------- -------------- -----------
  **Date**    **Total        **NWA       **Commuter   **Pre   **Savings**   **Post   **Reseq.    **Reseq.       **Savings
              Passengers**   Flights**   Flights**    Swap                  Swap A14 Flights**   Passengers**   Per
                                                      A14 %**               %**                                 Flight**

  7/31/1999   33667          294         131          64.6    \$75,774.31   68.4     300         23548          \$178.29

  8/1/1999    42673          330         140          83      \$39,902.78   87.3     325         29470          \$84.90

  7/30/1999   42753          363         172          82.6    \$44,347.53   86.2     283         24900          \$82.89
  ----------- -------------- ----------- ------------ ------- ------------- -------- ----------- -------------- -----------

The tables above rank each day of operation by the pre-resequencing A14%
arrival performance and compute an average saving per flight operation
for each of the hub airports. We note here that in the model, we exclude
cancelled flights, which are included in the usual DOT On-Time
Percentage figures, hence the A14% notation.

We originally plotted the savings per flight versus the A14% On-Time
data and noticed that the data were fit well by a straight line at each
hub. However, the Memphis result differed from the MSP and DTW results.
By analysis, we determined that there is also a dependence on the number
of flights at a hub. Multiplying by the number of flights that day to
the −0.8 power brought the three straight lines closer together. This
value was normalized by the number of flights at DTW on a nominal day
(530). The results of this analysis are shown in Figure 8.

  -----------------------------------------------------------------------
  ![](media/image9.wmf){width="5.291666666666667in"
  height="4.138888888888889in"}

  Figure 8. The fit for the savings at each of the three NWA hubs. The
  results are also shown when extra slots are used at DTW.
  -----------------------------------------------------------------------

From this analysis, we decided to use the MSP results for extrapolation
when no extra slots are available. Accordingly, we can predict the
savings/flight by the following formulas:

> $$\frac{\text{savings}}{\text{flight}} = \left( \frac{\text{flights}}{\text{530}} \right)^{0\text{.}8}\left( \text{354}\text{.}\text{95} - 3\text{.}\text{74} \ast A\text{14}\text{\%} \right)$$

for the case in which only NWA -- commuter swaps were used, and

> $$\frac{\text{savings}}{\text{flight}} = \left( \frac{\text{flights}}{\text{530}} \right)^{0\text{.}8}\left( \text{620}\text{.}\text{85} - 6\text{.}\text{52} \ast A\text{14}\text{\%} \right)$$

for the case in which all open slots were used. When the DOT On-Time
percentage is above about 95%, no savings can be achieved with the \$100
MRC, so the negative values for savings/flight predicted by these
formulas do not occur.

Plotting the predicted savings/flight versus the actual savings/flight
without extra slots can assess the goodness of this prediction. (The
formula fits the cases with extra slots almost exactly.) The results of
this analysis are shown in Figure 9.

  -----------------------------------------------------------------------
  ![](media/image10.wmf){width="5.9944444444444445in"
  height="3.497916666666667in"}

  Figure 9. A test of the formula for predicted savings per flight.
  -----------------------------------------------------------------------

We used these formulas and the DOT Statistics for NWA Hubs for the
period 01/01/98 through 11/20/99 to extrapolate our results to a longer
operational period. The results for Detroit are plotted in Figure 10,
which shows the A14% and the savings per flight with and without extra
slots.

  -----------------------------------------------------------------------
  ![](media/image11.wmf){width="5.990277777777778in"
  height="4.520138888888889in"}

  Figure 10. A14% (top) and the savings per flight (bottom) for NWA at
  Detroit.
  -----------------------------------------------------------------------

Using these data for the three NWA hubs for this period of almost 2
years, we add up the savings achievable by NWA for each hub. Then we
calculate the daily total, and annualize the results for the cases where
only NWA and Airlink slots are used for swaps and when extra free slots
are used. The results are shown in Table 10.

Table 10. Summary of projected savings for NWA hubs.

  ----------- -------------- ----------- -------------- ------------ ----------- --------------
              **NWA +                                   **Extra                  
              Airlink Slots                             Unused                   
              Only**                                    Slots**                  

              **Period of    **Daily**   **Annual**     **Period of  **Daily**   **Annual**
              Figure 10**                               Figure 10**              

  **DTW**     \$ 12,657,373  \$ 18,892   **\$           \$           \$34,062    **\$
                                         6,895,434**    22,821,259               12,432,477**

  **MEM**     \$ 1,722,540   \$ 2,571    **\$ 938,399** \$ 3,136,150 \$4,681     **\$
                                                                                 1,708,499**

  **MSP**     \$ 7,846,138   \$ 11,711   **\$           \$           \$21,116    **\$
                                         4,274,389**    14,148,033               7,707,510**

                                                                                 

  **Total**   **\$                       **\$                                    **\$
              22,226,051**               12,108,222**                            21,848,487**
  ----------- -------------- ----------- -------------- ------------ ----------- --------------

Using the DOT On-Time Performance Reports for January through September
1999, airline operations at the major hub airports were analyzed. At
medium density airports the formula for both the "intra-airline slot
swapping" and "all open slot" values were applied to project potential
savings, given an assumption that the NWA cost model generally applies
to these operations. At high density hubs (ATL, DFW & ORD) only the
"intra airline swapping" formula was applied as an airport-specific
determination of how many additional landing slots might exist at these
airports during peak arrival time would need to be undertaken before any
credit for additional slots could be taken. The results for all these
airline hub operations can be summarized to estimate an industry-wide
annualized savings, and are shown in Table 11.

Table 11. Summary of Annualized Savings.

  ----------------- ------------- ------------------------ -----------------------
                                  **Savings**              **Savings**

  **Airport**       **Airline**   **Airline only Slots**   **All Open Slots**

  **ATL\***         **DAL**       \$ 15,855,173            \$ 15,855,173

  **CLT**           **USA**       \$ 3,610,138             \$ 6,474,808

  **CVG**           **DAL**       \$ 1,471,161             \$ 2,652,239

  **DEN**           **UAL**       \$ 2,740,567             \$ 4,937,415

  **DFW\***         **AAL**       \$ 6,693,129             \$ 6,693,129

  **DFW\***         **DAL**       \$ 436,946               \$ 436,946

  **EWR**           **COA**       \$ 2,650,660             \$ 4,707,271

  **IAH**           **COA**       \$ 2,458,417             \$ 4,428,237

  **LAX**           **UAL**       \$ 1,518,791             \$ 2,708,316

  **ORD\***         **AAL**       \$ 4,571,899             \$ 4,571,899

  **ORD\***         **UAL**       \$ 7,671,878             \$ 7,671,878

  **PHL**           **USA**       \$ 2,993,007             \$ 5,308,449

  **PHX**           **AWA**       \$ 2,122,502             \$ 3,784,348

  **PIT**           **USA**       \$ 2,391,137             \$ 4,283,630

  **SFO**           **UAL**       \$ 3,112,731             \$ 5,529,491

  **SLC**           **DAL**       \$ 609,090               \$ 1,111,329

  **STL**           **TWA**       \$ 2,830,283             \$ 5,142,910

                                                           

  **DTW**           **NWA**       \$ 6,895,434             \$ 12,432,477

  **MEM**           **NWA**       \$ 938,399               \$ 1,708,499

  **MSP**           **NWA**       \$ 4,274,389             \$ 7,707,510

                                                           

                                                           

                    **Total**     **\$ 75,845,729**        **\$ 108,145,953**

  \*Intra-airline                                          
  swapping only                                            
  ----------------- ------------- ------------------------ -----------------------

#### Operational summary of resequencing

The model results were analyzed to determine if any patterns existed
that would allow the CTAS to resequence flights based upon some
predetermined criteria. The following discusses potential criteria:

**Sequence by Aircraft Type\
**The model results for cost savings due to aircraft resequencing do not
indicate any correlation between resequenced aircraft and aircraft type.
There are instances when it is advantageous to move a larger aircraft,
such as an A-320, back to give way to a DC-9 that is operating late. In
other cases, swaps between DC-9s are very cost effective.

In some cases, it was observed that swapping a commuter flight for a
larger jet was often cost-effective; however, more analysis on this
result is required. The model discriminates against commuter aircraft
because we have no crew rotations, and only tail numbers for the ARJs.
Therefore, there are almost no downline delay chains, and the number of
passengers (and hence their delay costs) is small. The results may also
be anomalous due to the way that NWA schedules commuter aircraft. These
results are not conclusive.

**Sequence Aircraft by Schedule\
**The cost savings that were determined from the analysis of the model
generally resulted from moving up a late operating flight to a slot
occupied by an early flight. Thus, a rule that resequences flights such
that the operation approaches its original schedule might be a general
rule that could produce cost savings. It is certainly in accord with the
airline\'s connectivity plans. In this case, CTAS would need to know how
each flight is operating relative to its original schedule, not relative
to an amended flight plan ETA. This could be accomplished by accessing
the original arrival schedule intent from ETMS data and having CTAS
create a sequence that brings the fleet closest to that original arrival
schedule.

As the resequenced data were analyzed, we found that while a general
movement of aircraft toward their original schedule often resulted in an
optimum sequence, there is no obvious simple rule that achieves this
result. In some cases, we observed flights that departed early and
arrived early, but had positive costs due to exceeding the flight crew's
block time. If these flights were moved closer to their original
schedules, the costs of these flights would actually increase. If no
extra slots are available, for each flight that is moved forward,
another flight must move backward; often, an on-time flight can be
delayed with no cost penalty to achieve this swap. Passenger
misconnection and ill will heavily influence cost savings. Therefore, a
flight with many potential misconnecting passengers would have the
potential to save more delay costs than a flight where all passengers
terminate at the hub, regardless of which flight was operating closer to
the original schedule.

It follows that a key ingredient to implementing resequencing is the
ability to calculate the cost for each flight to land in each available
landing slot (including downline effects). If this is known, correct
resequencing decisions can be made. Operationally, airlines have all the
required data, but the passenger component is not yet integrated into
the flight operations data stream. Because most of the costs are
attributable to passenger ill will and misconnection costs, the ability
to calculate the "worth" of a given flight in real time is currently
unavailable.

**Interaction with Airline Operational Centers (AOCs)\
**The cost savings presented here resulted from detailed analysis of the
data and an optimized resequencing algorithm. The implementation of this
methodology represents a real-time collaboration between an AOC and an
ATSP; however, decision support tools to achieve this collaboration in
real-time do not exist and are not under development at this time. In
order to create an operational environment that emulates the current
analysis, interactive communication between AOCs and ATSPs is required.

The determination of optimum cost savings appears to be a function of
many variables. These variables are ultimately known to the airline;
however, all the information to determine the lowest delay cost sequence
is not presently available in real-time to the airline. It is clear that
the airline business rules and cost structures are the most significant
element in the cost equation, and the delay costs are strongly
influenced by the amount of operational delay for each aircraft. At
present, CTAS does not have any information to determine the optimum
sequence, and a massive upload of AOC operational information, including
highly proprietary airline business rules would be required for CTAS to
perform these computations. A more natural distribution of this
functionality would be for CTAS to present the AOC with updated arrival
sequences, including current sequence and projected *on* times, and
allow the AOC to determine the optimum situation based upon internal
information and the CTAS-provided sequence. This interchange would
continue as the real-life situation evolved and the airline AOC tools
would react to the sequence reality. In this scenario, CTAS would need
the following additional capabilities:

-   Accept the AOC's desired arrival sequence,

-   Determine the optimum method for ATC implementation of the desired
    sequence, and

-   Integrate, arbitrate, and resolve conflicts between the requests
    from multiple AOCs at a single hub.

These conclusions are based upon the study of a single airline operation
over a 10-day window within a two-year period. It is highly likely that
other airline operations, such as Federal Express at MEM, will have
considerably different definition for what is optimum in their arrival
sequence. These additional rules may provide for an interaction between
CTAS and an airport surface management system, allowing the opportunity
to develop a complete arrival management system.

In addition to CTAS, MITRE's Self-Managed Arrival Sequencing Tool
\[[^7]\] and Sabre's Dependability Predictor Model \[[^8]\] provide the
tools that allow airlines to influence their arrival queues. The results
from this study should provide airlines the mechanism to correctly
assess the "worth" of the planes in their arrival queues so that they
can use such tools to maximum benefit.

# Conclusions

The summary of bank operations was derived from NWA hub operations
during the ten-day assessment period. Our model of NWA operations and
costs was applied to determine the cost differences that can be obtained
by swapping arrival slots, either among just NWA flights or by also
using open slots. Annual savings resulting from preferential arrival
ordering for NWA operations at DTW, MSP, and MEM range from
approximately \$12 million when only NWA slots are used, to \$22
million, when empty arrival slots are available and utilized for
resequencing. These results assume that the 10 days studied were a
representative sample, and are subject to the caveats mentioned in this
paper. If we extrapolate to the major airline's hubs, the annual savings
that could be achieved with only intra-airline swaps would be over \$75
million, and over \$100 million if other available slots can be used.

Further conclusions are as follows:

-   Ripple delay costs are often dominant. Therefore, the airline
    connectivity must be known and the downline costs evaluated, to
    determine the effect of a slot change.

-   There are significantly fewer delay chains when the crew turn time
    is reduced from 45 minutes to the 35 minutes used in this study.

-   We have developed a method for near-optimum resequencing that works
    on a bank-by-bank basis.

-   There is a tradeoff between the cost savings and the number of
    resequenced flights. The cost savings is optimized with an MRC of
    \$100, but the number of flights is almost halved, with just a
    little less savings, if the MRC is \$300.

-   Moving late flights forward certainly yields savings. But, there may
    be no cost penalty for making an on-time flight a little later to
    create a landing slot.

-   In general, the cost savings increase linearly with decreased DOT
    A14%.

-   The savings seem to also scale as the number of flights to the 0.8
    power.

-   Resequencing has little effect on the overall A14% if extra slots
    are not added.

-   Adding extra (available) slots almost doubles the savings.

-   The extra slots are used to move late flights at the start of a bank
    forward or to find a slot for stragglers at the end of a bank. Extra
    slots would help greatly in the middle of a bank but few are
    available.

-   In general, moving late flights forward towards their original
    schedule reduces costs. However, for each flight that moves
    forwards, another must move backwards unless extra unused slots are
    available.

Acknowledgements

The authors wish to thank Nageswara Rao of Oak Ridge National Laboratory
for his helpful analysis of the resequencing algorithm. Andrew W. Danz,
Jay A. Friedman , and Todd S. Ekstrom from Northwest Airlines provided
the airline data used in this study, answered questions about it, and
provided general advice and insight into Northwest's operations.

Acronyms

A14% daily percentage of flights that arrive less than 15 minutes late
(excluding cancellations)

AAR Airport arrival (or acceptance) rate

AOC Airline operational center

ARJ Advanced regional jet

ATCSCC Air Traffic Control System Command Center

ATSP Air traffic service providers

CODAS Consolidated Operations and Delay Analysis Systems

CTAS Center Tracon Automation System

DTW Detroit Metropolitan Wayne County Airport

ECT Effective connection time

ETA Estimated time of arrival

ETMS Enhanced Traffic Management System

FAA Federal Aviation Administration

FL Flight level. (Aircraft fly with altimeters set to the ISA Standard
Sea Level Pressure setting of 29.92 inches or 1013.2 HP)

FL100 Flight level in hundreds of feet. 100 = 10,000 feet pressure
level.

GMT Greenwich mean time (ZULU)

ITE Interrupted trip expense cost

KCAS Knot calibrated airspeed (this is indicated airspeed corrected for

> probe position, compression effects and indicating error)

KCAS250 250 knots calibrated airspeed In the US (and most other
countries)

> aircraft are required to limit speed to 250 knots or slower below
> 10,000
>
> feet

MEM Memphis International Airport

MRC Minimum resequencing cost

MSP Minneapolis-St. Paul International Airport

NASA National Aeronautics and Space Administration

NWA Northwest Airlines

OAG Official Airline Guide

OOOI Out-Off-On-In

Vth V-speed threshold. This is the target runway threshold crossing

> speed for the aircraft at its landing weight

Vth+10 This is the typical \"final approach target speed\" (sometimes

> referred to as Vprog). For a large transport category aircraft, this
> represents the Vth speed landing flaps + 10 knots KCAS.

Biographies

#### James A. Rome

Jim Rome received all his degrees in Electrical Engineering from the
Massachusetts Institute of Technology. After he graduated with the Sc.D
degree in 1971, he joined Oak Ridge National Laboratory. He spent 25
years doing theoretical Plasma Physics and is a Fellow of the American
Physical Society. He has been Editor of the international newsletter
*Stellarator News* since its inception 11 years ago. Since 1990, Dr.
Rome has been involved with air traffic modeling. He studied a month\'s
worth of data to try to determine the capacity of the airspace in 1991.
More recently, he has been modeling the economic impact of allowing
airlines to reorder arrival queues at major hubs. Dr. Rome is also
working on computer security for a Department of Energy project that
allows electron microscopes and beamlines to be operated remotely across
the Internet. He is President and co-founder of Scientific Endeavors
Corp., producer of the *GraphiC* Scientific Graphics Library (used for
many of the plots in this paper). More details of Dr. Rome's current
activities are found on his Web page <http://www.ornl.gov/~jar>

*George F. (Rusty) Bell*.

Rusty Bell is an aviation professional with over 30 years experience in
commercial air operations. He founded GFB & Associates in 1997, which
offers a wide range of aviation consulting services in both the science
and business of air operations. He started his career in 1970 with Pan
American World Airway where he held a variety of dispatcher and
management positions serving in Europe, Middle East, Asia, and Africa.
Following transfer to headquarters, he was appointed Director of Flight
Control where he was responsible for all day-to-day flight operations.
In 1991, he joined Delta Air Lines as a senior manager in flight
operations where he worked on the development of advanced flight and
operations control systems. Experienced in the worldwide theatre of
flight operations, he is recognized as an expert in the field of Airline
Operations Control and Air Traffic Management. Qualified as an aircraft
dispatcher, with formal training as a navigator he is an active general
aviation pilot.

#### James H. Cistone

Jim Cistone has been manager of Advanced Programs for Lockheed Martin
Management & Data Systems in King of Prussia, Pennsylvania. In this
capacity he lead several tasks in aviation research for NASA. He is
Program Manager for Lockheed Martin\'s Advanced Air Transportation
Technologies (AATT) Research Project, which was awarded in November
1997. Cistone's background includes software and systems engineering for
government and commercial automation systems, the development of
automation systems for aviation and air traffic managament, and program
and project management.

Jim is an active commercial and instrument-rated pilot working toward
his flight instructor\'s rating. He was graduated from Muhlenberg
College with a B.S. in Physics and received an M.S. in Physics from
Drexel University. He also completed the Ph.D. course requirements in
Physics and Atmospheric Science at Drexel University.

Cistone has just moved to Rockville, MD where he assumes new duties with
Lockheed Martin Air Traffic Management.

#### William (Bill) S. Leber Jr.

Bill Leber, as a Chief Flight Dispatcher with Northwest Airlines,
oversees the Air Traffic Coordinator position at NWA's System Operations
Control Center. He was a key developer of NWA's industry-leading
strategic planning team and advocate of its extension to the FAA's Air
Traffic Control System Command Center. He is currently a qualified
Aircraft Dispatcher, and has served as a check airman and an
international Chief Flight Dispatcher.

Bill has been a participant in the Collaborative Decision Making efforts
since the early 1990's where he was a key contributor to the
implementation of the Oakland and Anchorage Center Track Advisory
systems. He is presently a participant in several areas of the Air
Transport Association's Collaborative Decision Making efforts including
Co-Chairmanship of the Collaborative Routing -- Long-term Working Group
He has been a member of NASA's ATM ESC since 1999

He has 10 years of air traffic management experience coordinating with
FAA, JCAB, Euro-control and other air traffic service providers in
Europe, Russia and the Pacific Basin. He has been with Northwest
Airlines since 1983. Before joining Northwest Airlines he was employed
by McDonnel Douglas Astronautics division (now Boeing) in St. Louis as
an Engineering Planner.

Bill is the former President and Co-founder of the Airline Dispatchers
Federation a non-union professional association. He earned his B.S. in
Aeronautical Administration at Parks College of St. Louis University. He
holds both an Aircraft Dispatcher and Private Pilot certificate..

#### Simon D. Rose

Mr. Rose is a technical project manager for Oak Ridge National
Laboratory and is involved in transportation and safety initiatives that
involve several federal agencies including the Federal Aviation
Administration (FAA) and National Aeronautics and Space Administration
(NASA). Mr. Rose has a B.S. Degree in Physics from the University of
Kent, England and joined ORNL in 1980. He has extensive experience in
system safety analyses, modeling and simulation and information systems
development.

Mr. Rose has a wide experience within the Department of Transportation
and several Department of Defense programs. Work including safety
information systems work in support of the U.S. Coast Guard and
technical analyses and regulatory assessments concerning oil pollution
law for pipelines and other transportation related facilities for the
Office of Pipeline Safety. His aviation safety and analyses work
includes support to the Collaborative Decision Making program, the
Global Aviation and Information Network program, and the Advanced Air
Transportation Technologies program.

#### Ronald W. Lee

Ron Lee received a B.S. in Information and Computer Science from Georgia
Tech in 1985 and an M.S. in Computer Systems from the Air Force
Institute of Technology in 1986. As an intelligence systems staff
officer, Mr. Lee was involved in the design and implementation of
several intelligence support applications. From 1989 until 1994 he
worked in the Data Systems Research and Development Division of
Lockheed-Martin Energy Systems on a variety of tasks including military
decision support tools and flight message processing and distribution
systems for the FAA. He was one of the principle developers of the
prototype CONUS data access tool (CONDAT) and participated in a
Congressionally-mandated study of U.S. Airspace capacity. Since joining
ORNL in 1994, Mr. Lee has architected and implemented distributed,
platform-independent, Web-accessible tools and applications supporting
the Defense Intelligence Agency and Defense Threat Reduction Agency. He
has a broad range of experience in object-oriented and distributed
architectures, software engineering, data analysis, and graphic data
representation.

[^1]: This study was performed for NASA Ames Research Center by Lockheed
    Martin Management and Data Systems under Contract No. NAS2-98004 as
    part of the TO-13 *Benefits Assessment of Airline-Influenced Arrival
    Scheduling*.

[^2]: \[?\]. Roger Beatty, Rose Hsu, Lee Berry, and James Rome,
    *Preliminary Evaluation of Flight Delay Propagation Through an
    Airline Schedule*, Air Traffic Control Quarterly, **74** (4) 259-270
    (1999).

[^3]: \[?\]. R. Dear, *Dynamic Scheduling of Aircraft in the Near
    Terminal Area*, Technical Report R76-9, Flight Transportation
    Laboratory, M.I.T. (September 1976).

[^4]: \[?\]. H. Psaraftis, *A Dynamic Programming Approach to the
    Aircraft Sequencing Problem*, Technical Report R78-4, Flight
    Transportation Laboratory, M.I.T. (October 1978).

[^5]: \[?\]. C. S. Venkatakrishnan, Arnold Barnett, and Amedeo R. Odoni,
    *Landings at Logan Airport: Describing and Increasing Airport
    Capacity*, Transportation Science, **27** (3) 211-227 (August 1993).

[^6]: \[?\]. Gregory C. Carr, Heinz Erzberger, and Frank Neuman,
    *Airline Arrival Prioritization in Sequencing and Scheduling*, in
    2^nd^ USA/Europe Air Traffic Management R&D Seminar, Orlando FL
    (December 1988).

[^7]: \[?\]. http://www.mitre.org/news/articles_99/msr.html

[^8]: \[?\] http://www.sabre.com/airline/airline_planning.html