Resource Rationing and
Exchange Methods in Air Traffic
Management: Part 1
Michael Ball
R.H. Smith School of Business & Institute for Systems Research
University of Maryland
College Park, MD
joint work with Thomas Vossen
1
Motivation for Ground Delay Programs: airline
schedules “assume” good weather
SFO: scheduled arrivals:
VMC airport acceptance rate:
IMC airport acceptance rate:
SCHEDULED ARRIVALS AND CURRENT ARRIVAL RATE BOUNDARIES, REDUCED RATE
CONDITIONS
18
16
14
12
10
8
6
4
2
0
7
8
9
10
11
12
13
Arrivals
14
15
Facility Est.
16
17
Model Est.
18
19
20
21
Ground Delay Programs
delayed
departures
delayed departures
delayed arrivals/
no airborne holding
delayed departures
Collaborative Decision-Making
Traditional Traffic Flow Management:
• Flow managers alter routes/schedules of individual flights
to achieve system wide performance objectives
Collaborative Decision-Making (CDM)
• Airlines and airspace operators (FAA) share information
and collaborate in determining resource allocation; airlines
have more control over economic tradeoffs
CDM in GDP context:
• CDM-net: communications network that allows real-time
information exchange
• Allocation procedures that increase airline control and
encourage airline provision of up-to-date information
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]
Note:
- reduced capacity is partitioned into sequence of arrival slots
- ground delays are derived from delays in arrival time
Issues
• What is an ideal (fair) allocation?
• How can an allocation be generated that is
very close to the ideal while taking into
account dynamic problem aspects?
Issues
• What is an ideal (fair) allocation?
• How can an allocation be generated that is
very close to the ideal while taking into
account dynamic problem aspects?
Determining fair shares
Sketch:
• Assume slots are divisible
– leads to probabilistic allocation schemes
• Approach: impose properties that schemes need to satisfy
– fairness properties
– structural properties (consistency, sequence-independence)
OAG
Schedule
AA654
US345
AA455
…
…
…
vs
Slots
Available
Allocation Principles
How to allocate limited set
of resources among
several competing
claimants???
First-come, firstserved: strict priority
system based on oag times
⇔ RBS
1
Equal access: all
claimants have equal priority
⇔% slots received by airline
= % flights scheduled in time
period
1
2
1
3
1
4
1
5
1
6
1
7
1
Comparison
• First-come/first-served – RBS:
– implicitly assumes there are enough slots to go around,
i.e. all flights will be flown
– lexicographically minimizes max delay
– implicitly treats flights as independent economic
entities
• Equal Access:
– implicitly assumes there are not enough slots to go
around – some flight/airlines will not receive all the
slots they need
– does not acknowledge that some flights cannot use
some slots
– strict interpretation leads to Shapley Value
Equal Access to Usable Slots:
Proportional Random Assignment (PRA)
UA33
UA19
US25
US31
US19
Flight
shares
Slot 1
Slot 2
Slot 3
Slot 4
Slot 5
UA33
1/2
1/8
1/8
1/8
1/8
UA19
1/2
1/8
1/8
1/8
1/8
US25
-
1/4
1/4
1/4
1/4
US31
-
1/4
1/4
1/4
1/4
US19
-
1/4
1/4
1/4
1/4
1
1.25
1.50
1.75
2
.75
1.50
2.25
3
1
1
Cum wgt
UA
US
Airlines alloc
UA
US
1
1
1
Empirical Comparison
Deviation PRA vs. RBS (LaGuardia)
Minutes/flights
25
NWA
ACA
COA
UAL
AAL
DAL
USA
15
5
-5
-15
• On the aggregate, both methods give similar shares
• No systematic biases
4/2
4/0
1
4/1
7/0
1
4/1
0/0
1
4/3
/01
3/2
7/0
1
3/2
0/0
1
3/1
3/0
1
3/6
/01
2/2
7/0
1
2/2
0/0
1
2/1
3/0
1
2/6
/01
1/3
0/0
1
1/2
3/0
1
1/
9/
01
1/1
6/0
1
1/
2/
01
-25
GDP
Issues
• What is an ideal (fair) allocation?
• How can an allocation be generated that is
very close to the ideal while taking into
account dynamic problem aspects?
GDPs and Flight Exemptions
• GDPs are applied to an “included set” of flights
• Two significant classes of flights destined for the
airport during the GDP time period are exempted:
– Flights in the air
– Flights originating at airports greater than a certain
distance away from the GDP airport
• Question: Do exemptions induce a systematic
bias in the relative treatment of airlines during a
GDP??
Analysis of Flight Exemptions (Logan Airport)
4/2
1/0
1
AAL
4/1
4/0
1
4/7
/01
USA
3/3
1/0
1
DAL
3/2
4/0
1
3/1
7/0
1
UCA
3/1
0/0
1
3/3
/01
UAL
2/2
4/0
1
2/1
7/0
1
COA
2/1
0/0
1
CJC
2/3
/01
1/2
7/0
1
1/1
3/0
1
1/2
0/0
1
TWA
40
30
20
10
0
-10
-20
-30
-40
1/6
/01
Minutes/Flight
Deviation RBS (standard) vs RBS (+exemptions), Boston
GDPs
Flight exemptions introduce systematic biases:
• USA (11m/flt), UCA (18m/flt) “lose” under exemptions
GDPs as Balanced Just-in-Time Scheduling Problem
flts
Possible
deviation measures
horizontal deviation “ideal”
nb production rate
Xb Cumulative
production
Vertical deviation
na
time
• Airlines = products, flights = product quantities
• Minimize deviation between “ideal” rate and actual production
How do we measure deviation from ideal??
Number
allocated
to airline A
Ideal allocation to A
slots
How do we measure deviation from ideal??
Actual allocation to A
Number
allocated
to airline A
Ideal allocation to A
slots
Horizontal deviation: When did A get 3rd slot vs when should A get 3 rd slot??
Vertical deviation: After time t, how many slots did A receive vs how many
should have A received??
How do we minimize deviation from ideal??
Two models based on horizontal deviation
measure:
• Assignment model:
Min ∑ airlines∑slots (ideal slot k – actual slot k)2
• “Greedy Algorithm” – looks more like current
rbs
Also models based on vertical deviation
Flight Exemptions
USA
AAL
4/2
1/0
1
DAL
4/1
4/0
1
UCA
4/7
/01
UAL
3/3
1/0
1
COA
3/2
4/0
1
-40
1/6
/01
-40
4/2
1/0
1
-30
4/1
4/0
1
-30
4/7
/01
-20
3/3
1/0
1
-20
3/2
4/0
1
-10
3/1
7/0
1
-10
3/1
0/0
1
0
3/3
/01
0
2/2
4/0
1
10
2/1
7/0
1
10
2/1
0/0
1
20
2/3
/01
20
1/2
7/0
1
30
1/2
0/0
1
30
1/1
3/0
1
40
1/6
/01
40
CJC
3/1
7/0
1
TWA
3/1
0/0
1
AAL
3/3
/01
USA
2/2
4/0
1
DAL
2/1
7/0
1
UCA
2/1
0/0
1
UAL
1/2
7/0
1
COA
1/2
0/0
1
CJC
1/1
3/0
1
TWA
Deviation RBS ideal-Opt. model
2/3
/01
Deviation RBS ideal-RBS actual
• Minimize deviations using optimization model that incorporates
exemptions
• reduces systematic biases, e.g. USA from 11m/flt to 2m/flt,
UCA from 18m/flt to 5m/flt
Discussion
• Define “ideal” allocation
• Manage program dynamics based on models that
minimize deviation of actual slots allocated from
ideal allocation
• Provides single approach to both RBS and
compression
• Provides approach for mitigating bias due to
exemptions
• Other potential application, e.g. handling “pop-ups”