Data driven modeling of systemic delay propagation under severe meteorological conditions

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Report on one of the ComplexWorld Network's PhD research project's. Find further information at http://complexworld.eu/wiki/Uncertainty_in_ATM

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Data driven modeling of systemic delay propagation under severe meteorological conditions

  1. 1. Complex World | Seminar 2013 Data-driven modeling of systemic delay propagation under severe meteorological conditions Pablo Fleurquin José J. Ramasco Victor M Eguíluz @ifisc_mallorca www.facebook.com/ifisc http://ifisc.uib-csic.es - Mallorca - Spain
  2. 2. Outline Motivation Air-traffic data Network & Cluster construction Data Results Model definition Comparison: model – reality Effect of large scale disruptions on the system Conclusions http://ifisc.uib-csic.es
  3. 3. Why is it important? •  Total cost of flight delay in US in 2007 was 41B dollars. •  Rich transport dynamics. •  Cascading failure. 4% Air  Carrier   Delay 30% 25% Aircraft  Arriving  Late Security  Delay 0% National  Aviation   System  Delay 41% (http://www.transtats.bts.gov/) Extreme  Weather (http://www.eurocontrol.int ) http://ifisc.uib-csic.es
  4. 4. Database & network Database: Network: •  Airline On-Time Performance Data (www.bts.gov) •  Nodes: airports •  Edges: direct flights between airports •  Node attributes: average delay per flight Ø Schedule & actual departure (arrival) times Ø Origin & destination airports Ø Airline id Ø Tail number •  2010 flights: Ø  6,450,129 flights (74 %) Ø  18 carriers Ø  305 airports http://ifisc.uib-csic.es
  5. 5. Cluster definition Clusters: •  Formed by airports in problem Ø  average delay per flight > 29 min •  Must be connected (flight route between them) •  A group of airports connected by flights that their average delay is higher than 29 minutes Cluster(A( size(4( ( Cluster(B( size(2( ( http://ifisc.uib-csic.es
  6. 6. Cluster definition Clusters: •  Formed by airports in problem Ø  average delay per flight > 29 min •  Must be connected (flight route between them) •  A group of airports connected by flights that their average delay is higher than 29 minutes Cluster(A( size(4( ( Cluster(B( size(2( ( http://ifisc.uib-csic.es
  7. 7. Largest daily cluster Clusters: •  Formed by airports in problem Ø  average delay per flight > 29 min •  Must be connected (flight route between them) •  A group of airports connected by flights that their average delay is higher than 29 minutes Cluster(A( size(4( ( Cluster(B( size(2( ( •  April 19, 2010 •  Average delay per delayed flight: Ø  16.9 min http://ifisc.uib-csic.es
  8. 8. Largest daily cluster Clusters: •  Formed by airports in problem Ø  average delay per flight > 29 min •  Must be connected (flight route between them) •  A group of airports connected by flights that their average delay is higher than 29 minutes Cluster(A( size(4( ( Cluster(B( size(2( ( •  March 9, 2010 •  Average delay per delayed flight: Ø  25.7 min http://ifisc.uib-csic.es
  9. 9. Largest daily cluster Clusters: •  Formed by airports in problem Ø  average delay per flight > 29 min •  Must be connected (flight route between them) •  A group of airports connected by flights that their average delay is higher than 29 minutes Cluster(A( size(4( ( Cluster(B( size(2( ( •  March 12, 2010 •  Average delay per delayed flight: Ø  53.2 min http://ifisc.uib-csic.es
  10. 10. B 120 0 10 100 P(>size) A Largest cluster size ongestion and consequently delays are propagating through connected airports in Cluster size n intra-day time period. 80 60 40 -1 10 -2 10 slope ~ -0.0496 Characteristic Size: 20.1 20 0 0 60 120 180 Day 240 300 360 -3 10 0 20 40 60 80 100 120 Largest cluster size [Airports] Figure 3.13. (A) Daily size of the largest cluster. (B) Complementary cumulative distribution ofvariety of the largest cluster (log-normal scale). the size •  Great •  Consecutive days are very different each other. Taking into account all days of 2010 the largest connected cluster size is exlored as a function of the day (Figure 3.13 A). A strong variability is thus the http://ifisc.uib-csic.es
  11. 11. Intraday cluster evolution Evolution of clusters for March 12: http://ifisc.uib-csic.es
  12. 12. Cluster composition B 1 Jaccard Index Jaccard Index A 0.8 0.6 0.4 0.2 0 0 60 120 180 Day 240 300 360 0.6 Top 20 (best days) Top 20 (worst days) 0.4 0.2 0 0 5 10 Ranking 15 • Jaccard Index: • Great variety •  Consecutive days are very different each other •  For consecutive days not only they differ in the cluster size also the airports comprising the cluster are different. http://ifisc.uib-csic.es 20
  13. 13. addition to rotational reactionary delay, the need to wait for load, connecting   ssengers and/or crew from another delayed airplane from the same fleet (airline     ) may cause, as well, reactionary delay. Ø  Flight rotation (same tail number) Model definition Ø  Airport Congestion March 12 100 Ts Scheduled departure time Figure 4.4: Possible connections within flights of the same airline. Actual arrival time Flight A Actual departure time Flight A SAAR Scheduled arrival time 80 ATL ORD DEN 60 40 20 4a m 6a m 8a m 10 am 12 am 2p m 4p m 6p m 8p m 10 pm 12 pm 2a m For each flight at a particularc airport, connections delay that airport are ranfrom 0 Inbound delay Departure mly chosen as follows. Firstly, we take a T window prior to the scheduled Example of SAAR for three major airports: Atlanta International A Figure 4.6. (ATL), O’Hare Time Denver parture time of the flight. Secondly, we distinguish possible connections of the International Airport (ORD) and [EST] International Airport (DEN Scheduled turn around time me airline from other flights, that have a scheduled arrival time within the 29T Subprocesses § Schedule Airport Arrival Rate (SAAR) § Ts ndow (Flights B and D in the example of Figure 4.4). Finally, from these possi§  First Arrived First served e connections we§  Schedule (arrival/departure) select those with probability ↵ ⇤ flight connectivity factor. The When aircraft rotation and airport congestion is present the equation The equation that govern the rotation subprocess is given by: §  β ght connectivity factor was defined in 3.1.2 and ↵ is an e↵ective parameter of by: ntrol that allowsT j modify the strength of); T j e↵ect) in Ts ] model. For instance, T j (p ) = max[T j (p ); T j (p ) + T j (p ) + T ] to (pij ) = max[T j (pij this (pij + the (4.2) act.a ij s act.d sch.d act.a ij q ij sch.d ij = 0 means that there is no connection between flights with di↵erent tail number, act.d hile ↵ = 1 makes the fraction of connecting flights of the same airlinewhere q means the time spent by the aircraft in the queue waitin equal to where j corresponds to destination airport and i to the origin one. The e fractionØ Flight connectivity (different tail number) of connecting passengers in the given airport. In the simulations, ↵ is the full model dynamics is govern by a combination of th served. Finally, ndexes act.d,act.a and sch.d correspond respectively to Actual Departure, AcInitial Conditions Scheduled departure ried according to the case under study and T is always taken to be 180 minutes subprocesses: Arrival and Schedule Departure. time Actual departure time. §  From the data… hours). Sch. arrival Flight E | Airline X Flight E | Airline X j j j T selected. By -  j Known à when, Ts ; max[T jand the 0 | Airline X t us suppose that from the previous example Flight D was randomly act.d (pij ) = max[Tsch.d (pij ); Tq (pij ) + Tact.a (pij ) +where act.a (pi0 j )]], 8i 6= waiting time .2 Flight connectivity is subprocess an airplane is able to fly if and if only their connections have already departure delay for the first flight of Actual arrival time. rived to the airport, if not it has to wait until this condition is satisfied (Figure the sequence. Flight D | Airline X ddition to rotational reactionary delay, the need to only source of connecting 5). It is important to note that flight connectivity is thewait for load, stochasticity Initial conditions §  ΔT another delayed airplane from the same4.4 (airline Departure engers and/or crewlack of knowledge about the delay flight connections within the fleet the model due to a from real §  α Actual Departure time of the next flight leg is given §  Random initial conditions… may cause, as case the hedule. In thiswell, reactionary delay. by: Initial condition refers to the initial delay (min) -  Fixed situation of the first flight of an aircraft se j j j j Tact.d (pij ) = max[Tsch.d (pij ); Tact.a (pij ) + Ts ; max[Tact.a (pi0 j )]], 8i0meaning when, where% ofthe departure delay of planes 6= i (4.3) -  and initially delayed this flight. Variations situation can have a great impact on the delay propagation. In other wor dynamics of delays over the network is highly sensitive to the initial conditi time. Flight D We characterized initial conditions by http://ifisc.uib-csic.es for t the average delay per flight
  14. 14.       Delay propagation dynamics http://ifisc.uib-csic.es
  15. 15. Data/Model comparison Data and model comparison for March 12 and April 19 Data April 19 Model 40 1 20 am 4p m 8p m 12 pm 12 m 8a m 4a am 4p m 8p m 12 pm 12 m 0 8a m 0 m 12 am 4p m 8p m 12 pm Airport c 100 March 12 80 60 40 20 0 am 4p m 8p m 12 pm 3 2 60 4a Cluster size 100 March 12 80 D) m C) Connections Good agreement between model and reality. Time http://ifisc.uib-csic.es 12 Time (EST) 0 m m 12 am 4p m 8p m 12 pm 8a 4a m 0 m 12 am 4p m 8p m 12 pm 4a m 0 20 8a 20 40 8a 1 60 4a 40 100 March 12 80 m 2 60 8a Cluster size Data April 19 Model Plane 4a 3 100 March 12 80 B) Cluster size Full model Cluster size A)
  16. 16. Data/Model comparison 20 0 4 4aa m m 8 8aa m m 12 12 aam m 4p 4p m m 8p 8p m m 12 12 pm pm 2 1 0 Time (EST) D) Time Airport c 100 March 12 80 60 40 20 am 4p m 8p m 12 pm 0 m http://ifisc.uib-csic.es 12 am 4p m 8p m 12 pm am 4p m 8p m 12 pm 0 40 8a 44aam mm 12 88aam a1m m 12 2a m 4p 44apm mpm m 8p 88ppm mm 1 12 12 2ppm m pm 0 Data April 19 Model m 20 3 60 4a 20 m Airport congestion 80 8a 40 Data April 19 Model 1 0 Cluster size 60 Plane 0 100 March 12 Time (EST) Cluster size 40 B) 4 4aa m m 8 8aa m m 12 12 aam m 4p 4p m m 8p 8p m m 4a1122pp m mm 0 3 1 4 4aa m m 8 8aa m m 12 12 aam m 4p 4p m m 8p 8p m m 12 12 pm pm Cluster size 4 4aa m m 8 8aa m m 12 12 am am 4p 4p m m 8p 8p m m 12 12 pm pm 1 2 60 12 Time (EST) 0 Connections agreement between model and reality. 8a m 12 am 4p m 8p m 12 pm m 8a 4a m 12 am 4p m 8p m 12 pm m 8a 4a 0 40 20 Data April 19 Model 2 60 Time (EST) m 1 0 3 100 March 12 80 Time (EST) 100 March 12 80 20 0 C) Cluster size 40 0 Data April 19 Model Good 2 60 20 0 1 m 3 20 2 12 Airport congestion 100 March 12 80 40 4a Time (EST) 60 8a 0 4a m 8a m 12 am 4p m 8p m 12 pm 0 40 April 19 Plane rotation 100 March 12 80 Data April 19 Model D) Model m 20 Connections 3 2 Data 4 4aa m m 1 60 4a 40 4a m 8a m 12 am 4p m 8p m 12 pm Cluster size 2 60 D) Cluster size Data April 19 Model 100 March 12 80 3 Time (EST) 4a 3 0 Full model 0 m Cluster size 8a 44 maam m 12 88aa m a1m m 12 2aa 4p m m 4 4 mppm m 8p 88pp m mm 12 1122ppm pm m Plane rotation 100 March 12 80 20 100 March 12 C) 80 Cluster size B) 1 4 4aa m m 8 8aa m m 12 12 aam m 4p 4p m m 8p 8p m m 12 12 pm pm A) 40 B) 4a 88aa m mm 12 12 am 8a a m 4 mppm 4 12 88 m amppm m 4p1122ppm mm 8p m 12 pm Cluster size Cluster size A) Full model 3 100 March 12 Data April 19 Data and model comparison for March 12 Model 80 2 and April 19 60
  17. 17. Data/Model comparison Data and model comparison for March 12 and April 19 Data April 19 Model 40 1 20 am 4p m 8p m 12 pm 12 m 8a m 4a am 4p m 8p m 12 pm 12 m 0 8a m 0 m 12 am 4p m 8p m 12 pm Airport c 100 March 12 80 60 40 20 0 am 4p m 8p m 12 pm 3 2 60 4a Cluster size 100 March 12 80 D) m C) Connections Good agreement between model and reality. Time http://ifisc.uib-csic.es 12 Time (EST) 0 m m 12 am 4p m 8p m 12 pm 8a 4a m 0 m 12 am 4p m 8p m 12 pm 4a m 0 20 8a 20 40 8a 1 60 4a 40 100 March 12 80 m 2 60 8a Cluster size Data April 19 Model Plane 4a 3 100 March 12 80 B) Cluster size Full model Cluster size A)
  18. 18. System resilience •  With random initial conditions… March 12 α = 0.03 α = 0.1 April 19 •  Each day is potentially a bad day, if some initial conditions are met. •  Flight connectivity is a key factor for the rise of congestion in the network. •  Sensitivity to initial conditions. http://ifisc.uib-csic.es
  19. 19. What about October 27 ? http://ifisc.uib-csic.es
  20. 20. Data Basic model Baseline model 80 60 40 20 m 10 am 12 am 2p m 4p m 6p m 8p m 10 pm 12 pm 2a m 4a m m 8a 6a m 0 4a Cluster size per hour External perturbation Time [EST] http://ifisc.uib-csic.es
  21. 21. External perturbation: variants Ø  What about the declining phase ? •  Baseline + … •  Baseline + … •  Baseline + … •  Connectivity drops to 0 between 7 pm & 9 pm EST. •  Connectivity drops to 0.13 between 7 pm & 9 pm EST. •  Connectivity drops to 0.13 between 6 pm & 10 pm EST. Time [EST] Time [EST] C) Data Baseline model Variant 3 60 40 20 am 2p m 4p m 6p m 8p m 10 pm 12 pm 2a m 4a m 12 m am 10 m 8a m 0 6a am 2p m 4p m 6p m 8p m 10 pm 12 pm 2a m 4a m 12 am 0 80 4a 20 m am 2p m 4p m 6p m 8p m 10 pm 12 pm 2a m 4a m am 12 m 10 m 8a 6a 4a m 0 40 10 20 Data Baseline model Variant 2 60 m 40 B) 8a 60 80 m Data Baseline model Variant 1 6a A) 4a 80 Cluster size per hour Variant 3: Cluster size per hour Variant 2: Cluster size per hour Variant 1: Time [EST] •  Improve the matching. •  Make sense to interpret cancelation policies as a decrease on the network connectivity. •  Higher sensitivity to time period ΔTα . http://ifisc.uib-csic.es
  22. 22. Effect of the schedule •  For comparison purposes: schedule of October 20. §  This day showed a low level of congestion: largest cluster size of 2. Data Baseline model Schedule: Oct 20 100 80 60 40 20 am 2p m 4p m 6p m 8p m 10 pm 12 pm 2a m 4a m am 12 m 10 m 8a 4a m 0 6a Cluster size per hour •  Figure: Initial conditions of October 27 run using the schedule of October 20. Time [EST] •  Schedule of October 27 was not the reason for the unfolding of the delays. •  Real intervention measures on October 27 were a palliative to the delay spreading mechanism. http://ifisc.uib-csic.es
  23. 23. Conclusions •  We defined a way of measuring the network-wide spread of the delays Ø  Strong variability between days and intraday •  We introduced a model able to reproduce the cluster dynamics in the data Ø  Resilience of the system Ø  Non-negligible risk of system instability (systemic delay) Ø  Other transport modes •  Mimic external perturbations to the system. Ø  Perturbations could be model as a decrease in the airport capacity parameter. Ø  Intervention measures modeled as a decrease in the network connectivity. Articles: Ø  P. Fleurquin, J.J. Ramasco, V.M. Eguiluz, “Systemic delay propagation in the US airport network”, Scientific Reports 3, 1159 (2013). Ø  P. Fleurquin, J.J. Ramasco, V.M. Eguiluz, “ Data-driven modeling of systemic delay propagation under severe meteorological conditions”, Tenth USA/Europe Air Traffic Management Research and Development Seminar 2013. Ø  Spanish patent pending, filed December 14 2012, number P201231942. Ø  P. Fleurquin, J.J. Ramasco, V.M. Eguiluz, “Characterization of delay propagation in the airport network”, submitted to Proceedings of the 2012 Air Transport Research Society Conference. http://ifisc.uib-csic.es

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