An Air Traffic Control Model Based Local Optimization over the - PowerPoint PPT Presentation

An Air Traffic Control Model Based Local Optimization over the Airways Network B. Monechi 1 , Vito D. P. Servedio 2 , 1 , Vittorio Loreto 1 , 3 1 Sapienza University of Rome, 2 Institute for Complex Systems (ISC-CNR), 3 Institute for Scientific Interchange (ISI)

Analysis of Aircraft Radar Tracks ◮ Data about flight plans (before ATC) and radar updated tracks (after ATC) in Europe (DDR data.) ◮ Time resolution ∼ 2 min: conflicts cannot be spotted! ◮ Sectors structure. ◮ Safety Dataset: data about Short-Term Conflict Alerts (STCAs) [1] [1] Lillo, Fabrizio, et al. "Coupling and Complexity of Interaction of STCA Networks." EUROCONTROL 8th Innovative Research Workshop Exhibition. 2009.

Navigation Point Networks Planned Follows the airways structure. Real Topological changes due to ATC.

Navigation Point Networks 10 0 10 0 planned planned real real 10 -1 10 -1 P(k> κ ) P(s> σ ) 10 -2 10 -2 10 -3 10 -3 10 -4 0 50 100 150 200 250 300 1000 3000 5000 7000 9000 κ σ Degree Strength 0.10 planned real 0.08 0.06 P(d) 0.04 0.02 0.00 50 100 150 200 250 d (NM) Links’ Length ◮ Creation of longer links, the traffic over the network becomes more homogeneous

Delays 0.25 0.2 0.18 0.2 0.16 0.14 0.15 0.12 P( δ t enr ) P( δ t dep ) 0.1 0.1 0.08 0.06 0.05 0.04 0.02 0 0 -20 -15 -10 -5 0 5 10 15 20 -40 -20 0 20 40 60 80 δ t enr δ t dep En-route Delay Departure Delay ◮ δ t tot = δ t dep + δ t enr ◮ Delays of aircraft crossing the Italian Airspace in June 2011.

Delays: Correlations 60 R 2 = 0.96 R 2 = 0.32 40 40 20 20 δ t tot (min.) δ t tot (min.) 0 0 -20 -20 -40 -40 -60 -40 -20 0 20 40 -40 -20 0 20 40 δ t dep (min.) δ t enr (min.) 60 R 2 = 0.05 40 20 δ t enr (min.) 0 -20 -40 -60 -40 -20 0 20 40 δ t dep (min.)

Dynamical Metrics and STCAs ◮ Short-Term Conflict Alert (STCA) → n STCA & P n ( STCA ) ◮ Dynamical Metrics [2]: ◮ Horizontal Movements ( Frac , Fork . . . ) ◮ Vertical Movements ( Alt ) ◮ Generated Delays ( Positive Delays and Negative Delays ) [2] Vitali, S. et al. Statistical regularities in atm: network properties, trajectory deviations and delays.

40 ◮ Vertical Deviations used 0.1 static metrics 35 in critical and highly 30 0.0 trafficked nodes. 2nd Component 25 # of STCAs other dynamical metrics ◮ Horizontal Deviations 0.1 20 15 used in non-critical and horizontal movements metrics 0.2 10 low-trafficked nodes. 5 0.3 0 0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 1st Component

Air Traffic Model: Conflict Detection a) B) t n t n t m t m α β n n m m d) c) α t m t n t n t m α n n m m

Air Traffic Model: Conflict Resolution IN OUT Vectoring

Model Validation ◮ Simulation of full day schedules in a chosen airspace (Estonian, Greek and Italian) ◮ Data inferred management protocol: ◮ Vertical Deviations allowed ◮ IN-OUT protocol ◮ Direct Assignment ◮ Sectors Capacity Constraints ◮ External disturbances: penalty delay generating areas

Coarse Grained Validation ◮ Measure of Network Metrics Variations on the Airways Network due to ATC ◮ Degree k of a node: the number of other nodes that are linked to the considered one. ◮ Strength s of a node: the sum of the weights of all the links connected to the considered node (Traffic Load) ◮ Betweenness Centrality b of a node: this metric measures the “importance” of a node in the network.

Coarse Grained Validation 0.3 0.25 dataset dataset simulation simulation 0.25 0.2 0.2 0.15 P( δ k) P( δ s) 0.15 0.1 0.1 0.05 0.05 0 0 -20 -10 0 10 20 30 40 -100 -80 -60 -40 -20 0 20 40 60 80 100 δ k δ s Degree Strenght 0.3 0.035 dataset planned simulation radar updated 0.030 simulation 0.25 0.025 0.2 0.020 P( δ b) P(d) 0.15 0.015 0.1 0.010 0.05 0.005 0 0.000 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 20 40 60 80 100 120 140 160 180 200 δ b d (NM) Betweenness Links’ Length

Microscopic Validation ◮ Measure single trajectoriy variations from flight plans to real trajectories. ◮ δ l : variation in length. ◮ δ n : variation in the number of crossed navigation points. ◮ δ t enr : en-route delay.

Validation:Trajectories Statistics 0.04 0.5 dataset dataset simulation 0.45 simulation 0.035 0.4 0.03 0.35 0.025 0.3 P( δ n) P( δ l) 0.02 0.25 0.2 0.015 0.15 0.01 0.1 0.005 0.05 0 0 -200 -150 -100 -50 0 50 100 150 200 -20 -15 -10 -5 0 5 10 15 20 δ l (NM) δ n δ l δ n 0.50 dataset dataset (n ext =0) (n ext =200) 0.45 0.40 0.35 P( δ t enr ) 0.30 0.25 0.20 0.15 0.10 0.05 0.00 -15 -10 -5 0 5 10 15 -15 -10 -5 0 5 10 15 δ t enr (min. ) δ t enr (min. ) δ t enr (no ext. dist.) δ t enr (with ext. dist.)

High-Traffic Simulations ◮ Simplified conflict resolution protocols: IN-OUT, OUT-IN, Vectoring-OUT, IN-OUT(Vertical Deviations). ◮ Realistic protocol used in validation. ◮ Random schedule of N aircraft departing in a time frame of 2 h ◮ Simulation is over when every aircraft arrives at destination.

10.0 8.0 10 0 Estonia 6.0 Greece n conflicts n conflicts Italy 10 -1 4.0 Estonia 2.0 Greece 10 -2 Italy 0.0 10 -3 10 -1 10 0 10 1 10 2 10 -1 10 0 10 1 N f (t) N f (t) (rescaled) IN-OUT IN-OUT(scaling) 1.0 10 0 0.9 0.8 Estonia Estonia Greece Greece 0.7 Italy Italy 0.6 10 -1 n conflicts 0.5 n conflicts 0.4 0.3 10 -2 0.2 0.1 0.0 10 -3 10 -1 10 0 10 1 10 2 10 -2 10 -1 10 0 10 1 N f (t) N f (t) (rescaled) Vectoring-OUT Vectoring-OUT(scaling)

Efficiency of Global Optimum Planning ◮ The model is suited to test new trajectory planning and airspace structures. ◮ Built a new solution for the planned trajectories and use the model to compare them with the current ones. ◮ Local Optimization (ATC) → Global Optimization

Extremal Optimization Algorithm ◮ Based on the Self-Organized Criticality Phenomenon (SOC): optimization via avalanche dynamics. ◮ C ( γ ) = � i γ i . ◮ x i = { ( n start , t start ) , ( n 1 , t 1 ) , . . . , ( n stop , t stop ) } j =1 , j � = i m ( x i , x j ) (Fitness of the i th trajectory) � N ◮ γ i = l ( x i ) + ǫ 2 ◮ Parameter ǫ allows to modulate between straight and conflict-free flight plans. ◮ Sectors Capacity constraints are enforced.

Suboptimal Flight Plans 1.06 a) 1.05 1.04 <l(x i )> 1.03 1.02 1.01 1 0 0.5 1 1.5 2 2.5 3 ε 600 b) 500 400 n conflicts 300 200 100 0 0 0.5 1 1.5 2 2.5 3 ε

Suboptimal Flight Plans b) a) Current Sub-Optimal

Efficiency Againts Perturbations ◮ External disturbances have not been included in the optimization process ◮ How these solutions behave under their influence? ◮ What are the differences with respect to the current situation? ◮ Departure Delays: from a uniform distribution in [ − τ, τ ] ◮ External disturbances: penalty delay generating areas

Efficiency Againts Perturbations ◮ Every aircraft flies according to a flight plan obtained with the EO algorithm for various values of ǫ . ◮ The structure of the sectors is unvaried with respect to the current situation. After every redirection an aircraft is sent directly to its destination following a straight line. ◮ Directs in order to speed up the traffic are not considered. ◮ Controllers solve conflicts using the IN-OUT protocol. ◮ Capacity constraints are enforced. ◮ Efficiency: Number of Action Performed by the ATCs

Depature Delays 1400 10 0 1200 -10 1000 -20 < δ t enr > (sec.) # of actions current ε =0.5 ε =1 -30 800 ε =0 ε =0.75 ε =2 -40 600 -50 current ε =0.5 ε =1 -60 ε =0 ε =0.75 ε =2 400 -70 200 -80 0 -90 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 τ (sec.) τ (sec.) # of actions En-Route Delay

Perturbed Areas 3000 40 current ε =1 20 ε =0 ε =2 2500 0 2000 < δ t enr > (sec.) -20 current # of actions ε =0 -40 1500 ε =1 -60 ε =2 1000 -80 -100 500 -120 0 -140 0 50 100 150 200 0 50 100 150 200 n ext n ext # of actions En-Route Delay

Conclusions ◮ Developed a model of ATC using historical data ◮ The action of the ATC is modeled as a local optimization over the network of the Airways. ◮ Used the Extremal Optimization Algorithm to build sub-optimal flight plans. ◮ Their efficiency have been compared to the current flight plans.