Transcript How do we measure deviation from ideal??

A General Approach to Equity in Traffic
Flow Management and Its Application to
Mitigating Exemption Bias in Ground
Delay Programs
Michael Ball
University of Maryland, College Park, MD
Thomas Vossen
University of Colorado, Boulder, CO
Robert Hoffman, Michael Wambsganss
Metron Aviation, Herndon, VA
1
Motivation for Ground Delay Programs: airline
schedules “assume” good weather
SFO: scheduled arrivals:
VMC airport acceptance rate:
IMC airport acceptance rate:
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
Basic RBS Allocation Principle
OAG Schedule:
arrival rate = 60/hr
AAL has
3 slots in
1st 10 min
Degraded Conditions:
arrival rate = 30/hr
AAL has
3 slots in
1st 20 min
Key Properties of RBS
• Allocation independent of current status of flights

– Not affected by information provided by airlines  no
disincentive to provide information
• Based on simple, well-accepted priority scheme
(first-come, first-served  first-scheduled, firstserved).
• Delay allocation has all flights as “close to the
average as possible”.
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/
21
/0
1
AAL
4/
14
/0
1
4/
7/
01
USA
3/
31
/0
1
DAL
3/
24
/0
1
3/
17
/0
1
UCA
3/
10
/0
1
3/
3/
01
UAL
2/
24
/0
1
2/
17
/0
1
COA
2/
10
/0
1
CJC
2/
3/
01
1/
27
/0
1
1/
13
/0
1
1/
20
/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 3rd 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/
21
/0
1
DAL
4/
14
/0
1
UCA
4/
7/
01
UAL
3/
31
/0
1
COA
3/
24
/0
1
-40
1/
6/
01
-40
4/
21
/0
1
-30
4/
14
/0
1
-30
4/
7/
01
-20
3/
31
/0
1
-20
3/
24
/0
1
-10
3/
17
/0
1
-10
3/
10
/0
1
0
3/
3/
01
0
2/
24
/0
1
10
2/
17
/0
1
10
2/
10
/0
1
20
2/
3/
01
20
1/
27
/0
1
30
1/
20
/0
1
30
1/
13
/0
1
40
1/
6/
01
40
CJC
3/
17
/0
1
TWA
3/
10
/0
1
AAL
3/
3/
01
USA
2/
24
/0
1
DAL
2/
17
/0
1
UCA
2/
10
/0
1
UAL
1/
27
/0
1
COA
1/
20
/0
1
CJC
1/
13
/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
Distribution of delay among
flights by airline:
Current allocation
Allocation by new procedure
300
100
250
90
250
80
200
num
of
flights
70
200
60
150
50
150
100
40
100
30
50
20
50
10
0
0
15
30
45
60
75
90 105 120 135 150 165 180 >180
0
15
30
45
Delay in minutes
60
75
90
105 120 135 150 165 180 >180
15
30
45
60
75
90
105 120 135 150 165 180 >180
Distribution of delay among
flights by airline (cont):
Current allocation
Allocation by new procedure
num
of
flights
50
500
45
450
40
400
35
350
30
300
25
250
20
200
15
150
10
100
5
50
0
0
15
30
45
60
75
90 105 120 135 150 165 180 >180
15
30
45
60
75
Delay in minutes
90 105 120 135 150 165 180 >180
15 30 45 60 75 90 105 120 135 150 165 180 >180
Generality within GDPs
• Can easily be adapted to manage program dynamics:
whenever revisions to programs are required, make
changes to approximate “ideal” as best as possible.
• Can be modified to handle other “constraints” on
allocation, e.g. handling “pop-ups”.
• Provides single approach to both RBS and
compression.
• Could apply other measures/models of deviation
from idea, e.g “vertical” models.
• Could be used with other definitions of an ideal
allocation.
General Approach to Equity in
Air Traffic Management
• Define ideal allocation
• Generate optimization model that
minimizes deviation between actual
allocation and idea.