Validation of En Route Capacity Model with
Peak Counts from the National Airspace System
J. Welch and J. Andrews
MIT Lincoln Laboratory

J. PostFederal Aviation Administration
11 November 2010
* This work is sponsored by the Federal Aviation Administration under Air Force Contract #FA8721-05-C-0002. Opinions,interpretations, recommendations and conclusions are those of the author and are not necessarily endorsed by the United States
Government.

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Overview• Airspace capacity estimates are important– sector design– air traffic management• Current model accounts only for ‘transit’ workload– hand-offs at sector crossings• New model adds key workload components– conflict avoidance– recurring tasks• We have estimated capacities for 20 NAS* Centers– ~ 800 sectors

Capacities differ significantly center to center
Local Capacity << Inherent Capacity
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Outline• Review of Capacity Model• Regression Process• Center Capacities• Conclusions

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Workload Event Rates
Workload grows with three critical traffic-dependent event rates
Transit (boundary crossing) rate
lt = N/T
sector aircraft count N
mean sector transit time T

Conflict rate

lc = (2 N2/Q) Mh Mv V21
sector airspace volume Q
miss distances Mh and Mv
mean closing speed V21

Recurring (scanning/monitoring) rate
lr = N/P
recurrence period P

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Workload Intensity
Workload Intensity(fraction of controller time)

G = Gt + Gc + Gr
transitrecurringconflictService Times(empirical )Gt = tt [N/T]

Gc = tc [(2 N2/Q) Mh MvV21]
Gr = tr [N/P]

occurrence rates(calculated fromairspaceparameters)

Determining the unknown service times–Live approach
Measure controller performance–Regression approach
Observe Peak daily counts Np for many sectors
Calculate corresponding Model capacities Nm
Find service times that best fit Nm to Np bound20101111 EN-012 Slide 5
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Conflict Distance

Conflict Workload Intensity
Gc = tc [(2 N2/Q) Mh MvV21]
Global closing speed V21 is also unknown
Fit the product tcV21(separation lost while resolving a conflict)tcV21 ~ 2 nautical miles (for NAS)

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Effect of Altitude Changes
Aircraft with vertical rates cause increased uncertainty
Adapt by increasing vertical miss distance Mv••

Determine fraction Fca of aircraft with ≥2000 ft altitude change
As Fca grows, increase Mv linearly from 1000 ft to Mvmax

Vertical Miss Distance Mv , ft

2000Mvmax ≈ 1600 ft(For NAS)

1500

1000

500

000.2

0.4

0.6

0.8

1Altitude Change Fraction F ca
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Outline• Review of Capacity Model• Regression Process• Center Capacities• Conclusions

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Peak Daily Counts(790 NAS Sectors)
30

July and August 2007
Day with most operations for each center
Peak instantaneous count for each sector

Observed Peak Count25

Aircraft Count

20

15

10

500

10000

20000

30000

40000

50000

60000

70000

80000

Sector Volume (nm3)20101111 EN-012 Slide 9
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Peak Daily Counts and Fitted Capacities(790 NAS Sectors, July–August 2007)
30NAS Model Capacity
Observed Peak Count25

Aircraft Count

20151050010000

20000

30000

40000

50000

60000

70000

80000

Sector Volume (nm3)20101111 EN-012 Slide 10
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Asymmetric Objective Function(Fits Model to Peak Count Bound)50-10-9-8-7-6-5-4-3-2-1012345Np > Nm

Np < Nm

Score
Sector
Score
Sector-5-10-15-20-25

Difference Between Sector Peak Count and Model Bound, N p-N b

Difference Between Peak Count N and Model Capacity Npm
Difference between Peak Count N
p and Model Capacity Nm

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Asymmetric Objective Function(Fits Model to Peak Count Bound)
5Close Fits
0-10-9-8-7-6-5-4-3-2-1012345

Np > Nm

Np < Nm-5

Score
Sector
Score
SectorReward sectors
with close fits
-10-15-20-25

Difference Between Sector Peak Count and Model Bound, N p-N b

Difference Between Peak Count N and Model Capacity Npm
Difference between Peak Count N
p and Model Capacity Nm

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Asymmetric Objective Function(Fits Model to Peak Count Bound)
5High Counts

Close Fits
0-10-9-8-7-6-5-4-3-2-1012345

Np > Nm

Np < Nm-5

Score
Sector
Score
SectorReward sectors
with close fits

Penalize sectors
with highpeak counts-10-15-20-25

Difference Between Sector Peak Count and Model Bound, N p-N b

Difference Between Peak Count N and Model Capacity N

pm
Difference between Peak Count N
p and Model Capacity Nm

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Asymmetric Objective Function(Fits Model to Peak Count Bound)
5Low Counts

High Counts

Close Fits
0-10-9-8-7-6-5-4-3-2-101235

Np > Nm

Np < Nm-5ScoreSector
Score
Sector4

Low traffic demandno score assigned

Reward sectors
with close fits

Penalize sectors
with highpeak counts-10-15-20-25

Difference Between Sector Peak Count and Model Bound, N p-N b

Difference Between Peak Count N and Model Capacity Npm
Difference between Peak Count N
p and Model Capacity Nm

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Fitted Capacities versus Peak Counts(790 NAS Sectors July – August 2007)
30

NAS Model Capacity

25201510500510152025

Observed Peak Count
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Outline• Review of Capacity Model• Regression Process• Center Capacities• Conclusions

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Peak Sector Counts, Seattle Center (ZSE)
30

July and August 2007
10 days with highest center operations
Peak sector counts for those days
28 ZSE sectors
280 ZSE sector-days

ZSE Peak Daily Count25

Aircraft Count

20151050010000

20000

30000

40000

50000

60000

70000

80000

3Sector Volume (nm )20101111 EN-012 Slide 17
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MIT Lincoln LaboratoryZSE Sector Capacity from ZSE Regression
30

Capacity, ZSE Regression
ZSE Peak Daily Count25

Aircraft Count

20151050010000

20000

30000

40000

50000

60000

70000

80000

3Sector Volume (nm )20101111 EN-012 Slide 18
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MIT Lincoln LaboratoryZSE Sector Capacity from NAS Regression
30

Capacity, NAS Regression
Capacity, ZSE Regression
ZSE Peak Daily Count25Aircraft Count20

151050010000

20000

30000

40000

50000

60000

70000

80000

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Normalized Capacity Density• Local center capacities differ significantly• Meaningful capacity comparisons must normalize for– center size
– sector countNormalized capacity density

KNC = SCS / QZ / NSSCS = Sum of local capacities of all sectors
QZ = Center airspace volume (10,000 nmi3)
NS = Sector count(KNC for Seattle is 0.11 aircraft per 10,000 nmi3)
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Peak Counts
Washington DC Center
30

ZDC25

ZDC46 sectors
KNC = 0.41

Calendar Year 2007
8 days with highest ZDC operations(in March, April May, June, and November)

Aircraft Count

20151050010000

20000

30000

40000

50000

60000

70000

80000

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Peak Counts
Washington DC and Miami Centers
30

ZDC
ZMA
25

ZDC
46 sectors
KNC = 0.41

Calendar Year 2007

ZMA40 sectors
KNC = 0.07

Aircraft Count

20151050010000

2000030000

40000

50000

60000

70000

80000

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Normalized Capacity Density
NAS En Route Centers (July – August 2007)
ZMP
Minneapolis

ZSE
Seattle0.4

Aircraft / 10,000 nm 3 / Sector

ZAU
ChicagoZLC
Salt Lake city

0.45

ZOB
Cleveland

ZDV
DenverZNY

ZID
Indianapolis

ZKC
Kansas CityZOA
Oakland

ZBW
BostonZDC*0.35
ZLA

0.3

ZAB
Albuquerque

ZME
Memphis
ZFW
DallasZTL
Atlanta* ZDC notrestricted toJuly-August

ZJX
Jacksonville

0.25
ZHU
Houston0.2ZMAMiami

0.15
0.1
0.050ZDC ZID ZNY ZAU ZTL ZOB ZM E ZFW ZKC ZOA ZJX ZLA ZAB NAS ZDV ZBW ZSE ZM P ZLC ZHU ZM ACenter
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Equation for NAS Sector Capacity
Sector Capacity b  b 2  4ac
Nm 2awhere• a = 5.4(1+0.6 Fca)/Q, b = (a + 0.013 + 13/T), c = -0.7
• Fca = fraction of daily sector flights with ≥2000 ft altitude change• Q (nm3) = sector volume based on min and max daily altitudes• T (s) = mean transit time for aircraft in sector at time of peak

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Conclusions••

NAS regression provides inherent sector capacity
Individual center regressions provide local sector capacity–••

Peak count data reflect wide range of–Complexity–

Demand–Airspace characteristics

Single set of capacity parameters cannot capture current operations–•

Individual center regressions necessary

July - August 2007 peaks do not give peak demand for all Centers–•

can be significantly less than inherent capacity

Southern operations peak in winterWe plan to refine capacity calculations–Choose actual peak demand periods for all centers–

Increase data sets in all regressions

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End20101111 EN-012 Slide 26
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