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. 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?
What’s the current safety level?
What are major factors that will affect safety?
How?
Aviation traffic demand has been growing so fast that several major hub airports in the U.S. are operating close to or over their capacity limits, so we have to find a way to increase the system capacity to accommodate the demand. Reducing aircraft spacing at terminal approach phase is an effective method to increase the capacity of one of the choke points of the system. The potential capacity gain has been acknowledged but we need to clearly know how safety will be affected. Specifically, we should have an estimation of current safety level, what are significant factors that will influence safety, and how they do.

3. Safety-Capacity Hypothesis
More Safe
Safety/Capacity
IT Extension
Safety
(Departures / Hull Loss)
Less Safe
The safety-capacity tradeoff has been hypothesized by Dr.Donohue as convex-like curves. Given a certain level of technology and operation procedures, increasing capacity will make safety worse. If more advanced technology or more efficient procedures are deployed, given a capacity, safety will be better than it used to be.
Low
Capacity
(Departures / Year)
High
[Donohue et al., 2001]
[Shortle et al. 2004]

4. Safety Issues Considered
Simultaneous runway
occupancy/landing
Runway collision/landing
Accidents
Incidents
Wake-vortex-encounter/approach
Loss of control/approach
Airplane i+2
My research focuses on safety of terminal approach since statistics has shown that an accident is more likely to happen here than other phases, and final approach separation is one of the major constraints of the system capacity. To evaluate the safety of terminal approach, I consider two types of accidents, one is loss of control due to wake vortex encounter in air; the other is runway collision between two landing aircraft. The pre-cursor of the accidents are wake vortex encounter, and simultaneous runway occupancy.
Airplane i
Airplane i+1
Wake Vortex Encounter
Simultaneous Runway Occupancy

5. 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
The first issue of safety analysis is the selection of safety metrics. The accidents are clearly relevant to safety issues, but they rarely happen in reality, and when it happens, the system must have been unsafe for a while. In contrast to accidental metrics, incidents like wake vortex encounter, simultaneous runway occupancy, are directly related to accidents, and they happen much more frequently than accidents. When a system gets less safe, we can observe that the number of incident occurrences will increase significantly before an accident occurs. So the research methodology is to evaluate system safety using incident metrics, and based on incident estimation, we can infer accident estimation.
Metric relevance
This paper focuses on

6. Data Samples of Landing Time Interval
Loss Safety
Loss Capacity
The landing time interval is the time separation between two aircraft passing runway threshold. The curves shown in the graph are real observation of landing time interval in IFR or VFR in two airports, LGA and ATL. The black bar is the desired wake vortex separation. We can see that both in IFR and VFR, loss of separation happens. The separation on the left side of the bar indicates a worse safety, and separation on the right side indicates a waste of capacity.
Courtesy of Haynie, Doctoral dissertation, GMU, 2002

7. 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
Here I use ATL as a case study to analyze the landing safety. In 364 landings, there is one SRO observed. The frequency is The probability density functions of runway occupancy time and landing time interval are shown in the graph. The overlapped area indicates a positive probability of simultaneous runway occupancy. In the first order analysis, I use a shifted Gamma distribution to approximate LTI, and a normal to fit ROT. The result is much bigger than the observation. So we need a better method to estimate the safety.
Indicate a positive probability of Simultaneous
Runway Occupancy.

8. Analytical Model Vs. Simulation Model
Advantages of analytical models:
Computational efficiency
Consistency
Clarity
Accuracy
Disadvantages of analytical models:
Limited applicability
Over simplification
Dependencies

9. A Queuing Model for Safety Analysis
TRACON – Final Approach
Final Approach - Runway
aircraft
separation
aircraft
separation
Basically terminal approach is a queuing process, and queuing methods have been used to analyze flight delay. For the first time, we use queuing theory to evaluate landing safety. If an aircraft reaches final approach fix, and its distance with the previous one which is in final approach is less than then required separation, it has to wait until separation requirement is satisfied. When no aircraft is in final approach, or separation is larger than requirement, the aircraft arrive at final approach fix and go ahead to approach.
RWY Threshold
TRACON
RWY Exit

10. 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.

11. 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.

12. Analytical 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.

13. 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)*pd1+prob(server idle)*pd2
For an M/M/1 queue:
r<1
r>1

14. 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 1’s
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

15. Distribution of Service Time
Define the operator Y[X] = pXe' , p is the entrance vector
CDF of service time:
PDF of service time:

16. Inter-Departure Time in M/G/1

17. 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.

18. Landing Time Interval Distributions
Erlang’s
Mean Std.dev

19. 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

20. Factors That Affect Safety
Arrival rate
Mean and variance of
desired separation
runway occupancy time
Landing safety
Other incidents, e.g. human error, equipment failure,…

21. How ROT Affects Safety Mean and variance of runway occupancy time
Landing safety
ROT: Runway Occupancy Time

22. 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.)

23. Separation Vs. Safety Prob(SRO) Mean(Desired Separation) (sec.)
Deviation (sec.):
Prob(SRO)
Mean(Desired Separation) (sec.)

24. Capacity-Safety Landings/SRO Here we are! Landings/hour Separation
Deviation (sec.):
Landings/SRO
Here we are!
Landings/hour

25. Safety-Capacity Hypothesis
More Safe
Safety/Capacity
IT Extension
Safety
(Departures / Hull Loss)
Less Safe
The safety-capacity tradeoff has been hypothesized by Dr.Donohue as convex-like curves. Given a certain level of technology and operation procedures, increasing capacity will make safety worse. If more advanced technology or more efficient procedures are deployed, given a capacity, safety will be better than it used to be.
Low
Capacity
(Departures / Year)
High
[Donohue et al., 2001]
[Shortle et al. 2004]

26. Summary
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.