Evaluating Delay Cost Functions with
Airline Actions in Airspace Flow Programs
Michael Bloem
Haiyun Huang
yNASA Ames Research Centery
y
Science & Technology Corporation
Delft University of Technology
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ABC1
9:00
9:15
ABC2
2
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ABC1
9:00
9:15
ABC2
3
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ABC1
9:00
9:15
ABC2
30 flights/hour
4
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ABC1
10:00
9:00
10:30
9:15
ABC2
30 flights/hour
5
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ABC1
Slot #60
10:00
11:00
ABC2
Slot #90
10:30
12:00
6
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ABC1
Slot #60
10:00
11:00
ABC2
Slot #90
10:30
12:00
7
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Main Message
Evaluated sixteen functions that attempt to specify the cost
of delay to airlines
Quantified the consistency of the cost functions with airline
actions in Airspace Flow Programs
Airline delay costs increase in discrete steps as delay
exceeds thresholds and are larger for flights to hub airports
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Outline
The need for accurate airline delay cost functions
Evaluated delay cost functions
Data: airline actions in Airspace Flow Programs
Metrics to determine consistency of delay cost functions
with airline actions
Most consistent delay cost functions
Uncertainty in cost functions
Future work
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The Need for Accurate Delay Cost Functions
Accurate knowledge of airline delay cost functions enable air
navigation service providers to reduce airline delay costs
Example uses of delay cost functions:
Objective function for traffic flow management optimization
Simulate airline actions in new collaborative mechanisms
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Evaluated Delay Cost Functions
Number
1
2
3
4
5
6
7
8
9
10-16
Name
On-time Performance
Passenger Delay
Squared Delay
Squared Passenger Delay
Time-of-Day Delay
Connection Delay
Airline Connection Delay
Monetary Delay
Step Function
Combinations of numbers 1-9
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Connection Delay
100
Focus
Hub
Cost
50
Other
0
0
20
40
Delay [minutes]
60
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Step Function
400
Miss bag
connections
300
Miss next leg
Cost
200
100
0
0
Miss passenger
connections
Flight "late"
30
60
120
Delay [minutes]
180
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Outline
The need for accurate delay cost functions
Evaluated delay cost functions
Data: airline actions in Airspace Flow Programs
Metrics to determine consistency of delay cost functions
with airline actions
Most consistent delay cost functions
Uncertainty in cost functions
Future work
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Data Overview
“Simplified Substitution” messages specify flights, slots, and
airline matching
ABC1
Slot #60
10:00
11:00
ABC2
Slot #90
10:30
12:00
15
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Number of Messages per Airline
12
10
Number 8
of
6
Airlines
4
2
0
0
500
1000
Number of Messages
1500
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Number of Assigned Flights per Message
1200
1000
Number 800
of
600
Messages
400
Airline E
Airline G
200
0
0
50
100
Number of Assigned
Flights per Message
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Outline
The need for accurate delay cost functions
Evaluated delay cost functions
Data: airline actions in Airspace Flow Programs
Metrics to determine consistency of delay cost functions
with airline actions
Most consistent delay cost functions
Uncertainty in cost functions
Future work
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Airline Behavior Model
Assignment problem
Given: a cost for assigning each flight to each slot (from a
delay cost function)
Find: a way to assign each flight to exactly one slot with
the smallest total cost
ABC1
Slot #60
ABC1
Slot #60
10:00
11:00
10:00
11:00
ABC2
Slot #90
ABC2
Slot #90
10:30
12:00
10:30
12:00
First-Scheduled-First-Served
(FSFS) cost = 90
Minimum cost = 80
Airline cost = 80
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Costs Used in Metrics
Airline
matching
(from data)
Flights
& Slots
(from data)
FSFS
Optimal
cost
function k
FSFS
matching
Optimal
matching
cost
function k
Airline
cost
80
cost
function k
FSFS
cost
90
cost
function k
Minimum
cost
80
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First-Scheduled-First-Served Ratio
Cost function k
90
FSFS cost
80
Airline cost
Minimum cost
Airline cost
FSFS Ratio = FSFS cost
80
FSFS Ratio = 90
0
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Minimum Ratio
Cost function k
90
FSFS cost
80
Airline cost
Minimum cost
Airline cost
Minimum Ratio = Minimum cost
80
Minimum Ratio = 80 = 1
0
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Outline
The need for accurate delay cost functions
Evaluated delay cost functions
Data: airline actions in Airspace Flow Programs
Metrics to determine consistency of delay cost functions
with airline actions
Most consistent delay cost functions
Uncertainty in cost functions
Future work
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FSFS Ratio Results
Step Function is the first or second most consistent cost
function for every airline
400
300
Cost
200
100
0
0
30
60
120
Delay [minutes]
180
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Minimum Ratio Results
Connection Delay or Airline Connection Delay is the first,
second, or third most consistent cost function for every airline
100
Focus
Hub
Cost
50
Other
0
0
20
40
Delay [minutes]
60
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Outline
The need for accurate delay cost functions
Evaluated delay cost functions
Data: airline actions in Airspace Flow Programs
Metrics to determine consistency of delay cost functions
with airline actions
Most consistent delay cost functions
Uncertainty in cost functions
Future work
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Uncertainty in Cost Functions
delay cost = delay cost function + noise
Try to find the variance of the zero-mean Gaussian noise that
maximizes the likelihood of the observed airline actions
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Deterministic Simulation
ABC1
Slot #60
ABC1
Slot #60
10:00
11:00
10:00
11:00
ABC2
Slot #90
ABC2
Slot #90
10:30
12:00
10:30
12:00
Cost = 90
Minimum Cost = 80
1
Relative
0.5
Frequency
0
−100 −50
0
50 100 150 200
Cost
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Monte Carlo Simulations Using Cost Noise Estimate
ABC1
Slot #60
ABC1
Slot #60
10:00
11:00
10:00
11:00
ABC2
Slot #90
ABC2
Slot #90
10:30
12:00
10:30
12:00
Optimal in 44% of simulations
Optimal in 56% of simulations
0.4
Relative
0.2
Frequency
0
−100 −50
0
50 100 150 200
Cost
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Future Work
Use more complete data
Consider cancellations and route-outs
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Summary
Evaluated sixteen functions that attempt to specify the cost
of delay to airlines
Quantified the consistency of the cost functions with airline
actions in Airspace Flow Programs
Airline delay costs increase in discrete steps as delay
exceeds thresholds and are larger for flights to hub airports
[email protected]
[email protected]
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