Incorporating Stochastic Models and Stochastic Information Within Traffic Flow Management SystemsOutlineSources of Uncertainty in Traffic Flow ManagementMitigating UncertaintyNEXTOR Research on Uncertainty in ATMResearch on Stochastic Ground Holding ProblemResearch on Stochastic Ground Holding ProblemScenarios and Scenario TreeScenario “Tree” Doesn’t GrowIllustration of the Decision Making ProcessExperimental ResultsScenarios, Scenario Tree, and Cost RatioResultsApplication in CDMIntra-Airline Substitution BenefitsBenefits from CompressionEnroute Airspace Capacity ProblemModel FormulationDelay CalculationsCapacity ScenariosExperimental CaseSummaryWork in ProgressQuestions?Backup SlidesDynamic Substitution ModelDynamic Compression ModelConstraints ContinuedIncorporating Stochastic Models and Stochastic Information Within Traffic Flow Management SystemsSpeaker:Avijit MukherjeeUniversity of Maryland, College ParkOutline• Introduction• Background on stochastic models for Ground Delay Programs– Static vs. dynamic models• Recent work on dynamic model for GDP planning– Capacity scenarios and scenario tree– Experimental results– Application under CDM• Extension to enroute capacity problemÎ DFW corner post problem– Graphically explain the decision making process– Experimental results• Concluding remarks– Complexities associated with practical implementation– Future researchSources of Uncertainty in Traffic Flow Management• Demand (uncertain departure/arrival times)• Capacity (forecast uncertainty)• Control actions traffic managers may take• Effects of coordination and timing of inter-related activitiesMitigating Uncertainty• Reduce uncertainty by improving information quality.• Create plans that “hedge against” multiple possible future outcomes.• Create flexible systems that can dynamically react to changing conditions.NEXTOR Research on Uncertainty in ATM• Uncertainty in airport capacity– Richetta and Odoni (1993, and 1994)– Ball et al. (1999, 2003)– Wilson (2002)– Inniss and Ball (2001)– Mukherjee and Hansen (2003)– Liu et al. (2005)• Demand uncertainty– Vossen et al (2002)– Willemain (2002)• Enroute airspace capacity– Nilim et al. (2002, 2004)– Mukherjee and Hansen (2004)Research on Stochastic Ground Holding Problem• Static Stochastic Optimization Models– Richetta and Odoni (1993) – Ball et al.(2003)– Considers multiple scenarios of airport capacity profile along with their probability of occurrence– Interesting properties of the IP formulation– Can be applied repeatedly Î “partially” dynamicResearch on Stochastic Ground Holding Problem• (Partially) Dynamic Stochastic Optimization Model: Richetta and Odoni (1994)– Plans GDP in stages Î utilizes updated information on capacity– Unable to revise ground delays once they are assigned, even if the flight hasn’t departed. However, this increases predictability of flight departure times.• Dynamic Stochastic Optimization Model: Mukherjee and Hansen (2003)– Capacity scenarios and scenario tree– Utilizes updated information on capacity to revise ground delays of flights– Can incorporate non-linear measures of ground delayScenarios and Scenario TreeScenarios TreeAirport Capacity Scenarios1101 2 3 41220 1 2 3 4Scenario “Tree” Doesn’t Grow• Can be constructed based on probabilistic weather forecasts• Can be obtained by performing statistical modeling of historical data on actual airport capacity (Liu et al., 2005)Illustration of the Decision Making ProcessScenarios TreeAirport Capacity Scenarios10 1 2 3 4101 2 3 4122fdfaOne flight scheduled to depart during first time period and arrive by end of 2ndtime periodIf the flight is released at its scheduled time, it will arrive during the 2ndtime period under both scenarios 1 and 2, and hence face airborne delay of one time period if scenario 2 occursIf the flight is delayed by 1 time period, then it can be released under scenario 1 at beginning of time period 2Otherwise it may be delayed further and released at time period 3 if scenario 2 occursDecisions made during 1sttime period has to be same under both scenarios, because none of them can be distinguished at that timeIn the Static Model, decisions are made during the 1sttime periods, and not revised laterExperimental Results• Applied to Dallas Fort Worth Intl. Airport (DFW)• 351 flights• Six capacity scenarios• Four cases of varied model parameters• Results compared with that from existing stochastic models (Ballet al 2003, Richetta-Odoni, 1994)Scenarios, Scenario Tree, and Cost Ratio35150:00 8:00 8:30 9:00 9:30 10:00 10:30 12:00 Time of Day1ξ2ξ3ξ4ξ5ξ6ξ1.0}{;1.0}{;1.0}{;1.0}{;2.0}{;4.0}{654321======ξξξξξξPPPPPPProbability Mass Function3 RatioCost =λResults• Due to low cost ratio, airborne delays are faced in all models• Dynamic Model– Less total expected cost– Ground delays more severe– Less airborne delays• Delay reduction compared to Static Model– 10% in Dynamic Model– 2% in Richetta-OdoniBaseline Case0510152025303540Ball et al. Ricehtta-Odoni Mukherjee-HansenExpected Cost of Delay (Aircraft-Hr)Airborne DelayGround DelayBall et al. Richetta-Odoni Mukherjee-HansenApplication in CDM• Dynamic substitution model that can be used by individual airlines to perform scenario-contingent substitutions– Airlines cannot exceed the number of slots (during any hour) assigned to them in the initial stage (by the GH model)– While making substitutions, airlines must not violate the coupling constraints that account for limited information on airport capacity in future time periods• Dynamic compression model that can be used by the FAA– An optimization model that works like the Compression Algorithm currently used by the FAA– Vacant slots (due to cancellations) are utilized by making substitutions, and priority is given to canceling airline– No flight is assigned a later slot than it currently owns ÎEveryone is better offIntra-Airline Substitution BenefitsPercentage Reduction of Delay CostBenefits from Compression01234567891011AALAMTAMWAMXAWEBTACAACHQCOACOMDALDLHEGFFFTJZAKALMEPNWASCXSKWTRSUALUPSUSAAirlineExpected Ground Delay (Aircraft-Hours)Intial AssignmentAfter SubstitutionsAfter CompressionEnroute Airspace Capacity