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Determining an Optimal Airport Slot
Profile
Andrew Churchill
David Lovell
Michael Ball
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Goals
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Problem: How many slots should exist in different
time periods at an airport?
• Examine issues that influence how many slots
do/should exist
• Define methodology for determining this
number, considering mentioned issues
• Show case study for various scenarios at
LaGuardia
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Motivation
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• Cannot use simple IFR/VFR arrival rates to
define number of slots
– Not really one simple number for either of these
conditions
– Using the “IFR arrival rate” would leave the airport
underutilized most of the time
– Using the “VFR arrival rate” would leave the airport
very congested during marginal or worse conditions
• Need to define some criteria for finding a
middle ground
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Level of Service
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• Measure delays and cancellations
– Must balance these metrics against number of slots
available
• Number of slots closer to airport capacity
results in more delays and cancellations
• Airlines have the ability to make a tradeoff
between delays and cancellations
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Scheduling Value Trends
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• Some time periods are naturally more valuable
to travelers/airlines
– Scheduling – e.g. arrive before daylong meeting
– Geography – e.g. oceanic/transcontinental traffic
• Airlines know this – examine scheduling trends
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Scheduling Value Trends
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• JFK, July 16-20, 2007 (averaged weekdays)
More valuable
Less valuable
Number of scheduled arrivals
60 50 40 From ASPM
30 20 10 0 5 7 9 11 13 15 17 19 21 23 Time of day 6
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Recovery Periods
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• Well known that an airport cannot operate at
“peak” capacity during every hour of every day
• Schedule to peak capacity during most
desirable parts of the day
• Schedule to lower levels during less desirable
parts of the day to “recover” from earlier delays
– Earlier delay is most costly than later delay, as it can
propagate further through the NAS
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Recovery Periods
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• Example solution
40 Number of slots
30 High value
period
20 Recovery
period
10 0 6 8 10 12 14 16 Time of day 18 20 22 8
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Approach
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• Linear programming network flow approach D max D max Z 1 D max Z t­1 {q }
{X 1 ,q } Z t {q }
i 1 ,q i t­1 ,q {X t­1, q } {Y 1 ,q } ≤{C 1,q } D max Z T {q }
{X t,q } {Y t­2 ,q } {Y t­1 ,q } {Y t,q } ≤{ C t­1, q } ≤ {C t, q } Cancellation arcs
Landings
{q }
i t,q i T,q {X T,q } {Y T­1 ,q } {Y T,q } ≤ { C T, q } {Y T+1 ,q } {Y T+ U­1 ,q } ≤{C T +1, q } ≤{ C T +U, q } Delay arcs between periods
Individual time period
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Assumptions
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• Determine only the number of arrival or
departure slots
– The other will necessarily follow
• Number of slots in each time period
constrained by upper/lower bounds
– Allows for non-uniform slot profile
• Maximum delay length constrained
• Optimize across spectrum of capacity scenarios
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Capacity Scenarios
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Airport arrival capacity [arrivals/hour]
• Data from LGA 2003
40 40 30 30 20 20 Prob=0.49 Prob=0.40 10 0 10 7 9 11 1 3 5 7 9 11 0 40 40 30 30 20 7 9 11 1 3 5 7 9 11 20 Prob=0.07 Prob=0.03 10 0 From (Barry
Liu, Mark
Hansen
2005)
10 7 9 11 1 3 5 7 9 11 0 7 9 11 1 3 5 7 9 11 Time of day 11
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Assumptions
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• Determine only the number of arrival or
departure slots
– The other will necessarily follow
• Number of slots in each time period
constrained by upper/lower bounds
– Allows for non-uniform slot profile
• Maximum delay length constrained
• Optimize across spectrum of capacity scenarios
• All slots in time period have same “value”
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Slot “Values”
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• NEXTOR conducted congestion pricing strategic
simulation for LGA (2004)
– Ranged from $100 - $1200
• We use these prices to represent slot values in
each time period
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Mathematical Modeling Approach
NEXTOR • Objective: Maximize total value of slots
• Deterministic
queuing delay model å {
}
{
å
• Basic cancellation
{
} {
}
{
prediction model
{
{
} {
} • Specified delay
{
}
{
}
{
and cancellation
{
}
{
levels
å å
å ì
ü
max í Vt Z t ý
î t þ
Subject to Z t - X t ,q - i qt , q i = 0 "t Î 1, K, T , q Î 1, K , Q} X 1,q - Y1,q £ C1, q "q Î 1, K , Q
X t ,q + Yt -1,q - Yt ,q £ Ct , q "t Î 2, K, T , q Î 1, K , Q} Yt -1,q - Yt ,q £ Ct , q "t Î T + 1,K , T + U - 1} , q Î {1, K , Q} YT +U -1,q £ CT +U , q "q Î 1, K , Q
Dmin £ Z t £ Dmax "t Î 1,K , T
Yt , q £ Wt , q "t Î 1, K, T + U - 1 , q Î {1,K , Q} qt , q i £ Pi "t Î 1, K, T , q Î 1, K, Q} , i Î {1,K , N } X t ,q , Yt ,q , Z t , qt , q i Î ¥ +
"t Î 1, K, T , q Î 1, K , Q} , i Î {1,K , N } Yt, q - g
pq
q
Z t £ 0 t
t å p å åq
q
q
i
i t , q
t
- r å Z t £ 0 t Where
min{t +U , T +U } Wt ,q =
å
Ci, q "t Î {1, K, T + U - 1} , q Î {1, K, Q} 14
i =t +1 14
Results with Variable Profile
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• LaGuardia, using inputs shown earlier
40 40 30 30 Number of slots 20 10 0 6 10.0 mins, 2.00% 669 slots 10 14 18 22 20 10 0 6 40 40 30 30 20 10 0 6 15.0 mins, 2.00% 679 slots 10 14 18 22 20 10 0 6 Time of day
10.0 mins, 3.00% 680 slots 10 14 18 22 Non-uniform
slot profiles
permitted
15.0 mins, 3.00% 689 slots 10 14 18 22 15
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Results with Constant Profile
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• LaGuardia, using inputs shown earlier
37 Number of slots 36 9.9 mins, 1.97% 648 slots 0 6 10 14 18 22 9.9 mins, 2.99% 666 slots 0 6 Uniform slot
profiles
required
38 37 14.9 mins, 1.98% 666 slots 0 6 10 14 18 22 10 14 18 22 14.9 mins, 2.98% 684 slots 0 6 Time of day
10 14 18 22 16
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Comparison of Variable and Uniform
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• Difference in overall value of slots created
-5.83%
-4.93%
-4.74%
-3.66%
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Continuing Work
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• Develop criteria for determining to which
airports such a procedure is applied
• Consider other factors that influence when to
schedule operations (i.e. more than slot value)
• Change weighting used for each capacity
scenario
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