CENTER FOR AIR TRANSPORTATION SYSTEMS RESEARCHCENTER FOR AIR TRANSPORTATION SYSTEMS RESEARCH

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Landing Safety Analysis of An Independent Arrival Runway

Author: Richard Yue Xie

John Shortle

Presented by: Dr. George Donohue

22/11/2004

ICRAT 2004

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CATSRCATSRProblem Statement

• Growth of traffic demand requires more capacity both of airports and airspace.

• Separation reduction is an effective way of increasing capacity.

• How will safety be affected?• What’s the current safety level?

• What are major factors that will affect safety?

• How?

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CATSRCATSRSafety-Capacity Hypothesis

[Donohue et al., 2001]

[Shortle et al. 2004]

Capacity(Departures / Year)

Safety(Departures / Hull Loss)

HighLow

More Safe

Less Safe

Safety/CapacityIT Extension

4

CATSRCATSRSafety Issues Considered

Simultaneous Runway Occupancy

Airplane i+2

Airplane i+1 Airplane i

Wake Vortex Encounter

Simultaneous runway occupancy/landing

Wake-vortex-encounter/approach

Incidents Accidents

Runway collision/landing

Loss of control/approach

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CATSRCATSRKey Safety Metrics

Loss of wake vortex separation

Simultaneous runway occupancy

Wake vortex encounter

Runway collision

Loss of control due to turbulence

Ease of predicting

Metric relevance

Incidents Accidents

This paper focuses on

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CATSRCATSRData Samples of Landing Time Interval

Loss CapacityLoss Safety

Courtesy of Haynie, Doctoral dissertation, GMU, 2002

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CATSRCATSRAn Observation of ATL Landing Runways

LTI:Landing Time Interval

ROT: Runway Occupancy Time

SRO:Simultaneous Runway Occupancy

Mar.5 and 6, 2001 ATL 26L, 364 valid data (Haynie, 2002)

LTI

ROT

Indicate a positive probability of Simultaneous Runway Occupancy.

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CATSRCATSRAnalytical Model Vs. Simulation Model

• Advantages of analytical models:• Computational efficiency

• Consistency

• Clarity

• Accuracy

• Disadvantages of analytical models:• Limited applicability

• Over simplification

• Dependencies

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CATSRCATSRA Queuing Model for Safety Analysis

separation

TRACON – Final Approach

separation

Final Approach - Runway

TRACON RWY Threshold

RWY Exit

aircraft

aircraft

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CATSRCATSRSimplification in the Model

• Fleet mixture is not explicitly modeled (In VFR, separation

differences for different mix are not remarkable);

• Arrival process is approximated using a Poisson process,

although not justified theoretically;

• Service time, which is the desired separation, can be

approximated using a Gaussian distribution.

• Runway occupancy time follows a Gaussian distribution

N(48,82) seconds.

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CATSRCATSRModel Validation

•Simulation results of an M/G/1 model shows good consistency with observations. Arrival rate 29 acft/hour, G is Gaussian(80,112) in second.

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CATSRCATSRAnalytical Evaluation of Safety

• Prob(SRO) = Prob(LTI* < ROT) =

Prob(LTI-ROT <0)

• LTI is the inter-departure time of the M/G/1** queuing model.

• LTI is a function of M and G.

• LTI’s distribution = ?* LTI: Landing Time Interval** M means the arrival process is a Poisson process; G means the service time follows a non-exponential distribution.

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CATSRCATSRDeparture Process of A Queue

1. If server is busy, inter-departure time is the same as service time;2. If server is idle, inter-departure = inter-arrival + service

separation

aircraftobserver

2 1 2 2 1

0

[ ]( ) ( ) ( )t

dp p p t p h p t h dh

pd= prob(server busy)*pd1+prob(server idle)*pd2

For an M/M/1 queue:

dp (t)=

t

ut

e

ue

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CATSRCATSRService time in M/G/1

A Gaussian distribution can be approximated by a finite sum of xkexp(-ux).

P q P is transition matrix, q is exit vector is a vector of 1’s

Service rate matrix B is (1 )B M P

Define the completion rate matrix M as a diagonal matrix with elements Mii = i , where

i is the rate of leaving state i.

Service time matrix V is V = B-1

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CATSRCATSRDistribution of Service Time

( ) 1 [exp( )]S t tB CDF of service time:

PDF of service time:

( )( ) [ exp( )]

dS ts t B tB

dt

Define the operator [X] = pX' , p is the entrance vector

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CATSRCATSRInter-Departure Time in M/G/1

0

0 'd

pP

P

'

0

0dMM

'( )0d d d d

pB M I P

B

1

'

1

0d d

pVV B

V

1 1

( ) ( ) (1 )

[( ) ] [( ) exp( )]x

d t s t

I V e I V B xB

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CATSRCATSRInter-Departure Time in M/G/1

1 1

( ) ( ) (1 )

[( ) ] [( ) exp( )]x

d t s t

I V e I V B xB

If goes to 1, d(t) = s(t).

If goes to 0, (1-V) is close to 1, the inter-departure time will distribute like the inter-arrival time with the density function e-x.

For more information, please refer to Xie and Shortle, Landing Safety Analysis of An Independent Arrival Runway, ICRAT, 2004;Lipsky, Queuing Theory – A Linear Algebraic Approach, 1992.

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CATSRCATSRLanding Time Interval Distributions

Mean Std.dev70.7 9.7118 15.470 8.4

Erlang’s

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CATSRCATSRProb.(SRO)

0

Prob(SRO)=Prob(LTI<ROT)

( ) ( )LTI ROTf x z f x dxdz

Parameter values:Inter-arrival: exponential(124 sec)Mean of desired separation: 80 sec, std.dev is 11 sec.Mean of runway occupancy time is 48 sec., std.dev is 8 sec.

The calculated probability of SRO is 0.00312.

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CATSRCATSRFactors That Affect Safety

Arrival rate

Mean and variance of desired separation

Mean and variance of runway occupancy time

Landing safety

Other incidents, e.g. human error, equipment failure,…

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CATSRCATSRHow ROT Affects Safety

Mean and variance of runway occupancy time

Landing safety

ROT: Runway Occupancy Time

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CATSRCATSRHow Separation Affects Safety

Mean and variance of desired separation

Landing safety

Mean of desired separation (sec.)Std.Dev of desired separation (sec.)

Pro

b.(S

RO

)

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CATSRCATSRSeparation Vs. Safety

-0. 02

0

0. 02

0. 04

0. 06

0. 08

0. 1

0. 12

0. 14

40 50 60 70 80 90 100

5 7

9 11

Pro

b(S

RO

)

Mean(Desired Separation) (sec.)

Separation Deviation (sec.):

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CATSRCATSR

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

45 46 47 48 49 50 51 52 53 54 55

7 911 13

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Capacity-Safety

Landings/hour

Lan

ding

s/S

RO

Here we are!

Separation Deviation (sec.):

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CATSRCATSRSafety-Capacity Hypothesis

[Donohue et al., 2001]

[Shortle et al. 2004]

Capacity(Departures / Year)

Safety(Departures / Hull Loss)

HighLow

More Safe

Less Safe

Safety/CapacityIT Extension

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CATSRCATSRSummary

• An M/G/1 queuing model can effectively represent a randomly,unsynchronizedly scheduled airport’s arrival process.

• Landing safety is significantly affected by variances of runway occupancy time and separation

• Both average value and variance should be considered in policy making.