A V I A T I O N O P E R A T I O N S R E S E A R C H

N A T I O N A L C E N T E R O F E X C E L L E N C E F O R

N E X T O R

Analysis of Demand Uncertainty in Ground Delay Programs

Mike Ball

University of Maryland

A V I A T I O N O P E R A T I O N S R E S E A R C H

N A T I O N A L C E N T E R O F E X C E L L E N C E F O R

N E X T O R

destinationairport

flights

Uncertainty in Arrival Stream

airbornequeue

open slots

slots w multiple flights

Sources of uncertainty: cancellations, pop-ups, drift

A V I A T I O N O P E R A T I O N S R E S E A R C H

N A T I O N A L C E N T E R O F E X C E L L E N C E F O R

N E X T O R

destinationairport

flights

Planned vs Actual Airport Acceptance Rate

AAR: airport acceptance rate – rate at which flights land at airport

Planned AAR (PAAR)

Actual AAR

queueIn order to fully utilize arrivalcapacity, a queue must be maintained “to keep the pressure on the airport”This is done by regulating the value of the PAAR

A V I A T I O N O P E R A T I O N S R E S E A R C H

N A T I O N A L C E N T E R O F E X C E L L E N C E F O R

N E X T O RModels

• Integer Program– considers only flight cancellations

– variables: PAAR in each time period, Pr{k flights in airborne queue at end of period i}

– obj fcn: min total exp airborne delay

– inputs: flight cancellation prob, overall slot utilization, AAR

• Simulation– Considers cancellations, pop-ups, drift

A V I A T I O N O P E R A T I O N S R E S E A R C H

N A T I O N A L C E N T E R O F E X C E L L E N C E F O R

N E X T O RAirborne Delay vsCancellation Prob

(IP Model)

Exp Num of Open Slotsin Program

0

2

4

6

8

0 0.1 0.2 0.3

Cancellation Probability

Per-

Flig

ht

Air

-Bor

ne

Dela

y(in

m

in)

4.5

5

6

7

A V I A T I O N O P E R A T I O N S R E S E A R C H

N A T I O N A L C E N T E R O F E X C E L L E N C E F O R

N E X T O R“Marginal” Effects of Uncertainty in Presence of Cancellations, Pop-ups,

Drift (Sim Model)

Effect of Cancellation Probability (lambda = 20, drift = [-5,15])

05

101520

0.05 0.075 0.1 0.125 0.15 0.175 0.2

Cancellation Probability

Air

bo

rne

Ho

ldin

g

(min

ute

s/fl

t)

Utilization = 0.97 Utilization = 0.96

Utilization = 0.95 Utilization = 0.94

A V I A T I O N O P E R A T I O N S R E S E A R C H

N A T I O N A L C E N T E R O F E X C E L L E N C E F O R

N E X T O R

Effect of Drift (p_cnx = 0.1, lambda = 20)

0

10

20

30

[-15,25] [-10,20] [-5,15] [-2.5,7.5] [-1,4]

Drift

Air

bo

rne

Ho

ldin

g

(min

ute

s/fl

t)

Utilization = 0.97 Utilization = 0.96

Utilization = 0.95 Utilization = 0.98

“Marginal” Effects of Uncertainty in Presence of Cancellations, Pop-ups

Drift (Sim Model)

A V I A T I O N O P E R A T I O N S R E S E A R C H

N A T I O N A L C E N T E R O F E X C E L L E N C E F O R

N E X T O R

scheduleddeparture times

arrival times

Prelude to Understanding Compression Impact: Delay vs Arrival Times

departure times

grounddelay

airbornedelay

Delay(f) = arr_time(f) – sched_dep_time(f) – dir_en_route_time(f)Delay(f) = arr_time(f) – sched_arr_time(f)

Tot_delay = arr_time(f) – sched_dep_time(f) – dir_en_route_time(f)

As long as the overall set of arrival times (arrival slots used) remains the same total delay remains the same

A V I A T I O N O P E R A T I O N S R E S E A R C H

N A T I O N A L C E N T E R O F E X C E L L E N C E F O R

N E X T O RCompression Benefits

Compression has filled in holes in the PAAR which has reduced the amount of assigned ground delay

Possible system effects:• Holes in AAR have been filled in and total delay has been reduced• There were no holes in AAR so reduced ground delay has been

replaced by airborne delay• Uncertainty in the arrival stream has been reduced enabling a

reduction in the PAAR required to achieve a given AAR and a reduction in overall airborne delay

Of course, each individual airline generally derives substantial benefits based on internal cost reductions.

A V I A T I O N O P E R A T I O N S R E S E A R C H

N A T I O N A L C E N T E R O F E X C E L L E N C E F O R

N E X T O RAnalysis

• Looked at PAAR vs Actual AAR (arrivals) for 1st program hr, 2nd program hr, etc. for three airports; tried to group like GDPs, e.g. only morning GDPs at SFO– ATL and BOS: used command center logs for PAAR and

AAR– SFO: used command center logs for PAAR, tower counts for

AAR.

• Important Questions:– Is PAAR or AAR increasing or decreasing (improvement =

increase in AAR)– Is deviation of PAAR from AAR changing (improvement:

PAAR and AAR closer together)

A V I A T I O N O P E R A T I O N S R E S E A R C H

N A T I O N A L C E N T E R O F E X C E L L E N C E F O R

N E X T O R

4TH HOUR MOVING AVG- 15 DAY INTERVAL AT SFO

05

10152025303540

0 100 200 300Samples taken from '97 to '00

Arr

iva

l Ra

tes

PAAR

TOWER

1997 1998 1999 2000

Moving AVG- 15 DAY FOR 1ST HOUR AT SFO

25

26

27

28

29

30

31

32

0 100 200 300Samples taken from '97 to '00

Arr

iva

l Ra

tes

1997 1998 1999 2000

MOVING AVG - 15 DAY FOR 2ND HOUR AT SFO

0

5

10

15

20

25

30

35

0 50 100 150 200 250Samples taken from '97 to '00

Arr

iva

l Ra

tes

1997 1998 1999 2000

3RD HOUR MOVING AVERAGE- 15 DAY INTERVAL AT SFO

27

28

29

30

31

32

33

34

0 50 100 150 200 250

Samples are taken from '97 to '00

Arr

ival

Rat

es

1997 1998 1999 2000

SFOPAAR Actual AAR

A V I A T I O N O P E R A T I O N S R E S E A R C H

N A T I O N A L C E N T E R O F E X C E L L E N C E F O R

N E X T O R

4th Hour Moving Average- 10 day interval for ATL

66

68

70

72

74

76

78

80

82

0 20 40 60 80Samples taken from mar'98 to nov'00

Arr

ival

Rat

es

200019991998

3rd Hour Moving Average - 10 day interval for ATL

66

68

70

72

74

76

78

80

82

0 20 40 60 80Samples taken from mar'98 to nov'00

Arr

iva

l Ra

tes

1st Hour Moving Average-10 day interval for ATL

0102030405060708090

0 20 40 60 80Samples taken from mar'98 to nov'00

Arr

iva

l Ra

tes

2000 1999 1998

2nd Hour Moving Average-10 day interval for ATL

0

20

40

60

80

100

0 20 40 60 80Samples taken from mar'98 to nov'00

Arr

iva

l R

ate

s

2000 1999 1998

PAAR Actual AARATL

A V I A T I O N O P E R A T I O N S R E S E A R C H

N A T I O N A L C E N T E R O F E X C E L L E N C E F O R

N E X T O R

Moving Average(20 day Interval) - 4th hour BOS

05

1015202530354045

0 50 100 150

Samples taken form mar'98 to nov'00

Arr

iva

l Ra

tes

200019991998

Moving Average(20 day interval) - 3rd hour BOS

0

5

10

15

20

25

30

35

40

45

0 20 40 60 80 100 120 140

Samples taken from mar'98 to nov'00

Arr

ival

Rat

es

200019991998

1st Hour Moving Average- 20 day interval at BOS

0

10

20

30

40

50

0 50 100 150Samples taken from mar'98 to nov'00

Arr

ival

Rat

es

2000 1999 1998

Moving Average of 20 day interval - 2nd hour BOS

0

5

10

15

20

25

30

35

40

45

0 20 40 60 80 100 120 140

Samples taken from mar'98 to nov'00

Arr

ival

Rat

es

2000 19991998

PAAR Actual AARBOS

A V I A T I O N O P E R A T I O N S R E S E A R C H

N A T I O N A L C E N T E R O F E X C E L L E N C E F O R

N E X T O RTypical PAARs Used Today

353433323130292827

PAAR

1 2 3 4 5 6 7Time Period

(hour)

1 2 3 4 5 6 7

A V I A T I O N O P E R A T I O N S R E S E A R C H

N A T I O N A L C E N T E R O F E X C E L L E N C E F O R

N E X T O RSample PAARs Recommended

by IP Model

353433323130292827

PAAR

1 2 3 4 5 6 7Time Period

(hour)

1 2 3 4 5 6 7

A V I A T I O N O P E R A T I O N S R E S E A R C H

N A T I O N A L C E N T E R O F E X C E L L E N C E F O R

N E X T O RConclusions

• Reducing uncertainty is extremely important– Pop-ups– Cancellations w/o notification– Wide departure windows (may be most important)

• No evidence found (yet) that improved prediction accuracy of CDM has been transformed into actual uncertainty reduction benefits (more analysis necessary)

• Command Center (and FSM) should consider change in manner of setting AARs