Air Transportation Network Load
Balancing using Auction-Based Slot
Allocation
for Demand Management
George L. Donohue
Loan Le and C-H. Chen
Air Transportation Systems Engineering Laboratory
Dept. of Systems Engineering & Operations Research
George Mason University
Fairfax, VA
Harvard University
18 March, 2004
Outline
Necessity of Demand Management
History of US Demand Management
Auction model for airport arrival slots
 auctioneer optimization model
 airline optimization model
Atlanta airport case study
 simulated scenarios
 results and interpretation
Observations
Why Demand Management?
Over-scheduling causes delay and
potentially compromises safety
Number of Operations
TOTAL SCHEDULED OPERATIONS AND CURRENT
OPTIMUM RATE BOUNDARIES
60
50
40
30
20
10
0
7
8
9
10
11
12
Schedule
13
14
15
16
Facility Est.
17
18
19
20
Model Est.
Atlanta Airport - FAA Airport Capacity Benchmark 2001
21
Data Indicates Loss of Separation
Increases at High Capacity Fraction
Over-scheduling causes accident pre-cursor
events and potentially compromises safety
Hazard Reports 1988-2001
#reports
120
100
80
Near Midair Collision
Runway Incursion
Lost of Legal Separation
60
40
20
0
35
40
45
50
55
60
65
70
Percentage Capacity Used
Statistics at ATL, BWI, DCA and LGA airports (Haynie)
Observed WV Separation
Violations vs. Capacity Ratio
Number of < WVSS
Incidents Expected in
15 Minutes
Figure 6-5
Ratio of Incidents to Capacity Used
8
6
4
2
0
0
Haynie, GMU 2002
50
100
150
200
Percent of Capacity Used in 15 Minutes
BWI
LGA
Quadratic Model
Flight Banking at Fortress Hubs Creates
Inefficient Runway Utilization
Over-scheduling causes accident pre-cursor
events and potentially compromises safety
Under-scheduling wastes runway capacity
Number of Operations
TOTAL SCHEDULED OPERATIONS AND CURRENT
OPTIMUM RATE BOUNDARIES
60
50
40
30
20
10
0
7
8
9
10
11
12
Schedule
13
14
15
16
Facility Est.
17
18
19
20
21
Model Est.
Atlanta Airport - FAA Airport Capacity Benchmark 2001
Enplanement Capacity is More
Important than Operational Capacity
Small aircraft make inefficient use of runway
capacity
A TL
to ta l
ATL
total operations (OAG Summer
2000)
400
1
0 .9
0 .8
0 .7
350
300
seats/aircraft
250
0 .6
0 .5
200
0 .4
150
cumlativeshr
Cumulative
seat share
op
0 .3
100
0 .2
50
0 .1
0
0
0
00
.1
0
.2
0
.3
0
.4
0
.5
0
.6
0
.7
0
.8
.9
1
c u m u l a ti v
e
 Cumulative
flight share
Cumulative Seat Share vs. Cumulative Flight Share and Aircraft Size
fl i g
Excess Market Concentration May Lead
to Inefficient Use of Scare Resources
HHI is a Metric used to Measure Market
Concentration
Hirschman-Herfindahl Index
(HHI) is standard measure of
market concentration
Department of Justice uses to
measure the competition within
a market place
HHI=(100*si)2 with si is
market share of airline i
Ranging between 100 (perfect
competitiveness) and 10000
(perfect monopoly)
In a market place with an index
over 1800, the market begins to
demonstrate a lack of
competition
HHI Index
6000
5000
4000
3000
HHI Index
2000
1000
0
ATL EWR LAS LAX LGA MSP ORD PHX SEA STL
Airport
History of US Demand
Management
LGA Airport Slot Control
High-DensityRule
Slot ownership
Deregulation
1968
- Limited #IFR slots
during specific time
periods
- Negotiation-based
allocation
1978
1985
AIR-21
Apr
2000
Exempted from
Use-it-orHDR certain
lose-it rule
flights to
based on
address
80% usage
competition
and small
market
access
Lottery
Jan
2001
End of HDR.
What’s next?
2007
Cap of the -Congestion
#exemption pricing?
slots
-Auction?
Demand Management
Approaches
Administrative
 negotiation-based IATA biannual conferences
Economic
 weight-based landing fee: no incentive for large
aircraft – inefficient Enplanement capacity
 time-based congestion pricing: not reveal the true
value of scarce resources
 DoT supervised Market-based Auctions of
Arrival Metering-Fix Time Slots
Hybrid
Auction Model
Design Issues
 Feasibility
 package slot allocation for arrival and/or departure slots
 politically acceptable prices
 Optimality
 efficiency: throughput (enplanement opportunity) and delay
 regulatory standards: safety, flight priorities
 equity:
 stability in schedule
 airlines’ need to leverage investments
 airlines’ competitiveness : new-entrants vs. incumbents
 Flexibility
 primary market at strategic level
 secondary market at tactical level
Design Approach
 Objective:
 Obtain Better Utilization of Nation’s Airport Network
Infrastructure – Network Load Balancing
 Provide an Optimum Fleet Mix at Safe Arrival Capacity
 Ensure Fair Market Access Opportunity
 Increase Schedule Predictability - reduced queuing delays
 Assumptions
 Airlines will make optimum use of slots they license
 Auction rules: Bidders are ranked using a linear combination of:
 monetary offer (combination of A/C equipage credit and cash)
 flight OD pair (e.g. international agreements, etc.)
 throughput (aircraft size) ?
 airline’s prior investment ?
 on-time performance ?
Strategic Auction
Analytical Approach
Auction Model
Network Model
1
2
Bids
Schedules
Slots
Airlines
-Auctions only at
Capacitated Airports
-Auction Licenses
good for 5 to 10 years
5
3
Auctioneers
4
NAS
Analysis &
Feedback
Auction Model Process
Determine factor weights,
initial bids and increments
Simultaneous
bidding of
15-min intervals
More bids
than capacity
No
End auction process
Yes
Call for bids
Submit information
and bids
Sort the bids in
decreasing ranks
Local optimum
fleet mix order:
smalllarge
757heavy
Sequence flights
for each intervals
Auctioneer’s action
Airline’s action
Auctioneer Model
money
#seats
…
Bid vector Pj=
X= (x1
ARR
DEP
Package
Time window
1
…
i
i+1
…
96
P1
…
…
xj
Pj
…
Pj+1
xn)T
…
Weight vector
W = (w1 w2)T
1
1
Package
Time window
…
i
i+1
i+2
i+3
96
LP :
s.t.
P1
…
Pj
Pj+1
…
1 if Pj wins a round
0 otherwise
Pn
1
1
xj =
Pn
Rank of a bid vector : W·Pj
C = (WT·P1 … WT·Pj … WT·Pn)T
1
1
1
1
max
z = CTX
(ARR·X)i, (DEP·X)i lies within the Pareto frontier i
airlines’ combinatorial constraints
Atlanta’s VMC Auction Model
Capacity constraints for 15-min
bins:
100,100
arrival per hour
(ARR·X)i  25
(DEP·X)i  25
Let:
A=
ARR
,
DEP
b=
max
s.t.
ATL’s VMC capacity (April 2000)
25
25
departure per hour
z = C TX
AX  b
airlines combinatorial constraints
Airline Bidding Model
Bidding is all about scheduling
 Determine markets, legs, frequencies and departure
times
 Fleet assignment :
 (aircraft type,leg)
 line-of-flying (LOF): sequence of legs to be flown by an aircraft in the
course of its day
B
2,4
1,3
1,5
F
2,6
A
E
3,7
4,8
D
C
Simple Flight Schedule Example
Bidding is all about scheduling
 Determine markets, legs, frequencies and departure times
 Fleet assignment :
 (aircraft type,leg)
 line-of-flying (LOF): sequence of legs to be flown by an aircraft in the
course of its day
Daily arrivals and departures at A of one LOF:
B
time
2,4
1,3
1,5
F
C
Package
ARR
2,6
A
Time window
1
…
i
i+1
…
96
E
3,7
4,8
D
DEP
…
Pj
Pj+1
1
1
P1
…
…
Pn
1
1
1
Package
Time window
…
i
i+1
i+2
i+3
96
P1
1
1
Pj
Pj+1
…
Pn
1
1
1
1
1
1
simple package bidding
1
Schedule Banking Constraints
Bidding is all about scheduling
 Determine markets, legs, frequencies and departure times
 Fleet assignment :
 (aircraft type,leg)
 line-of-flying (LOF): sequence of legs to be flown by an aircraft in the
course of its day
Daily arrivals and departures at A of one LOF:
B
time
2,4
1,3
1,5
F
C
Package
ARR
2,6
A
Time window
1
…
i
i+1
…
96
E
3,7
4,8
D
DEP
…
Pj
Pj+1
1
1
P1
…
…
Pn
1
1
1
Package
Time window
…
i
i+1
i+2
i+3
96
P1
1
1
Pj
Pj+1
…
Pn
1
1
1
1
1
1
complex package bidding
1
Assume the Airlines have a Near Optimal
Schedule and Try to Maintain in Auction
 Airlines’ elasticity for changing schedule
15min
bids
withdrawn
15min
original scheduled
15-min interval
bids
withdrawn
 Airlines bid reasonably and homogeneously by setting an
upper bid threshold proportional to #seats (revenue)
 No fleet mix change
Airline Agent Tries to
Maximize Profit
Objective function: Maximize revenue and ultimately maximize
profit
Maximise
Subject to:
 (P  B )
s
s
s
Bs  M  ys
( B0T ) s  Bs  M  (1  ys )
To
bid or
not
Upper
bound
Lower
bound
to bid
for
forbids
bids
Bs    Ps
 ' min(  ( Ba,s ))   ( BA,s )

 Bs 
 ( B0T ) s   ys    Ps  ys
(W )5


( ( Ba,s ))   ( BA,s )


 ' min

T
a
B


(
B
)
s
0
s

  Bs  M  (1  y s )
(W ) 5




Airlines’ package bidding constraints
Variables:
{Bs}
{Ps}
M
ys
1
ys  
0
Bo

Bs ’
T
set of monetary bids
airline expected profit by using a slot
big positive value
binary value
if airline bids for slot s
otherwise
airport threshold vector
airline threshold fraction
old bid for slot s in previous round
Network Model used to
Evaluate Auction Effectiveness
11-node network
DEN
SFO
LAX
PHX
MSP
ORD DTW LGA
BWI
IAD
DFW
ATL
Runway capacity determined by
 Wake Vortex Separation Standards
(nmiles/seconds) (M. Hanson)
Trailing aircraft
Leading aircraft
Small
Large
B757
Heavy
Small
Large
B757
Heavy
2.5/80
4/164
5/201
6/239
2.5/68
2.5/73
4/115
5/148
2.5/66
2.5/66
4/102
5/136
2.5/64
2.5/64
4/101
4/104
 and a scale factor to account for runway
dependency
departure separation
arrival separation
Simulation scenarios
 Assumptions:
 Aircraft can arrive within allocated slots with Required Time-ofArrival errors of 20 seconds (using Aircraft RTA Capabilities)
 Auction items: Metering Fix Arrival Slots
 No combinatorial package bidding
 Bid values and minimum increments are relative to the value of initial
bid
 Input:
 Summer 2000 OAG schedule of arrivals to ATL (1160 flights)
 Scenario 1 (Baseline):
 OAG schedule
 Scenario 2 (Simple auction):
 Monetary Offer is the only determining factor
 Auction-produced schedule
Traffic levels and estimated
queuing delays during VMC
Scheduled arrivals (#operations/quarter hour)
50
40
30
ATL reported
optimum rate
20
10
0
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Estimated Average Runway Queuing Delay (min)
20
15
10
5
0
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Time (15-min bins)
Original Schedule
Auctioned Schedule
45 min maximum schedule deviation allowed,
no flights are rerouted
Results : Flight Deviations
~70%
-60
-40
-20
0
20
40
min
15-min max allowed
30-min max allowed
45-min max allowed
 Bell-shaped curves are consistent to the model assumption about airline
bidding behavior
 Curves are skewed to the right due to optimum sequencing that shifts
aircraft toward the end of 15-min intervals
Results : Auction metrics
#Flights to be rerouted
100
80
Average cancelled
arrivals in summer 2000:
23
60
40
23
20
0
#Seats to be rerouted
8000
6000
4000
2000
50
0
#Rounds
110
40
100
90
30
80
70
2.5
Average Auction Revenue Per Flight
(x $Initial Bid)
20
10
2
1.5
0
1
10
15
30
45
Maximum schedule deviation allowed (min)
30
50
70
90
V1
110
130
#seats of rerouted flights
Observations on
Research to Date
Simple Auctions could Exclude small airlines
and/or small markets from Hub Airports
 Simple Bidding Rules can Prevent this Problem
Number of flights to be rerouted is comparable to
the number of cancelled flights
Combinatorial Clock Auctions Offer a Promising
Market-Based approach to Demand Management
Auction Proceeds could be used as Incentives to
the Airports for Infrastructure Investments and to
the Airlines for Avionics Investments
Airlines Could bid with Avionics
Investment Promissory Notes
Increased Hub airport capacity is Dependent on
Aircraft being able to maintain Accurate TimeBased Separation (ROT and WV safety constraints)
Data Links, ADS-B, FMS-RTA and New Operational
Procedures will be required
Airlines could Bid with Script that constituted a
contract to equip their Aircraft with-in X years (i.e.
½ bid price)
Cash Bids could be used to replace PFC’s and go
directly to the Capacitated Airport’s Infrastructure
Investment Accounts
Future work
More airline and airport inputs
 Experimental auction Participation
Include Efficiency Rules
Include combinatorial bidding
Include pricing
Conduct experimental auctions
Backup
Observed Runway Incursions
One formal simultaneous runway occupancy
When
Where
Leader\Exit_time
Trailer\Thr_time
5,Mar,2002
ATL 26L
Large\8:27:31
B757\8:27:17
-14 sec
Several “near” simultaneous runway occupancies
When
Where
Leader\Exit_time Trailer\Thr_time
5,Mar,2002
ATL 26L
Large\8:22:06
Large\8:22:06
5,Mar,2002
ATL 26L
Large\8:22:50
Large\8:22:50
5,Mar,2002
ATL 26L
Small\9:05:32
Large\9:05:30
5,Mar,2002
ATL 26L
Large\1:16:04
Large\1:16:04
6,Mar,2002
ATL 26L
Large\2:43:32
Heavy\2:43:32
6,Mar,2002
ATL 26L
B757\8:35:06
Large\8:35:06
Out of 364 valid data points
ATL and LGA Aircraft
Inter-arrival Times
LGA & ATL Arrival Histograms
14
LGA in VMC N=168
Aircraft / RW / Hr (20 Sec. Bins)
12
LGA in IMC N=124
10
ATL IN VMC N=114
ATL in VMC N=323
8
6
4
2
0
20
40
60
80
100
120
140
160
Inter-Arrival Time (Seconds)
180
200
LGA Arrival Histograms Normalized by Arrival Rate
Displaying Positive or Negative Deviation from WVSS
Adherence
10
8
6
4
2
0
140
100
60
20
-20
VFR 33.8 Arr/hr
IFR 34 Arr/Hr
VFR 30.9 Arr/Hr
VFR 27 Arr/Hr
-60
Aircraft / RW / Hr (20 Sec.
Bins)
Perfect WVSS Adherence = 0
Seconds Deviation per Aircraft From
Perfect WVSS Adherence Value
ATL Arrival Histograms RW 27 Normalized by Arrival Rate
Displaying Positive or Negative Deviation from WVSS Adherence
15
10
D1P1 31 Arr/Hr
D1P2 35 Arr/Hr
D2P1 34 Arr/Hr
5
Secs. Deviation per Aircraft From Perfect
WVSS Adherence Value
140
120
100
80
60
40
20
0
-20
-40
0
-60
Aircraft/RW/Hr (20 Sec.
Bins)
Perfect WVSS Adherence Value = 0
ATL Arrival Histograms RW 26 Normalized by Arrival Rate
Displaying Positive or Negative Deviation from WVSS Adherence
20
15
D1P1 36 Arr/Hr
D1P1 39 Arr/Hr
D2/P2 39 Arr/Hr
10
5
Seconds Deviation per Aircraft From Perfect
WVSS Adherence Value
140
120
100
80
60
40
20
0
-20
-40
0
-60
Arrivals for 1 Runway in 20
Second Bins
Perfect WVSS Adherence Value = 0
Perfect WVSS Adherence Value = 0
10
8
6
4
2
0
180
140
100
60
20
-20
VFR 33.8 Arr/Hr
IFR 34 Arr/Hr
VFR 30.9 Arr/Hr
VFR 27 Arr/Hr
IFR 18.7 Arr/Hr
-60
Arrivals for 1 Runway in 20
Second Bins
Aircraft Wake Vortex Separation
Violations : LGA & BWI
Seconds Deviation per Aircraft From Perfect
WVSS Adherence Value
FAA Barriers to Change
FAA has an Operational and Regulatory
Culture
 Inclination to follow training that has
seemed to be Safe in the Past
FAR has NOT Changed to Provide
Operational Benefits from Introduction of
New Technology
Assumption that Aircraft Equipage would
be Benefits Driven did not account for
Lack of an ECONOMIC and/or SAFETY
Bootstrapping Requirement
FAA Investment Analysis Primarily
focus on Capacity and Delay
OMB requirement to have a B/C ratio > 1
leads to a modernization emphasis on
Decreasing Delay
In an Asynchronous Transportation
Network operating near it’s capacity
margin, Delay is Inevitable
Delay Costs Airlines Money and is an
Annoyance to Passengers BUT
 is Usually Politically and Socially
Acceptable
Hypothesis: Most Major Changes to the
NAS have been due to Safety Concerns
 1960’s Mandated Introduction of Radar Separation
 1970’s Decrease in Oceanic Separation Standards
Required a Landmark Safety Analysis
 1970’s Required A/C Transponder Equipage
 1970’s Required A/C Ground Proximity Equipage
 1990’s Required A/C TCAS Equipage
 1990’s Required A/C Enhanced Ground Prox.
Equipage
 1990’s TDWR & ITWS Introduction
 1990’s Mandated Development of GPS/WAAS