landing safety analysis of an independent arrival runway
DESCRIPTION
Landing Safety Analysis of An Independent Arrival Runway. Author: Richard Yue Xie John Shortle Presented by: Dr. George Donohue 22/11/2004. ICRAT 2004. Problem Statement. Growth of traffic demand requires more capacity both of airports and airspace. - PowerPoint PPT PresentationTRANSCRIPT
CENTER FOR AIR TRANSPORTATION SYSTEMS RESEARCHCENTER FOR AIR TRANSPORTATION SYSTEMS RESEARCH
1
Landing Safety Analysis of An Independent Arrival Runway
Author: Richard Yue Xie
John Shortle
Presented by: Dr. George Donohue
22/11/2004
ICRAT 2004
2
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?
3
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
26
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.