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. Monechi1, Vito D. P. Servedio2,1, Vittorio Loreto1,3

1Sapienza University of Rome, 2Institute for Complex Systems

(ISC-CNR), 3Institute 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

10-4 10-3 10-2 10-1 100 50 100 150 200 250 300 P(k>κ) κ planned real

Degree

10-3 10-2 10-1 100 1000 3000 5000 7000 9000 P(s>σ) σ planned real

Strength

0.00 0.02 0.04 0.06 0.08 0.10 50 100 150 200 250 P(d) d (NM) planned real

Links’ Length

◮ Creation of longer links, the traffic over the network becomes

more homogeneous

Delays

0.05 0.1 0.15 0.2 0.25

• 20
• 15
• 10
• 5

5 10 15 20 P(δ tenr) δ tenr

En-route Delay

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

• 40
• 20

20 40 60 80 P(δ tdep) δ tdep

Departure Delay

◮ δttot = δtdep + δtenr ◮ Delays of aircraft crossing the Italian Airspace in June 2011.

Delays: Correlations

• 40
• 20

20 40

• 40
• 20

20 40 δ ttot (min.) δ tdep (min.) R2 = 0.96

• 60
• 40
• 20

20 40 60

• 40
• 20

20 40 δ ttot (min.) δ tenr (min.) R2 = 0.32

• 60
• 40
• 20

20 40 60

• 40
• 20

20 40 δ tenr (min.) δ tdep (min.) R2 = 0.05

Dynamical Metrics and STCAs

◮ Short-Term Conflict Alert (STCA) → nSTCA & Pn(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.

0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 1st Component 0.3 0.2 0.1 0.0 0.1 2nd Component static metrics horizontal movements metrics

• ther dynamical metrics

5 10 15 20 25 30 35 40 # of STCAs

◮ Vertical Deviations used

in critical and highly trafficked nodes.

◮ Horizontal Deviations

used in non-critical and low-trafficked nodes.

Air Traffic Model: Conflict Detection

m n tm tn

α

a) m n tm tn

β

B) m n tm tn

α

c) m n tm tn

α

d)

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

0.05 0.1 0.15 0.2 0.25 0.3

• 20
• 10

10 20 30 40 P(δk) δk dataset simulation

Degree

0.05 0.1 0.15 0.2 0.25

• 100
• 80
• 60
• 40
• 20

20 40 60 80 100 P(δs) δs dataset simulation

Strenght

0.05 0.1 0.15 0.2 0.25 0.3

• 0.04
• 0.03
• 0.02
• 0.01

0.01 0.02 P(δb) δb dataset simulation

Betweenness

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 20 40 60 80 100 120 140 160 180 200 P(d) d (NM) planned radar updated simulation

Links’ Length

Microscopic Validation

◮ Measure single trajectoriy variations from flight plans to real

trajectories.

◮ δl: variation in length. ◮ δn: variation in the number of crossed navigation points. ◮ δtenr: en-route delay.

Validation:Trajectories Statistics

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

• 200
• 150
• 100
• 50

50 100 150 200 P(δl) δl (NM) dataset simulation

δl

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

• 20
• 15
• 10
• 5

5 10 15 20 P(δn) δn dataset simulation

δn

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

• 15
• 10
• 5

5 10 15 P( δ tenr ) δ tenr (min. ) dataset (next=0)

δtenr (no ext. dist.)

• 15
• 10
• 5

5 10 15 δ tenr (min. ) dataset (next=200)

δtenr (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.

0.0 2.0 4.0 6.0 8.0 10.0 10-1 100 101 102 nconflicts Nf(t)

Estonia Greece Italy

IN-OUT

10-3 10-2 10-1 100 10-1 100 101 nconflicts Nf(t) (rescaled) Estonia Greece Italy

IN-OUT(scaling)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 10-1 100 101 102 nconflicts Nf(t) Estonia Greece Italy

Vectoring-OUT

10-3 10-2 10-1 100 10-2 10-1 100 101 nconflicts Nf(t) (rescaled) Estonia Greece Italy

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):

• ptimization via avalanche dynamics.

◮ C(γ) = i γi. ◮ xi = {(nstart, tstart), (n1, t1), . . . , (nstop, tstop)} ◮ γi = l(xi) + ǫ 2

N

j=1,j=i m(xi, xj) (Fitness of the ith trajectory) ◮ Parameter ǫ allows to modulate between straight and

conflict-free flight plans.

◮ Sectors Capacity constraints are enforced.

Suboptimal Flight Plans

1 1.01 1.02 1.03 1.04 1.05 1.06 0.5 1 1.5 2 2.5 3 <l(xi)> ε a) 100 200 300 400 500 600 0.5 1 1.5 2 2.5 3 nconflicts ε b)

Suboptimal Flight Plans

a)

Current

b)

Sub-Optimal

Efficiency Againts Perturbations

◮ External disturbances have not been included in the

• ptimization 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

200 400 600 800 1000 1200 1400 50 100 150 200 250 300 350 # of actions τ (sec.) current ε=0 ε=0.5 ε=0.75 ε=1 ε=2

# of actions

• 90
• 80
• 70
• 60
• 50
• 40
• 30
• 20
• 10

10 50 100 150 200 250 300 350 <δ tenr> (sec.) τ (sec.) current ε=0 ε=0.5 ε=0.75 ε=1 ε=2

En-Route Delay

Perturbed Areas

500 1000 1500 2000 2500 3000 50 100 150 200 # of actions next current ε=0 ε=1 ε=2

# of actions

• 140
• 120
• 100
• 80
• 60
• 40
• 20

20 40 50 100 150 200 <δ tenr> (sec.) next current ε=0 ε=1 ε=2

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.