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Incorporating Weather Uncertainty in Airport Arrival Rate Decisions. FAA-NEXTOR-INFORMS Conference on Air Traffic Management and Control Joyce W. Yen Zelda B. Zabinsky Catherine A. Serve’. 5 June 2003. Objective.

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incorporating weather uncertainty in airport arrival rate decisions

Incorporating Weather Uncertainty in Airport Arrival Rate Decisions

FAA-NEXTOR-INFORMS

Conference on Air Traffic Management and Control

Joyce W. Yen

Zelda B. Zabinsky

Catherine A. Serve’

5 June 2003

objective
Objective
  • Investigate the trade-off between ground delay and air delay given uncertainties in the weather prediction
  • To examine, “How do inaccuracies in weather forecasts affect flow decisions?”
agenda
Agenda
  • Air Traffic Background
  • Stochastic Optimization Formulation
  • Sample Test Case
  • Sensitivity Analysis on Weather Forecast Accuracy
  • Next Steps
flow control decisions
Flow Control Decisions
  • A collaborative decision is made between Air Traffic Control (ATC), the Airline Operational Control (AOC), and affected centers
  • Decisions result in some form of ground delay or air delay
    • Ground holding (delay on ground)
    • Miles-in-Trial (delay in air)
decision representation
Decision Representation
  • Single airport with multiple arrivals
  • How to make delay decisions to minimize total delay or cost of delay?
agenda1
Agenda
  • Air Traffic Background
  • Stochastic Optimization Formulation
  • Sample Test Case
  • Sensitivity Analysis on Weather Forecast Accuracy
  • Next Steps
stochastic optimization formulation assumptions
Stochastic Optimization Formulation - Assumptions
  • Due to weather uncertainty, there is a probabilistic reduction of capacity, airport acceptance rate (AAR)
  • Modeled decisions as a stochastic optimization problem
  • Model Assumptions
      • Single airport
      • Flights aggregated by scheduled arrival
  • Previous work
      • Octavio Richetta and Amedeo Odoni (1993,1994)
      • Min E[Cost of ground delay] + E[Cost of air delay]
      • Dynamic formulation
stochastic optimization formulation utility function
Stochastic Optimization Formulation - Utility Function
  • New objective function included utility of flight as function of total delay
stochastic optimization formulation utility function1
Stochastic Optimization Formulation - Utility Function
  • 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
  • This new objective would be a utilitarian point of view; good for both ATC and AOC
  • Max (Utility - Cost)
  • Delay Costs
    • Air delay cost = Ground delay cost
    • Air delay cost = 2* Ground delay cost
    • Air delay cost = 5* Ground delay cost
expansion into stochastic formulation
Expansion into Stochastic Formulation

Network

component

for q=1

Network

component

for q=2

Network

component

for q=Q

stochastic optimization formulation
Stochastic Optimization Formulation
  • Two sets of decision variables determine rescheduled number of arrivals (RNA) for each time period
    • First stage decisions (Xij) reschedule the arrival time of flights from i to j
    • Recourse decisions ( ) assign actual arrival time k (which may differ from the original arrival time i or rescheduled arrival time j)
  • Probability of scenario q, (pq ) weather uncertainty
agenda2
Agenda
  • Air Traffic Background
  • Stochastic Optimization Formulation
  • Sample Test Case
  • Sensitivity Analysis on Weather Forecast Accuracy
  • Next Steps
experimental design demand vector
Experimental Design - Demand Vector
  • Sixteen time period model - 15 min intervals

Based On Official Airline Guide

Boston Logan Airport Arrival Data

Demand for Monday 8AM to 12PM

experimental design scenario setup
Experimental Design – Scenario Setup
  • Forecast gives capacity for each time period
  • Five capacity cases (each with three possible forecasts) created to represent various weather conditions
      • Fair Weather
      • Late Storm
      • Intense Storm
      • Mid-time Storm
      • Unpredictable Weather
  • Four probability cases represent different distributions of capacity forecasts
  • Twenty scenarios
experimental design probability cases
Experimental Design - Probability Cases
  • Each capacity case has three possible forecasts
model run results time length of delays
Model Run Results – Time & Length of Delays
  • As cost of air delay increases see more flights

rescheduled in later time periods

Averaged over all weather cases

model run results summary of insights
Model Run Results – Summary of Insights
  • Decisions sensitive to value of total delay and relative costs of air delay and ground delay

If only minimize cost of air and ground (and ignore total delay), assign more ground delay and not value opportunity to take advantage of clearing weather

  • When air delay cost > ground delay cost, schedules more ground delay
  • Unpredictable & Late Storm scheduling longer delays
  • As relative cost of air delay increases see more flights rescheduled in later time periods
agenda3
Agenda
  • Air Traffic Background
  • Stochastic Optimization Formulation
  • Sample Test Case
  • Sensitivity Analysis on Weather Forecast Accuracy
  • Next Steps
sensitivity analysis objective
Sensitivity Analysis - Objective
  • Currently attempting to understand effects of weather forecast accuracy on model
  • Constructed three new capacity cases each again with three possible forecasts
      • Late Storm
      • Early Storm
      • Intense Storm
sensitivity analysis objective1
Sensitivity Analysis - Objective
  • Created five probability profiles to reflect varying inaccuracies of forecasts each with three probability cases (distributions for forecasts)
  • Examining changes in scheduling decisions as confidence in timing of storm varies
sensitivity analysis experimental setup
Sensitivity Analysis - Experimental Setup
  • Created capacity cases representing a early, late, and intense storm
sensitivity analysis experimental setup1
Sensitivity Analysis - Experimental Setup

Created 5 probability profiles each reflecting a different % inaccuracy in forecast

sensitivity analysis results total delay make up

1x 2x 5x

Sensitivity Analysis - Results Total Delay Make-up

F1 .5

F2 .3

F3 .2

F1 .2

F2 .5

F3 .3

F1 .3

F2 .2

F3 .5

sensitivity analysis results total delay make up1
Sensitivity Analysis - ResultsTotal Delay Make-up

F1 .75

F2 .2

F3 .05

F1 .85

F2 .10

F3 .05

F1 .5

F2 .3

F3 .2

F1 .6

F2 .2

F3 .2

F1 .65

F2 .25

F3 .10

sensitivity analysis results total delay make up2
Sensitivity Analysis - ResultsTotal Delay Make-up

F1 .75

F2 .2

F3 .05

F1 .85

F2 .10

F3 .05

F1 .5

F2 .3

F3 .2

F1 .6

F2 .2

F3 .2

F1 .65

F2 .25

F3 .10

sensitivity analysis results total delay make up3
Sensitivity Analysis - ResultsTotal Delay Make-up

F1 .85

F2 .10

F3 .05

F1 .65

F2 .25

F3 .10

F1 .75

F2 .2

F3 .05

F1 .5

F2 .3

F3 .2

F1 .6

F2 .2

F3 .2

sensitivity analysis results timing of rescheduling
Sensitivity Analysis - ResultsTiming Of Rescheduling
  • Decision variables Xij indicate when flights are being rescheduled
sensitivity analysis summary of insights
Sensitivity Analysis - Summary of Insights
  • When cost of air delay is same as cost of ground delay see insensitive ground delay decisions
  • More ground delay is taken as cost of air increases
  • As the forecast certainty increases better able to assign proper amount ground delay
next steps
Next Steps
  • More examination of demand effects especially when relative cost of air is greater than 5x ground
  • Investigate possible application to particular real weather scenarios, such as morning fog effects in San Francisco
contact information
Contact Information

Joyce W. Yen

joyceyen@u.washington.edu

206-543-4605

Zelda B. Zabinsky

zelda@u.washington.edu

206-543-4607