Fig 1.
Typical structure of a national airspace and phases of a flight.
(a) Navigation point network in the Italian Airspace. White nodes are navigation points, red nodes are Airports. (b) Two-dimensional projection of the sectors in the Italian Airspace during one typical day of operation (sector structures may change depending on traffic load). (c) Phases of a flight: the time line at the bottom indicates the phases of route where the delays δtdep at departure and δtenr during flight, are generated.
Fig 2.
Global effects of the Air Traffic Control (ATC) activity.
(a) Histograms of the total, departure and en-route delays for all the aircraft that have crossed the Italian Airspace in the period covered by our data set. (b) Inverse cumulative distribution of the strength of the nodes of the planned and real European navigation point network built by aggregating all the trajectories in the data set.
Fig 3.
Conflict avoidance strategies.
(a) Redirection of aircraft towards nodes inside the current sector, depicted in pink color (IN Strategy); (b) Redirection towards nodes inside nearby sectors (OUT Strategy); (c) Possible redirections towards nodes in the sector that do not belong to the navigation point network (Vectoring). The node highlighted with a red cross is the conflicted node towards which the aircraft is supposed to fly according to its flight plan.
Fig 4.
Comparison of actual traffic density with theoretical conflict thresholds.
Average number of flying aircraft per second for various days of the dataset in the Italian Airspace. The different curves correspond to different flight levels and their maxima are attained during weekends. The black horizontal dotted line is the estimated threshold value above which the conflict phase emerge with the IN-OUT protocol integrated with flight level changes. The red horizontal dotted line is the threshold with the same IN-OUT protocol with FL changes enriched with the direct assignment procedure.
Fig 5.
Comparison between the distributions of the en-route delays from data set and simulations.
(a) Simulation without external disturbances. (b) Simulation with next = 200 external disturbances. (c) Simulation with next = 2000 external disturbances.
Fig 6.
Synthetic boundary-free airspace.
Representation of a synthetic airspace, built by using a Fibonacci Grid on a sphere.
Fig 7.
Transition in synthetic and national airspaces.
(a) Transition for the IN-OUT protocol in the synthetic airspaces with N = 185, N = 371 and N = 779. (b) Transition for the IN-OUT, Vectoring, IN-OUT with vertical deviations and IN-OUT with vertical deviations and direct assignment in the Estonian airspace. (c) Transition for the IN-OUT protocol in the Estonian, Greek and Italian National Airspaces. (d) Scaling property of the transition for the IN-OUT protocol in the synthetic and real airspaces; in the case of the synthetic airspace the horizontal axis has been rescaled by N0.40, while in the real airspace by N0.43.