A Parametric Analysis of Air Traffic Flow Control Options Under Weather Uncertainty November 17, 2002 INFORMS Annual Meeti...
Objective <ul><li>Conduct a parametric analysis on flow control options to gain a better understanding of their effects on...
Agenda <ul><li>Air Traffic Background </li></ul><ul><li>Simple Policy-Based Approach </li></ul><ul><li>Stochastic Optimiza...
Flow Control Decisions <ul><li>A collaborative decision is made between Air Traffic Control (ATC), the Airline Operational...
Question <ul><li>How do we make decisions regarding ground delay and air delay to minimize either the total delay or the c...
Probabilistic Problem <ul><li>Consider a set of planes arriving at a single airport </li></ul><ul><li>Due to weather uncer...
Simple Policy-Based Approach to Determine Ground and Air Delay <ul><li>Reschedule the flights based on the probabilistic a...
Probabilistic Arrival Rate Example
 
 
Summary of Policy-Based Approach <ul><li>A more conservative decision (lower AAR) results in a higher expected delay, but ...
Stochastic Optimization Formulation <ul><li>Pose as a stochastic optimization problem </li></ul><ul><li>Consider flights a...
Modification of Objective Function <ul><li>In addition to cost of ground delay and air delay, the value of the system shou...
Utility of Total Delay <ul><li>Total delay is important </li></ul><ul><li>Utility of a flight is based on total delay </li...
Modified Stochastic Optimization Problem <ul><ul><li>Decision variables determine the AAR for each time period and distrib...
Mathematical Formulation (TEX slide)
Example Problem <ul><ul><li>* Time 4 is the slack time where we have the ability to recover the schedule  </li></ul></ul>
Comparison of Policies
Parametric Analysis <ul><li>Utility of a flight </li></ul><ul><ul><li>Constant </li></ul></ul><ul><ul><li>Slightly decreas...
Analysis of Utility <ul><li>Linear  </li></ul><ul><ul><li>Constant ,  slightly decreasing ,  moderately decrease </li></ul...
Parametric Experiments
Monic Quadratic  Moderately Decreasing Linear Moderately  Decreasing Linear Constant
Parametric Experiments
Constant Slightly Decreasing Moderately Decreasing
2 4 6 8 10 20 40 60 80 100
2 4 6 8 10 20 40 60 80 100
Summary of Parametric Analysis <ul><li>When cost of air delay is greater than cost of ground delay, choose a lower AAR </l...
Future Work <ul><li>Multiple decision points with updated information (dynamic formulation) </li></ul><ul><li>Solve on lar...
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A Parametric Analysis of Air Traffic Flow Control Options Under Weather Uncertainty

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  • I would like to thank Aslaug Haraldsdottir, Matt Berge, and Craig Hopperstad for providing advise and direction for my research. Often airport and airspace capacity becomes reduced due to weather conditions which are probabilistic in nature. Air Traffic Control (ATC) must impose flow control to limit the number of planes arriving at an airport. These flow control options result in either ground or air delay for flights. It is our wish to be able to make decisions regarding these options that optimize the goals of the air traffic system.
  • A Parametric Analysis of Air Traffic Flow Control Options Under Weather Uncertainty

    1. 1. A Parametric Analysis of Air Traffic Flow Control Options Under Weather Uncertainty November 17, 2002 INFORMS Annual Meeting Lisa Grignon, IE, University of Washington Aslaug Haraldsdottir, ATM Group, The Boeing Company Joyce Yen, IE, University of Washington Zelda Zabinsky, IE, University of Washington
    2. 2. Objective <ul><li>Conduct a parametric analysis on flow control options to gain a better understanding of their effects on a dynamic air traffic system </li></ul><ul><li>We would like to compare the trade-off between ground delay and air delay given uncertainties in the weather prediction </li></ul>
    3. 3. Agenda <ul><li>Air Traffic Background </li></ul><ul><li>Simple Policy-Based Approach </li></ul><ul><li>Stochastic Optimization Formulation </li></ul><ul><li>Next Steps </li></ul>
    4. 4. Flow Control Decisions <ul><li>A collaborative decision is made between Air Traffic Control (ATC), the Airline Operational Control (AOC), and affected centers </li></ul><ul><li>Flow control options result in either some form of ground delay or air delay </li></ul><ul><li>Two major flow control options </li></ul><ul><ul><li>Ground holding (delay on the ground) </li></ul></ul><ul><ul><li>Miles-in-Trail (delay in the air) </li></ul></ul>
    5. 5. Question <ul><li>How do we make decisions regarding ground delay and air delay to minimize either the total delay or the cost of delay? </li></ul>
    6. 6. Probabilistic Problem <ul><li>Consider a set of planes arriving at a single airport </li></ul><ul><li>Due to weather uncertainty, there is a probabilistic reduction of capacity, airport arrival rate (AAR) </li></ul>
    7. 7. Simple Policy-Based Approach to Determine Ground and Air Delay <ul><li>Reschedule the flights based on the probabilistic arrival rate and calculate the ground delay </li></ul><ul><li>Using the arrival rate profiles, assess the actual landing times and calculate the expected air delay, using FIFO policy </li></ul><ul><li>Use these calculations to estimate the expected total delay </li></ul>
    8. 8. Probabilistic Arrival Rate Example
    9. 11. Summary of Policy-Based Approach <ul><li>A more conservative decision (lower AAR) results in a higher expected delay, but may result in lower expected costs </li></ul><ul><li>Although we can choose the best of the three policies based on cost information, not all possible policies have been considered </li></ul>
    10. 12. Stochastic Optimization Formulation <ul><li>Pose as a stochastic optimization problem </li></ul><ul><li>Consider flights arriving at a single airport </li></ul><ul><li>Aggregate flights in groups based upon the original scheduled arrival </li></ul><ul><li>Octavio Richetta and Amedeo Odoni (1993,1994) </li></ul><ul><ul><li>Min E[Cost of ground delay] + E[Cost of air delay] </li></ul></ul><ul><ul><li>Dynamic formulation </li></ul></ul>
    11. 13. Modification of Objective Function <ul><li>In addition to cost of ground delay and air delay, the value of the system should include the utility of the flights based on their total delay </li></ul><ul><li>This new objective would be a utilitarian point of view; good for both ATC and AOC </li></ul>
    12. 14. Utility of Total Delay <ul><li>Total delay is important </li></ul><ul><li>Utility of a flight is based on total delay </li></ul><ul><li>A two hour delay results in 50% utility </li></ul>
    13. 15. Modified Stochastic Optimization Problem <ul><ul><li>Decision variables determine the AAR for each time period and distribute the arrival rate to flights according to their originally scheduled arrival time </li></ul></ul><ul><ul><li>First stage decisions ( X ij ) reschedule the arrival time of flights from i to j </li></ul></ul><ul><ul><li>Recourse decisions ( Ω ijk ) assign actual arrival time k (which may differ from the original arrival time i or rescheduled arrival time j ) </li></ul></ul>
    14. 16. Mathematical Formulation (TEX slide)
    15. 17. Example Problem <ul><ul><li>* Time 4 is the slack time where we have the ability to recover the schedule </li></ul></ul>
    16. 18. Comparison of Policies
    17. 19. Parametric Analysis <ul><li>Utility of a flight </li></ul><ul><ul><li>Constant </li></ul></ul><ul><ul><li>Slightly decreasing </li></ul></ul><ul><ul><li>Moderate decrease, such that a 2 hour delay results in 50% utility </li></ul></ul><ul><li>Delay costs </li></ul><ul><ul><li>Air delay cost = Ground delay cost </li></ul></ul><ul><ul><li>Air delay cost = 2*Ground delay cost </li></ul></ul><ul><ul><li>Air delay cost = 5*Ground delay cost </li></ul></ul>
    18. 20. Analysis of Utility <ul><li>Linear </li></ul><ul><ul><li>Constant , slightly decreasing , moderately decrease </li></ul></ul><ul><li>Monic Quadratic </li></ul><ul><ul><li>Slightly decreasing , moderately decrease </li></ul></ul><ul><li>Nonmonic Quadratic </li></ul><ul><ul><li>Slightly decreasing , moderately decrease </li></ul></ul>2 4 6 8 10 20 40 60 80 100
    19. 21. Parametric Experiments
    20. 22. Monic Quadratic Moderately Decreasing Linear Moderately Decreasing Linear Constant
    21. 23. Parametric Experiments
    22. 24. Constant Slightly Decreasing Moderately Decreasing
    23. 25. 2 4 6 8 10 20 40 60 80 100
    24. 26. 2 4 6 8 10 20 40 60 80 100
    25. 27. Summary of Parametric Analysis <ul><li>When cost of air delay is greater than cost of ground delay, choose a lower AAR </li></ul><ul><li>Steeper utility function offsets the high cost of air delay </li></ul><ul><li>Similar functions yield similar results </li></ul><ul><li>Policy decisions depend on objective function properties </li></ul>
    26. 28. Future Work <ul><li>Multiple decision points with updated information (dynamic formulation) </li></ul><ul><li>Solve on larger, representative problem </li></ul><ul><li>Explore error in forecasting </li></ul>

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