Introduce a new method Ration-by-Weight of Efficiency (RBW) and Equity in the field of air traffic management flow control

1. Ration-by-Weight of Efficiency and Equity
A new allocation method in ground delay program
planning
Rong Wang, David J. Lovell, Michael O. Ball
University of Maryland ,College Park
1

2. Agenda
• Introduction: Background
• Introduction: Method of “Ration-by”
• Example of Three “Ration-by” Allocation Methods
• Practical Results of Three “Ration-by” Allocation Methods
• Ration-by-Weight of Efficiency and Equity (RBW) Method
• Practical Results of RBW Method
• Equity-based RBW (E-RBW)
• New Concept: Efficiency-Equity Ratio
• E-RBW Practical Results
• Solutions based on RBW
• Contribution & Conclusion
2

3. Introduction: Background
• Benefit of GDP: safer, costs less
• Scenario: if GDP is cancelled early
• Goal: compromise between efficiency and
equity
• This is a flight assignment problem
3

4. Introduction: Method of “Ration-by”
• The idea of Ration-by Method
1. Set up priority for flights by a certain standard
2. Assign slots to flights according to the priority
• RBS: Ration-by-Scheduled Time of Arrival
• RBD: Ration-by-Distance
• Can we try Ration-by-Scheduled Time of
Departure?
4

5. Example of Ration-by Allocation Methods
• Limit: STA ≤ CTA or the assigned slot time
RBS
f1
f2
f3
8:10
8:20
8:30
f1
f2
f3
8:10
8:20
8:30
RBD Ration-by-STD
f1
f2
f3
8:10
8:20
8:30
Flight STA Length STD
f1 8:00 60 min 7:00
f2 8:05 80 min 6:45
f3 8:10 83 min 6:47
STA Length STD
f1 f3 f2
f2 f2 f3
f3 f1 f1

6. Practical Results of Three Allocation Methods
• 4-hour GDP, 2 hours early cancellation time
• Efficiency: total expected delay
• Equity: total positive deviation from RBS slot time
• Max deviation: maximum deviation from RBS slot time of
a single flight
Methods Efficiency Equity Max deviation
RBD 2072 minutes 2346 minutes 244 minutes
Ration-by-STD 2413 minutes 1688 minutes 82 minutes
RBS 2988 minutes 0 minutes 0 minutes

7. Ration-by-Weight of Efficiency and Equity
(RBW) Method
• STD = STA – Length
w = k * STA – (1-k) * Length
• Give priority to flights with small value of w
• Ration-by-Weight of efficiency and equity
7
k w Method
0 - Length RBD
0.5 0.5*STD Ration-by-STD
1 STA RBS

8. Practical Results of RBW Method
• With increasing k , total
delays increase; equity
and max deviation
decrease monotonically.
• Earlier cancellation 
less total delays.
• Max deviation can be 244
minutes
• When k > 0.7, max
deviation ≤ 50 minutes
8
Figure1 Efficiency
Figure2 Equity & Max Deviation
0 0.2 0.4 0.6 0.8 1
0
1000
2000
3000
4000
Totaldelay
k
No early Cnx
1 hr. early Cnx
2 hrs. early Cnx
3 hrs. early Cnx
4 hrs. early Cnx
0 0.2 0.4 0.6 0.8 1
0
500
1000
1500
2000
2500
Equity
0 0.2 0.4 0.6 0.8 1
0
50
100
150
200
250
Equity
Max deviation
MaxDeviation
k

9. Equity Based RBW (E-RBW)
• Max deviation limit δ, slot time ≤ RBS+δ
• f1 , f2 , f3 with increasing scheduled time of arrival.
• w2 < w3 < w1 for a certain k, priority queue: f2 , f3, f1
9
Slot 1
Slot 2
Slot 3
Slot 4
f1
f2
f3
f3
f2
f1
f2
f1
f3
f2
f1
f3
f2
f3
f1
f2
f3
f1

10. Efficiency-Equity Ratio
• R =( dRBS – efficiency)/equity
• How valuable the slot exchanges are:
if flights in a GDP get N minutes additional
delay totally, the delay decrease of the
whole system is R*N minutes
10

11. E-RBW Practical Results
• Keep the same trend
as RBW but total
delays and equity
don’t change
monotonically
• Minimum total delay
does not necessarily
happen at k=0.
11
Figure 3 Efficiency
Figure 4 Equity & Max Deviation
0 0.2 0.4 0.6 0.8 1
0
500
1000
1500
Equity
0 0.2 0.4 0.6 0.8 1
0
10
20
30
k
Maxdeviation
Max deviation (Minutes)
Equity (Minutes)
0 0.2 0.4 0.6 0.8 1
500
1000
1500
2000
2500
3000
3500
4000
k
Totaldelay
No early Cnx
1 hr. early Cnx
2 hrs. early Cnx
3 hrs. early Cnx
4 hrs. early Cnx
k

12. E-RBW Practical Results
• 3 hours early Cnx
Max R = 0.565, k = 0.74
• 2 hours early Cnx
Max R = 0.275, k = 0.85
• When a GDP is cancelled
earlier, the Efficiency-
Equity Ratio is bigger.
• Higher max deviation
limit, better efficiency-
equity ratio.
12
Figure 6 Ratio at different δ
Figure 5 Max Ratio (SFO δ = 30)
0 0.2 0.4 0.6 0.8 1
0.1
0.2
0.3
0.4
k
Efficiency-equityRatio
Max deviation limt = 30
Max deviation limt = 20
Max deviation limt = 50
0 0.2 0.4 0.6 0.8 1
0.2
0.4
0.6
0.8
1
k
Efficiency-equityratio
2 hrs. early Cnx
3 hr. early Cnx

13. Which k Can Give Minimum Delay?
• Total delays decrease
when a GDP is
cancelled early.
• No rules for values of
k which give
minimum delay at
different cancellation
time.
13
Figure 7 k & Minimum Delays
(SFO)
Figure 8 k & Minimum Delays
(EWR)
5050 100 150 200 240
30003000
1000
2000
4000
Minimumdelay
24024050 100 150 200
0.750.75
0.25
0.5
1
k
k
Minimum Delay
Early Cancellation Time (Minutes)
Early Cancellation Time (Minutes)
24050 100 150 200
30003000
1000
0
2000
4000
Minimumdelay
24050 100 150 200
0.750.75
0.25
0.5
1
k
Minimum delay
k

14. Which k Can Give Max Efficiency-Equity Ratio?
• δ = 30 minutes.
• Max Ratios increase with
increasing earlier GDP
cancellation time.
• For SFO airport, the
interval of k is [0.7,1], if
we ignore two jumps.
• For EWR airport, the
interval of k is [0.8 ,1] ,if
we ignore one jump.
• The interval of k depends
on airports.
14
Figure 9 Ratio at difference Cnx (SFO)
Figure 10 Ratio at difference Cnx (EWR)
24050 100 150 200
0.750.75
0.25
0.5
1
MaxRatio
0 50 100 150 200
0.750.75
0.25
0.5
1
k
Max ratio
k
Early Cancellation Time (minutes)
24024050 100 150 200
0.750.75
0.25
0.5
1
Maxratio
0 50 100 150 200
0.750.75
0.25
0.5
1 k
k
Max ratio
Early Cancellation Time (minutes)

15. Solutions based on RBW & E-RBW
• Give weight of equity (k) or weight of efficiency (1-k)
directly.
• Give max deviation limit δ , and choose the solution with
minimum total delay.
• Give max deviation limit δ , and choose the solution with
maximum efficiency-equity ratio.
• Give max deviation limit δ , and choose average delay no
more than a certain value.
15

16. Contributions
• E-RBW provides a robust framework for
designing rationing methods based on a
small parameter space
• A new metric (efficiency-equity ratio) for
measuring rationing method performance
• A more efficient implementation of E-RBD
16

17. Conclusions
• This is an easily implementable framework
for rationing methods
• The design framework has been established,
but further guidance is needed to understand
the consequences of different design options
17

18. Acknowledgement
• I appreciate my parents’ support from
China. Dr. Michael O. Ball and Dr. David J.
Lovell also contributed a lot for the
research.
18

19. Count Delay
• Length(f1)<length(f2)
• STD(f1)<STD(f2)
• Under RBD, choose flight2
S(
i)flight2
flight1
t

20. RBD RBW Sequence Shift Comparison
-300
-250
-200
-150
-100
-50
0
50
100
1
7
13
19
25
31
37
43
49
55
61
67
73
79
85
91
97
103
109
115
121
127
133
139
145
151
157
163
169
175
181
187
193
199
205
211
217
223
229
235
241
247
RBD flight sequence No. minus RBS flight sequence No. at Slot1
RBD
-100
-80
-60
-40
-20
0
20
40
60
80
1
7
13
19
25
31
37
43
49
55
61
67
73
79
85
91
97
103
109
115
121
127
133
139
145
151
157
163
169
175
181
187
193
199
205
211
217
223
229
235
241
247
RBW flight sequence No. minus RBS flight sequence No. at Slot1
RBW

21. RBW vs. E-RBW
• When k = 0.85, we get best efficiency-equity ratio
for 2 hours early cancellation time
21
k=0.85 Efficiency Equity Max
Deviation
Efficiency-
Equity
Ratio
E-RBW 2667 1160 30 0.2753
RBW 2667 1170 42 0.2743
RBW 2673 1160 42 0.2716
RBW 2672 900 32 0.3511
RBW 2672 892 26 0.3543

22. RBW vs. E-RBW
2100 2200 2300 2400 2500 2600 2700 2800 2900 2988
0
500
1000
1500
2000
2364
Efficiency
Equity
• RBW can give some
solution with small
total delay.
• In some part, E-RBW
gives better solution
both in efficiency and
equity.
22
2640 2660 2680 2700 2720 2740 2760
950
1000
1050
1100
1150
1200
1250
1300
Figure 11 Efficiency-Equity Pair
Figure 12 Part of Efficiency-Equity Pair

23. RBW vs. E-RBW
0 0.2 0.4 0.6 0.8 1
0
20
40
60
80
100
120
140
160
180
200
k
NumberofUniqueFlightSequences
0 0.2 0.4 0.6 0.8 1
0
20
40
60
80
100
120
140
160
180
200
k
NumberofUniqueFlightSequences
Step 0.001 0.0005
RBW 957 1637
E-RBW 247 373
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
k
k
u

24. The Whole Picture
24

25. k in Four Quadrant (RBW)
25
2000 2500 3000 3500
0
500
1000
1500
2000
2500
3000
Efficiency
Equity
1st Quadrant
2nd Quadrant 3rd Quadrant
4th Quadrant