Resource Rationing and Exchange
Methods in Air Traffic Management
Part II
Thomas Vossen,
University of Colorado at Boulder
Michael Ball,
University of Maryland
GDPs under CDM
Resource Allocation Process:
• FAA: initial “fair” slot allocation
[Ration-by-schedule]
• Airlines: flight-slot assignments/reassignments
[Cancellations and substitutions]
• FAA: periodic reallocation to maximize slot
utilization
[Compression]
Compression Example
Slot made available
by canceled or delayed
flight
4:05
Earliest time
of arrival = 4:20
4:50
5:10
AAL 672
AAL 95
Compression Example
4:05
Earliest time of
arrival = 4:20
4:20
USA 51
UAL 234
USA 345
4:50
AAL 672
5:10
AAL 95
Slot Exchange Alternatives
• Compression as Reallocation
– Dynamic changes to airline “demand profiles”
necessitate (re)rationing
• Compression as Slot Trading
– e.g., Slot Credit Substitutions:
“I am willing to cancel flight f 1 if I can move up
flight f2”.
Slot Trading Opportunities
160
40
140
35
Cum. cnx (% of flts in gdp)
Cum. Subs (% of flts in gdp)
Airline Substitution/Cancellation Patterns
120
100
80
60
40
20
0
30
25
20
15
10
5
0
1
75 149 223 297 371 445 519 593 667 741 815
Cumulative minutes (from start of program)
1
51 101 151 201 251 301 351 401 451 501 551 601 651 701 751
Cumulative minutes (from start of program)
Consider potential benefits of extending slot
trading framework
– e.g., Increase offers submitted by airlines
Mediated Slot Trading
General Framework:
• Each airline submits a set of offers
• Offer:
– Oa,t : slots willing to give up
– Ra,t : slots required in return
• Mediator (FAA) determines which offers to
select and execute
– Alternate interpretation of Compression Procedure
Approach:
From 1-for-1 trades to 2-for-2 trades
• Compression
– 1-for-1 trading system, i.e. offers involve giving up
one slot and getting one in return (many offers
processed simultaneously)
• What about k-for-k or k-for-n offers, e.g. 2-for-2:
Trade??
Possible 2-for-2 trades:
1 up for 1 down: reduce
delay on 1
flight/increase delay on
another;
Model as reduce delay at
least d- on f1 in
exchange for increasing
delay at most d+ on f2.
2 down: reduce
delay on two
flights; handled by
2 “reduce delay”
single flight trades.
2 down: increase
delay on two
flights; not
reasonable.
Motivation
• Operationally significant delay levels often
follow a “staircase” pattern
45 Minutes and more
25 Minutes and more Crews misconnect
15 Minutes and more Passengers misconnect
Bags misconnect
1-15 Minutes
On-time performance
Minutes of Delay
Formulation of 2-for-2 trading problem as network
flow problem w side constraints:
slots
flights/slots
at least
side
constraint
at most
classes
Case Studies
Different Airline Objectives:
1. Maximize On-Time Performance
2. Minimize Passenger Delay Costs
Airline Objective:
On-time Performance
• Offers proposed:
“I am willing to delay flight f1, in return for a
delay reduction that will let flight f2 arrive
on time” (< 15 minutes delay)
– Additional use of “aspiration levels” to limit
additional delay
• Mediation Problem:
– Maximize number of offers executed
25
20
15
%Improvement
Global Max.
GDP
bo
s0
1-0
6-0
1
bo
s0
115
-0
1
bo
s0
119
-0
1
bo
s0
1-3
0-0
1
bo
s0
208
-0
1
bo
s0
214
-0
1
bo
s0
221
-0
1
bo
s0
2-2
6-0
1
bo
s0
310
-0
1
bo
s0
313
-0
1
bo
s0
321
-0
1
bo
s0
3-2
3-0
1
bo
s0
330
-0
1
bo
s0
4-0
8-0
1
bo
s0
4-1
8-0
1
bo
s01
-06
-01
bo
s01
-15
-01
bo
s01
-19
-01
bo
s01
-30
-01
bo
s02
-08
-01
bo
s02
-14
-01
bo
s02
-21
-01
bo
s02
-26
-01
bo
s03
-10
-01
bo
s03
-13
-01
bo
s03
-21
-01
bo
s03
-23
-01
bo
s03
-30
-01
bo
s04
-08
-01
bo
s04
-18
-01
% improvement
Airline Objective:
On-time Performance
Compression Benefits
2-for-2 Trading Model
• compression executed after flts
with excessive delay (>2hrs) are
canceled
• proposed offers: all at-least, atmost pairs that improve on-time
perf.
Compression
Global Max
40
40
35
35
30
30
10
10
5
5
0
0
GDP
Trading Model
25
20
15
Airline Objective:
On-time Performance
• Impact of limiting offers proposed:
– Use of “aspiration levels” to restrict willingness to delay
flights
Trading Improvement
40
35
% improvement
30
25
20
15
10
5
0
0
15
30
45
60
Aspiration Levels
75
90
105
Airline Objective:
On-time Performance
Summary
• 2-for-2 trading offers significant
improvement over Compression
– Approximates “global” optimum
• 2-for-2 trading improvements are “robust”
– Gradual performance degradation as offers are
restricted
Airline Objective:
Passenger Delay
• Offers proposed:
“I am willing to delay flight f1, in return for a
delay reduction on flight f2 that will reduce
net passenger delay by at least D minutes”
– Additionally, use of “staircase” pattern to
represent passenger delays
• Mediation Problem
– Maximize number of offers executed
Airline Objective:
Passenger Delay
• Two passenger delay minimization objectives
Improvement from
slot trading model:
90
90
80
80
Passenger Delays
70
70
Staircase Objective
60
60
% Improvement
50
40
30
50
40
30
20
20
10
10
0
0
01 1 1 1 01 1 1 1 01 1 1 1 1 01 1 1
20 /200 /200 /200 3/20 /200 /200 /200 3/20 /200 /200 /200 /200 7/20 /200 /200
/
6
1/ 1/13 1/20 1/27 2/ 2/10 2/17 2/24 3/ 3/10 3/17 3/24 3/31 4/ 4/14 4/21
GDP
1/6
/20
1/1 01
3/2
0
1/2 01
0/2
00
1/2 1
7/2
00
2/3 1
/20
2/1 01
0/2
0
2/1 01
7/2
0
2/2 01
4/2
00
1
3/3
/20
3/1 01
0/2
00
3/1 1
7/2
0
3/2 01
4/2
0
3/3 01
1/2
00
1
4/7
/20
4/1 01
4/2
0
4/2 01
1/2
00
1
% Improvement
Maximum achievable
improvement:
GDP
Airline Objective:
Passenger Delay
Summary:
• Trading benefits rely on “staircase”
structure of airline preferences
• Trading benefits limited by carriers which
operate smaller aircraft
– Potential benefits of allowing side payments
to compensate carriers for delay