MIT
MIT
ICAT
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MIT
International
Center
for
Air
Transportation
Virtual Hubs:
A Case Study
Michelle Karow
karow@mit.edu
John-Paul Clarke
johnpaul@mit.edu
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Presentation Overview:
• Motivation
• Definition
• Characteristics
• Problem formulation
• Application at a major US carrier
• Limitations and future considerations
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Irregular operations at a hub airport can be crippling to an
airline schedule
• Reduction in capacity typically necessitates cancellations and delays
• Effects resonate network-wide and on all levels of operation (fleet,
maintenance, crew and passengers)
• Majority of irregularities caused by weather
Could airlines reduce the number of delays and cancellations by rerouting entire connecting banks to an airport with excess capacity?
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Re-directing flights through a virtual hub can provide relief to
the original hub with minimal disruption
• Shift connecting demand over two hubs, decreasing strain on the original hub
• Continuity of passenger flow, insuring a reduction in total passenger delay
• Capitalize on under-utilized airports
Definition:
A virtual hub is a predetermined alternative airport that during
irregular operations at the original hub, hosts connection
complexes to maximize passenger flow through the network.
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Sample virtual hub network
Origin
Original
Hub
Passengers destined
for the hub
Origin
Origin
Passengers connecting
to destinations not
served by the virtual
hub
Destination
Destination
Destination
Destination
Origin
Destination
Origin
Origin
Origin
Destination
Virtual
Hub
Destination
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Virtual hubs can be identified by the following characteristics:
• Low average daily delays
 Check FAA’s Airport Capacity
Benchmark report for delay rankings of
US airports
• Geographically equivalent location to
the original hub
Geographical
location
Average
Delays
Virtual Hub
Candidates
 Check relative location to existing
hub
•Excess capacity
 Track airline gate utilization
throughout the day, given low delays
indicate excess airport capacity
Excess
Capacity
Virtual
Hub
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Implementing a virtual hub network consists of two phases:
The Virtual Hub Model and The PRM
Virtual Hub Model
Accommodated Passengers
Disrupted Passengers
Add to the next
time window
Passenger Re-accommodation Module
(PRM)
Passengers that can be reaccommodated (and
itineraries)
Passengers that cannot be
accommodated
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Phase I: Implementing a virtual hub network
Anticipated Weather/ Ground Delay
Program
•Implemented in the
hours before the weather
is predicted to impact
the operations at the
original hub
• Solved iteratively over
connecting bank timewindows until weather
has cleared
Update Variables for
Next Time Window
• Maximizes passenger
flow, in turn minimizing
total passenger delay
Airport
Capacities
Passenger
Itineraries
Aircraft
Capacities
Time Window t1
Time Window t2
Maximize
Passenger Flow
Maximize
Passenger Flow
Original
Hub Flights
Virtual Hub
Flights
Original Flight
Schedule
Time Window tn
….
Delayed/
Cancelled Flights
Maximize
Passenger Flow
Adjusted
Itineraries
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Key Assumptions:
• Ground resource availability
• Crew and maintenance flexibility
• Passenger connections within a time window
• Passenger consent
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The virtual hub model is formulated as a mixed integer network
flow problem.
Input data:
• Size of the time windows
• Passenger itineraries
• Original flight schedules
• Airport capacities
• Aircraft capacities
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Objective function: Maximize passenger flow
Maximize    dij zijk
iO jD kH
Where:
O
D
H
dij
zijk
set of origins
set of destinations
set of hub airports {OH, VH, VHs}
demand from origin i to destination j
positive variable representing the fraction of demand traveling on
the network from origin i to destination j through hub k
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Subject to:
Definition of zijk: A path exists from origin to destination through a hub
zijk  wijk
i  O, j  D,k  H
wijk  xik
wijk  yik
i  O, j  D, k  H
wijk  xik  ykj  1
z
kH
ijk
1
i  O, j  D, k  H
i  O, j  D, k  H
i  O, j  D
Where:
wijk
binary decision variable that the network exists from origin i to
destination j through hub k
xik
binary decision variable that the network exists from origin i to
hub k
ykj
binary decision variable that the network exists from hub k to
destination j
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Subject to:
Airport capacity: Upper bounds on aircraft sent to a hub
x
iO
ik
 ck
k  H
Where:
xik
binary decision variable that the network exists from origin i to
hub
ck
capacity of hub k
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Subject to:
Aircraft Capacity: Upper bounds on the number of passengers on an aircraft
 
dij zijk  pi
i  O
 
dij zijk  q j
j  D
jD kOH ,VH 
iO kOH ,VH 
d
jD
d
iO
z  fi
i  O, k  VH s
z  gj
j  D, k  VH s
ij ijk
ij ijk
Where:
dij
demand from origin i to destination j
zijk
binary decision variable that the network exists from origin i to
destination j through hub k
pi, qj
aircraft capacity to and from the hub, respectively
fi,, gj
excess aircraft capacity on scheduled flights to and from the
virtual hub, respectively
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Subject to:
Hub choice: A flight is served either by the virtual hub or the original hub

kOH ,VH 
ykj  1

j  D
kOH ,VH 
xik  1
i  O
Conservation of Flow: Upper bounds on aircraft departures from hubs
x  y
iO
ik
jD
kj
 bk  0
k
Where:
xik
ykj
bk
binary decision variable that the network exists from origin i to
hub k
binary decision variable that the network exists from hub k to
destination j
number of aircraft on the ground from the previous time window
at hub k
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Phase II: Re-accommodating disrupted passengers
After the scheduling decisions are made for a time window, some passengers will
be disrupted and require re-accommodation.
Disrupted passengers for the virtual hub network include the following:
•A connecting passenger with their original flight from their origin serviced by the
virtual hub and their original flight to their destination serviced by the original hub.
•A connecting passenger with their original flight from their origin serviced by the
original hub and their original flight to their destination serviced by the virtual hub.
•A non-stop passenger with their original flight either to or from the original hub
serviced by the virtual hub.
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1st Leg diverted to
VH + 2nd leg on VHs
Destined
for OH
Accommodated
on a later flight
to OH
Originating
at OH
Accommodated
on a later flight
from OH
1-leg
itinerary
Disrupted
Passengers
from Virtual
Hub Model
1st Leg
diverted
to VH
2-leg
itinerary
1st Leg on VHs + 2nd leg
rescheduled from VH
2nd Leg
rescheduled
from VH
Accommodated
on a later flight
from VH
Accommodated
on a later flights
through OH
Accommodated
on a later flights
through OH
Accommodated
on a later flight
to VH
Re-accommodated Passengers
An overview of the Passenger Re-accommodation Module (PRM)
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A closer look:
Application of the Virtual Hub Network to a Major US Carrier
A thunderstorm was present at the original hub airport on March 9, 2002
while the virtual hub remained relatively unaffected.
For this day, throughout the network:
Domestic and International Flights
4,000
Number of Passengers
99,000
Distinct Itineraries
38,000
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Major delays plague the original hub while relatively minor
effects are felt at the virtual hub
Delayed Flights per Hub on March 9, 2002
180
Flights
delayed >15
minutes
160
Number of Flights
140
Flights
delayed >30
minutes
120
Flights
delayed >45
minutes
100
80
Flights
delayed >60
minutes
60
40
Cancelled
flights
20
0
OH Departures
OH Arrivals
VH Departures
VH Arrivals
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Input data: Size of the Time Window
The two-hour time window was selected to accommodate both the need for high
scheduling accuracy and a large percentage of passengers connecting in distinct
time windows.
Average Connection Time
151 minutes
Highest Frequency Markets
1 flight per 60
minutes
Size of the Time Window
120 minutes
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Input data: Passenger Itineraries
• Only the flight legs originating or arriving at the original hub were considered.
• Itineraries with international flight legs were treated as originating or arriving at
the original hub
• Itineraries with connections overlapping two time windows were separated into
two itineraries, originating and arriving at the original hub
Traveling through the original hub during
the period of irregular operations
Itineraries
Passengers
4,342
19,291
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Input data: Original Flight Schedules
• Only domestic flights are eligible for diversion to the virtual hub
• International flights operated by the airline are assumed to depart or arrive
within one time window of their schedule.
• International flights operated by the airline’s code-share partners are also
assumed to depart or arrive within one time window of their schedule.
Flights between 8am and 6pm at the
original hub
Domestic
International
548
46
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Input data: Virtual Hub Airport Capacities
• Track cumulative operations at the virtual hub airport throughout the day
• Bias the data to produce positive aircraft totals at the airport throughout the
day (account for aircraft kept overnight)
• Subtract the number of operations at the airport from the number of gates
to find the excess capacity per time window
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Throughout the day, the virtual hub is does not reach it’s
maximum gate capacity of 45 gates
Cumulative
Number of Aircraft for the Airline at the VH on March 9, 2002
45
40
30
25
20
15
10
5
Time in Hours
00
24
00
23
00
22
00
21
00
20
00
19
00
18
00
17
00
16
00
15
00
14
00
13
00
12
00
11
0
00
10
90
0
80
0
70
0
60
0
50
0
0
40
Number of Aircraft
35
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Subtracting the cumulative number of aircraft from the total
number of gates provides a measure of excess capacity
Excess Capacity for the Airline at the VH on March 9, 2002
50
45
35
30
25
20
15
10
5
Time in Windows
00
24
00
23
00
22
00
21
00
20
00
19
00
18
00
17
00
16
00
15
00
14
00
13
00
12
00
11
0
00
10
90
0
80
0
70
0
60
0
50
0
0
40
Number of Aircraft
40
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The excess capacity over the day is compressed into two hour time
windows to determine the VH excess capacity during irregular ops
100
Excess Capacity for the Airline at the VH on March 9, 2002
90
Number of Aircraft
80
70
60
50
40
30
20
10
0
800 -1000
1001-1200
1201-1400
Time Windows
1401-1600
1601-1800
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Input data: Virtual and Original Hub Airport Capacities
• The capacity at the original hub was reduced by 1/3 to reflect the reduction in the
airport arrival rate required by the ground delay program.
• The capacity at the virtual hub was the minimum number of gates to
accommodate all diverted flights.
Time Window
Scheduled
Domestic
Arrivals
Scheduled
Domestic
Departures
cOH:
Original Hub
Capacity
cvh:
Virtual Hub
Capacity
800 to 1000
35
57
21
19
1001 to 1200
41
58
28
19
1201 to 1400
47
42
32
19
1401 to 1600
59
53
40
19
1601 to 1800
33
37
22
19
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Input data: Aircraft Capacities
• Flights remain assigned to their originally schedule aircraft, regardless of which
hub airport they are sent to.
• Capacity for flights traveling through the original hub is the number of seats on
the aircraft.
• Capacity for scheduled flights through the virtual hub is the number of seats
minus the number of passengers booked on the flight (i.e., excess capacity).
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Phase I Implementation: The Virtual Hub Model
• Solution times for the time windows range from 5 minutes to over an hour,
depending on the sparsity of the data set.
• In each time window, the maximum number of aircraft were sent to the original
hub.
Time Window
Number of
Passengers
Constraints
Variables
Passengers Served
(Objective Function)
800 to 1000
4,436
26,304
12,247
4,037
1001 to 1200
6,191
31,311
14,566
5,747
1201 to 1400
5,139
26,019
12,112
4,753
1401 to 1600
6,298
41,100
19,099
5,852
1601 to 1800
3,122
16,639
7,762
2,978
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Phase II Implementation: PRM
• Passengers (and itineraries) not accommodated by the virtual hub model were
entered into the PRM after each time window.
• International passengers were considered disrupted if their domestic leg was
delayed by more than 4 hours (i.e., two time windows).
• Un-accommodated passengers are passengers that could not be accommodated by
the end of the day on flights traveling through either hub airport.
Time
Window
Passengers Not
Accommodated by
Virtual Hub Model
Re-accommodated
Passengers
Disrupted
International
Passengers
Un-accommodated
Passengers
800 to 1000
399
340
53
6
1001 to 1200
444
321
107
16
1201 to 1400
386
361
21
4
1401 to 1600
446
356
58
32
1601 to 1800
144
131
9
4
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Comparing Actual Recovery to the Virtual Hub Network
Actual Recovery
Virtual Hub
Network
Total Passengers
19,291
19,291
Number of Cancelled Flights
123
0
Passengers Requiring ReAccommodation
774
1,665
Disrupted International
Passengers
237
248
Un-Accommodated Domestic
Passengers
207
67
Passengers Delayed Over Two
Hours
14,123
838
94% reduction
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Limitations and Future Considerations:
• Number of airline gates is somewhat flexible; cannot ensure airports
will maintain good virtual hub candidacy.
•Crew constraints and contract conditions could limit feasibility and
increase diversion costs.
• Availability of ground resources may constrain the capacity of the
virtual hub.
• Iterating over time windows under-estimates abilities of weather
forecasting while optimizing over multiple time windows adds
complexity and non-linearity.
•Consideration of re-accommodating passengers on scheduled non-stop
flights will provide a better (or equivalent) solution.