Landing Safety Analysis of An Independent Arrival Runway

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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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Problem 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?
• Whats the current safety level?
• What are major factors that will affect safety?
• How?

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Safety-Capacity Hypothesis
More Safe
Safety/Capacity
IT Extension
Safety (Departures / Hull Loss)
Less Safe
High
Low
Capacity (Departures / Year)
Donohue et al., 2001 Shortle et al. 2004
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Safety Issues Considered
Simultaneous runway occupancy/landing
Runway collision/landing
Accidents
Incidents
Wake-vortex-encounter/approach
Loss of control/approach
Airplane i2
Airplane i
Airplane i1
Wake Vortex Encounter
Simultaneous Runway Occupancy
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Key Safety Metrics
Ease of predicting
Loss of wake vortex separation
Loss of control due to turbulence
Wake vortex encounter
Simultaneous runway occupancy
Runway collision
Incidents
Accidents
Metric relevance
This paper focuses on
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Data Samples of Landing Time Interval
Loss Safety
Loss Capacity
Courtesy of Haynie, Doctoral dissertation, GMU,
2002
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An Observation of ATL Landing Runways
Mar.5 and 6, 2001 ATL 26L, 364 valid data
(Haynie, 2002)
LTI Landing Time Interval ROT Runway Occupancy
Time SRO Simultaneous Runway Occupancy
ROT
LTI
Indicate a positive probability of Simultaneous
Runway Occupancy.
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Analytical 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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A Queuing Model for Safety Analysis
TRACON Final Approach
Final Approach - Runway
aircraft
separation
aircraft
separation
RWY Threshold
TRACON
RWY Exit
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Simplification 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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Model 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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Analytical Evaluation of Safety

• Prob(SRO) Prob(LTI lt ROT)
• Prob(LTI-ROT lt0)
• LTI is the inter-departure time of the M/G/1
  queuing model.
• LTI is a function of M and G.
• LTIs 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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Departure 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
observer
aircraft
separation
pd prob(server busy)pd1prob(server idle)pd2
For an M/M/1 queue
rlt1
rgt1
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Service time in M/G/1
A Gaussian distribution can be approximated by a
finite sum of xkexp(-ux).
P is transition matrix, q is exit vector e is a
vector of 1s
Define the completion rate matrix M as a diagonal
matrix with elements Mii mi , where mi is the
rate of leaving state i.
Service rate matrix B is
Service time matrix V is V B-1
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Distribution of Service Time
Define the operator YX pXe' , p is the
entrance vector
CDF of service time
PDF of service time
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Inter-Departure Time in M/G/1
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Inter-Departure Time in M/G/1
If r goes to 1, d(t) s(t). If r goes to 0,
(1-lV) is close to 1, the inter-departure time
will distribute like the inter-arrival time with
the density function le-lx.
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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Landing Time Interval Distributions
Erlangs
Mean Std.dev 70.7 9.7 118 15.4 70
8.4
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Prob.(SRO)
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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Factors 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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How ROT Affects Safety
Mean and variance of runway occupancy time
Landing safety
ROT Runway Occupancy Time
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How Separation Affects Safety
Mean and variance of desired separation
Prob.(SRO)
Landing safety
Std.Dev of desired separation (sec.)
Mean of desired separation (sec.)
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Separation Vs. Safety
Separation Deviation (sec.)
Prob(SRO)
Mean(Desired Separation) (sec.)
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Capacity-Safety
Separation Deviation (sec.)
Landings/SRO
Here we are!
Landings/hour
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Safety-Capacity Hypothesis
More Safe
Safety/Capacity
IT Extension
Safety (Departures / Hull Loss)
Less Safe
High
Low
Capacity (Departures / Year)
Donohue et al., 2001 Shortle et al. 2004
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Summary

• An M/G/1 queuing model can effectively represent
  a randomly,unsynchronizedly scheduled airports
  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.