Air Traffic Flow Management for the National Airspace System - PowerPoint PPT Presentation

Air Traffic Flow Management for the National Airspace System Christopher Maes MIT Operations Research Center November 21, 2011

Outline 1 Model formulation 2 Estimating model parameters 3 Performance analysis and preliminary results 4 Conclusions and further work

Model formulation

Bertsimas, Lulli, and Odoni model • Planes fly between airports and through sectors with defined capacity • Deterministic and discrete time model • Produces an optimal assignment of delays to flights • Flights may be dynamically rerouted to avoid congestion • Origin-destination routes represented as directed acyclic graph P f L f j i orig f dest f i j Christopher Maes Air Traffic Flow Management for the NAS 3 / 24

Bertsimas, Lulli, and Odoni model • Planes fly between airports and through sectors with defined capacity • Deterministic and discrete time model • Produces an optimal assignment of delays to flights • Flights may be dynamically rerouted to avoid congestion • Origin-destination routes represented as directed acyclic graph P f L f L f j i i orig f dest f i j Christopher Maes Air Traffic Flow Management for the NAS 3 / 24

Bertsimas, Lulli, and Odoni model • Planes fly between airports and through sectors with defined capacity • Deterministic and discrete time model • Produces an optimal assignment of delays to flights • Flights may be dynamically rerouted to avoid congestion • Origin-destination routes represented as directed acyclic graph P f P f L f L f j j i i orig f dest f i j Christopher Maes Air Traffic Flow Management for the NAS 3 / 24

Bertsimas, Lulli, and Odoni model • Planes fly between airports and through sectors with defined capacity • Deterministic and discrete time model • Produces an optimal assignment of delays to flights • Flights may be dynamically rerouted to avoid congestion • Origin-destination routes represented as directed acyclic graph P f L f j i f [ T f i ] i , T orig f dest f i j Christopher Maes Air Traffic Flow Management for the NAS 3 / 24

Bertsimas, Lulli, and Odoni model • Planes fly between airports and through sectors with defined capacity • Deterministic and discrete time model • Produces an optimal assignment of delays to flights • Flights may be dynamically rerouted to avoid congestion • Origin-destination routes represented as directed acyclic graph P f L f j i u l iu orig f dest f i j l iv v Christopher Maes Air Traffic Flow Management for the NAS 3 / 24

Decision variables � 1 if flight f arrives at sector j by time t w f j , t = 0 otherwise w f j , t only defined for those sectors j in f ’s graph, within the feasible f time interval [ T f j , T j ] t f T f w f w f w f T j j , t − 1 j , t j , t +1 j Christopher Maes Air Traffic Flow Management for the NAS 4 / 24

Constraints Capacity Constraints 1 # flights arriving at airport k at time t must not exceed A k ( t ) 2 # flights departing airport k at time t must not exceed D k ( t ) 3 # flights in sector j at time t must not exceed S j ( t ) Christopher Maes Air Traffic Flow Management for the NAS 5 / 24

Constraints Capacity Constraints 1 # flights arriving at airport k at time t must not exceed A k ( t ) 2 # flights departing airport k at time t must not exceed D k ( t ) 3 # flights in sector j at time t must not exceed S j ( t ) Turnaround time for connecting flights 4 If ( g , f ) are a pair of connecting flights, g f flight f cannot depart until s f minutes after g has arrived Christopher Maes Air Traffic Flow Management for the NAS 5 / 24

Constraints Capacity Constraints 1 # flights arriving at airport k at time t must not exceed A k ( t ) 2 # flights departing airport k at time t must not exceed D k ( t ) 3 # flights in sector j at time t must not exceed S j ( t ) Turnaround time for connecting flights 4 If ( g , f ) are a pair of connecting flights, g f flight f cannot depart until s f minutes after g has arrived Definition of decision variables 5 If f has arrived at j by time t , it has arrived by time t + 1 Christopher Maes Air Traffic Flow Management for the NAS 5 / 24

Rerouting constraints Sector traversal time 6 A flight cannot arrive at sector j by time t if it has not arrived at a preceding sector j ′ ∈ P j by j time t − l f j ′ j Christopher Maes Air Traffic Flow Management for the NAS 6 / 24

Rerouting constraints Sector traversal time 6 A flight cannot arrive at sector j by time t if it has not arrived at a preceding sector j ′ ∈ P j by j time t − l f j ′ j Subsequent sector f 7 If flight f has arrived in sector i by T i , it must arrive in at least one sector i ′ ∈ L f f i by T i ′ i 8 Flight f can be in at most one sector i ′ ∈ L f f i by T i ′ Christopher Maes Air Traffic Flow Management for the NAS 6 / 24

Rerouting constraints Sector traversal time 6 A flight cannot arrive at sector j by time t if it has not arrived at a preceding sector j ′ ∈ P j by j time t − l f j ′ j Subsequent sector f 7 If flight f has arrived in sector i by T i , it must arrive in at least one sector i ′ ∈ L f f i by T i ′ i 8 Flight f can be in at most one sector i ′ ∈ L f f i by T i ′ Total flight time 9 The total flight time must not exceed the maximum duration of the flight Christopher Maes Air Traffic Flow Management for the NAS 6 / 24

Model parameters • Airport capacities A k ( t ) , D k ( t ) for all airports k , time t • Sector capacities S j ( t ) for all sectors j , times t • The directed acyclic graphs that describe the flight routes f • Time intervals: [ T f j , T j ] • Time to fly from sector i to sector j : l f ij • Maximum flight duration: max f • Connecting flight pairs ( g , f ) and turnaround time s f Christopher Maes Air Traffic Flow Management for the NAS 7 / 24

Estimating model parameters

Data sources Model requires large amounts of data from multiple sources Data from John Cho, Richard DeLaura, and Ngaire Underhill: • ETMS provides sector entrance/exit times for flight graphs • SDAT provides sector entrance/exit times for flights • ASPM provides arrival and departure times for flights • RITA provides delay information and tail numbers (for tracking connecting flights) • APM provides airport arrival and departure capacities • Weather-impacted sector capacities from workload model of Cho, Welch, Underhill Christopher Maes Air Traffic Flow Management for the NAS 8 / 24

Airport capacities • Estimates from two months of historical APM data • Number of arrivals and departures in 15 min interval • Construct estimates for different runway configurations and weather conditions (VMC or IMC) Christopher Maes Air Traffic Flow Management for the NAS 9 / 24

Airport capacities • Estimates from two months of historical APM data • Number of arrivals and departures in 15 min interval • Construct estimates for different runway configurations and weather conditions (VMC or IMC) 35 26R, 27L | 8R 9L VMC 26R, 27L, 28 | 26L, 27R VMC 26R, 27L, 28 | 26L, 27R IMC 30 25 26R, 27L, 28 | 26L, 27R, 28 IMC arrival capacity 20 26R, 27L | 26L, 27R, 28 IMC 15 10 26R, 27L | 8R, 9L IMC 5 0 10 20 30 40 50 60 model time Christopher Maes Air Traffic Flow Management for the NAS 9 / 24

Weather-impacted sector capacities • Use impacted sector capacities from Cho, Welch, Underhill • Use SDAT data to compute fraction of time spent in sector for each non-model flight • Lower sector capacities to account for non-model flights ZHU 63 capacity and utilization 12 10 8 6 4 2 0 0 10 20 30 40 50 60 model time 1 0.8 wx Blockage Fraction 0.6 0.4 0.2 0 0 10 20 30 40 50 60 model time Christopher Maes Air Traffic Flow Management for the NAS 10 / 24

Time spent in sector • Model uses 15 minute time intervals • Necessary to obtain airport and sector capacities • Flights often spend much less than 15 min in a sector • Drop sectors occupied for less than 8 minutes f • Maintains total flight time (through [ T f j ], l f j ′ j ) j , T • But ignores effect on sector capacity 4 Distribution of sector crossing times x 10 14 12 Mean: 9.6 minutes 10 8 6 4 2 0 0 5 10 15 20 25 30 35 40 minutes Christopher Maes Air Traffic Flow Management for the NAS 11 / 24

Constructing flight graphs Use 25 days of ETMS data to construct a graph of sectors traversed by flights ( e.g. flights from JFK to LAX): Christopher Maes Air Traffic Flow Management for the NAS 12 / 24