Systemic delay propagation in the US airport network

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1 Complex World ATM Seminar 213 Systemic delay propagation in the US airport network Pablo Fleurquin José J. Ramasco Victor M Mallorca - Spain

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

3 Why is it important? Total cost of flight delay in US in 27 was 41B dollars. Rich transport dynamics. Cascading failure. 4% Air Carrier Delay 25% 3% Aircraft Arriving Late Security Delay % 41% National Aviation System Delay Extreme Weather ( ( )

Database & network Database: Airline On-Time Performance Data (www.bts.

4 Database & network Database: Airline On-Time Performance Data ( Ø Schedule & actual departure (arrival) times Ø Origin & destination airports Ø Airline id Ø Tail number Network: Nodes: airports Edges: direct flights between airports Node attributes: average delay per flight 21 flights: Ø 6,45,129 flights (74 %) Ø 18 carriers Ø 35 airports

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( (

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( (

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, 21 Average delay per delayed flight: Ø 16.9 min

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

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, 21 Average delay per delayed flight: Ø 25.7 min

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, 21 Average delay per delayed flight: Ø 53.2 min

10 Cluster size Largest cluster size Day B P(>size) slope ~ Characteristic Size: Largest cluster size [Airports] Great variety Consecutive days are very different each other.

11 Intraday cluster evolution Evolution of clusters for March 12:

12 A Jaccard Index B Jaccard Index Cluster composition Top 2 (best days) Top 2 (worst days) Day Ranking 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.

Model definition Ø Flight rotation (same tail number) Scheduled arrival time T s Schedule

Flight D Airline X ΔT α Inbound delay Actual arrival time Flight A Scheduled turn around

Departure delay Actual departure time Flight A Departure delay T j act.

Flight E Airline X Actual arrival time. Flight D Airline X T j act.d (p ij) =max[t j sch.

a(p i j)]], 8i 6= i Ø Airport Congestion SAAR 1 8 6 4 2 6am 1am March 12 Time [EST] ATL ORD

Initial Conditions From the data - Known à when, where and the departure delay for the

13 Model definition Ø Flight rotation (same tail number) Scheduled arrival time T s Schedule (arrival/departure) Ø Flight connectivity (different tail number) Sch. arrival time. Flight D Airline X ΔT α Inbound delay Actual arrival time Flight A Scheduled turn around time c Scheduled departure time Flight E Airline X Scheduled departure time waiting time Departure delay Actual departure time Flight A Departure delay T j act.d (p ij) =max[t j sch.d (p ij); T j act.a(p ij )+T s ] Ts Actual departure time. Flight E Airline X Actual arrival time. Flight D Airline X T j act.d (p ij) =max[t j sch.d (p ij); T j act.a(p ij )+T s ;max[t j act.a(p i j)]], 8i 6= i Ø Airport Congestion SAAR am 1am March 12 Time [EST] ATL ORD DEN 2pm 6pm 1pm 2am Schedule Airport Arrival Rate (SAAR) First Arrived First served β Initial Conditions From the data - Known à when, where and the departure delay for the first flight of the sequence. T j act.d (p ij) =max[t j sch.d (p ij); T j q (p ij )+T j act.a(p ij )+T s ] Random initial conditions - Fixed initial delay (min) - % of initially delayed planes

14 Delay propagation dynamics

15 B) D) A) B) March Data and model comparison for Data April 19 8 Model and April Cluster size Cluster size1 Plane rotation 3 Data Model March 12 April Time (EST) Airport congestion 3 Data Model A) C) March 12 April Time (EST) Full model 3 Data Model March 12 Time (EST) April 19 8C) Connections D) Data 4 2 Cluster size1 size1 Cluster size1 Cluster Time (EST) Connections Data/Model comparison Full model Plane rotation 3 Data 8 Model 1 size1 Cluster Good agreement between model and reality March 12 April Time (EST) Airport congestion 3 Data Model March 12 April 19 March 12 April 19 Model Time (EST) size1 Cluster Time (EST)

16 System resilience With random initial conditions April 19 March 12 α =.3 α =.1 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.

17 What about October 27?

External perturbation Cluster size per hour 8 6 4 2 6am

18 External perturbation Cluster size per hour am 1am 2pm Time [EST] Data Basic model Baseline model 6pm 1pm 2am

19 External perturbation: variants Cluster size per hour Ø What about the declining phase? Variant 1: Baseline + Connectivity drops to between 7 pm & 9 pm EST A) 6am 1am 2pm Time [EST] Improve the matching. Data Baseline model Variant 1 6pm 1pm 2am Cluster size per hour Variant 2: Baseline + Connectivity drops to.13 between 7 pm & 9 pm EST. Variant 3: Baseline + Connectivity drops to.13 between 6 pm & 1 pm EST. Make sense to interpret cancelation policies as a decrease on the network connectivity. Higher sensitivity to time period ΔT α B) 6am 1am 2pm Time [EST] Data Baseline model Variant 2 6pm 1pm 2am Cluster size per hour C) 6am 1am 2pm Time [EST] Data Baseline model Variant 3 6pm 1pm 2am

20 Effect of the schedule For comparison purposes: schedule of October 2. This day showed a low level of congestion: largest cluster size of 2. Figure: Initial conditions of October 27 run using the schedule of October 2. Cluster size per hour am 1am 2pm Time [EST] Data Baseline model Schedule: Oct 2 6pm 1pm 2am 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.

21 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 (213). Ø Spanish patent pending, filed December , number P Ø P. Fleurquin, J.J. Ramasco, V.M. Eguiluz, Characterization of delay propagation in the airport network, submitted to Proceedings of the 212 Air Transport Research Society Conference.

Supplementary Information for Systemic delay propagation in the US airport network

Supplementary Information for Pablo Fleurquin,, José J. Ramasco & Víctor M. Eguiluz Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Palma de Mallorca, Spain. Innaxis Foundation