Transcript Examples of OR Practices at FAA

Federal Aviation
Administration
Examples of OR
Practices at FAA
WINFORMS
Nastaran Coleman, Ph.D.
January 28, 2014
Goal and Disclaimer
• Goal
– To encourage young and future operations research
practitioners to consider a career with the Federal Aviation
Administration (FAA).
• Disclaimer
– The opinion expressed in this presentation and following slides are solely those
of the presenter and not necessarily those of FAA. FAA does not guarantee the
accuracy nor is reliable for the information provided herein.
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Mixed Integer Programs
Optimize mix of legacy, new
navigation services
– Very High Frequency Omnidirectional Range (VOR) is ground-based
Navigational Aid (Navaid).
– Navigation and landing systems evolving from ground-based Navaids to
satellite-based navigation (SATNAV) system.
– During the transition to SATNAV system, FAA planning to phase out some
ground-based Navaids, including some VORs.
– Users not equipped with SATNAV avionics will still rely on VORs.
– Users equipped with SATNAV avionics may rely on VOR for backup in case of
disruption to the satellite-based system.
– When is it cost-effective to phase out VORs?
• How many?
• Which?
– What are impacts on flying public?
• Non-equipped aircraft rely on legacy Navaids.
• How many and which city pairs will be disconnected from VOR network?
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Mixed Integer Programs (cont.)
Optimize mix of legacy and new
navigation services (cont.)
– Modeled VOR network as mixed integer program.
– Eliminated infeasible variables in very creative way.
• Reduced number of variables from several billion to ~5 million.
• This is most important, biggest adjustment made to
transform problem from being “too complex” to being
solvable.
– Used relaxation techniques to solve mixed integer program
as linear program which almost always produces integer
results.
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Mixed Integer Programs (cont.)
Use optimization model to find most cost-beneficial
mixture of NAVAIDs by specific location and see
whether Wide Area Augmentation System (WAAS)
part of any of these mixtures.
• Designed model to include
– Efficiency, i.e., avoided disruptions.
– Cost savings from ground-based NAVAID decommissioning,
not commissioning and maintaining new Instrument Landing
Systems (ILSs).
– Some complex procedure benefits.
– Safety Benefits.
• Ran model with various assumptions including
equipage levels.
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Mixed Integer Programs (cont.)
Optimize scheduling of air traffic controller
shift start times, shift assignments
– Was designed to validate results of contractor
scheduler to be used by various facilities.
However, this tool can be used to answer
questions like
• Does facility consolidation increase efficiency?
• Do you need additional controllers if you add rest
times between shifts or change other constraints
• What are effects of adding abilities to control
traffic from remote sites?
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Mixed Integer Programs (cont.)
Estimate look-ahead conflict detection
counts related to controllers' workloads
• One parameter defining complexity of air traffic controller work is
detecting and resolving potential future conflicts.
• Objective is to find way to approximate number of potential
conflicts in next X minutes in sector, use number to assign
complexity level to that sector.
• Linear program predicts possible conflicts between two aircraft.
• Programming problem
•
Number of linear programming runs can be enormous (e.g., hundreds of millions for one
Center, one day.)
• Solution
• Many filtering techniques reduce this number of programs to around
1 million linear programs/day for each en route Center.
• Many adjustments reduce processing time.
• Batch files
• Memory leak prevention
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Mixed Integer Programs (cont.)
•
•
Model National Airspace System (NAS) with all its airports, fixes, routes as
network.
Maximize network flow
–
•
Maximum flow problems often used to find maximum amount of flow (aircraft traveled)
through network when paths (routes between fixes) have capacity limits.
Objective is to design tool to provide Rough Order of Magnitude (ROM)
estimates for questions like:
– What are potential benefits of reduced separations in en route airspace?
• When separation standard remains same in terminal area.
• With various airport capacity assumptions.
– How much more traffic can NAS handle?
• By spreading demand evenly throughout day, not changing airspace, airport
capacities.
• Use existing capacity at smaller regional airports.
– What are NAS’s bottlenecks?
– Estimate impacts of weather phenomena like blizzards.
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Queueing models
Introduced an analytical approach, using
ANALYTICA, to estimate future delays by
airport for various hourly capacity and demand
scenarios.
• This model, variants used to estimate future delays to provide
ROM estimates for many new technologies, procedures.
• Model approximates percent changes in delays due to capacity or
demand changes on hourly basis using steady-state, G/G/1
(general arrival and service distributions) queue with First-In FirstOut (FIFO) discipline.
• Average airport capacity first estimated using percent arrivals
versus departures, and standardized Pareto curves under various
ceiling and visibility conditions.
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Queueing Models (cont.)
Effects of reduced unimpeded taxi-out times on
departure delays at capacity-constrained airports
•
•
•
•
Unimpeded taxi time represents time aircraft travels from gate to runway
or vice versa, given no conflicting traffic. Actual taxi times exceed
unimpeded times when traffic exists: Aircraft must yield or wait.
Will reducing unimpeded taxi-out times through new technology result in
taxi-out time savings? These savings not intuitively obvious at capacityconstrained airports where aircraft often wait in departure queues.
Using queueing theory, simulation model, have shown that variance of
interarrival times into departure queue is only parameter that influences
queue waiting time.
If equipage less than 100% (mixed equipage) and interarrival time
variance same for equipped, unequipped aircraft, then combined variance
increases, offsetting some time savings.
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Statistical Analyses
Trends of scheduled hourly aviation demand
distributions at 35 major airports, 1982-2006.
• Do shapes of hourly demand distributions change as demand or
capacity increases over time?
– Build hourly scheduled demand distributions by airport, study shapes of
distributions over the year.
– Adjust for seasonal variations, day of week by creating hourly distributions
using entire year.
– Define potential metrics for evaluating changes in hourly schedule
demand, capacity over the year.
– Create hourly demand distributions by airport and year. Hourly demand
pattern changes as demand increases over the years.
• How to evaluate hourly demand pattern (peaking versus depeaking)?
–
Regression results suggests that peak growth is .64% of total demand
growth.
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Statistical Analysis (cont.)
• Using actual data, fit to existing probability distributions
or build user-defined distributions for various
component of flight.
– Do interarrival times to “Fix,” i.e., in-air waypoint, follow
Exponentially Modified Gaussian (EMG) distribution? Is
Exponential Gaussian Hybrid (EGH) better fit?
– How to estimate parameters.
• Use moments, but EGH lacks closed-form expression/
• Use graphical measurement to estimate lambda of exponential
part, variance of normal part of EGH.
• Sample mode is the best estimate of EGH normal mean.
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Statistical Analyses (cont.)
• Historical accident statistics can be used to
– Predict future accident rates for various alternatives.
– Evaluate effects of safety program by comparing data before, after
program implementation
– Identify safety risks so that return on investment is maximized
• Historical accident data can help
– Derive pool of safety benefits.
– Establish the effectiveness of new programs.
• Some observations:
– Most accidents happen during daylight. No significant difference in rate of
fatal accidents in absence of daylight.
– Approach, landing, descent most dangerous phases of flight.
• Study correlation between various weather conditions and
accidents
– Turbulence causes most air carrier accidents (mainly non-fatal.)
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