Air Traffic Restructuring with Airstreams
G. Mykoniatisa,d, S. Moyob, I. Davidsonb, R. Lima de Carvalhoc, D. Dohyd,
F. Mora-Caminoa,b,c,e,*a, georges.mykoniatis@enac.fr, ENAC, Toulouse, France,b, dvcrie@dut.ac.za, InnocentD@dut.ac.za, Durban University of Technology-DUT, South Africa,c, Rafael.lima@mail.uft.edu.br, Universidade Federal do Tocantins-UFT, Brazil,d, Didier.dohy@neometsys.fr, Neometsys, Toulouse, France,e, moracamino@hotmail.fr, Universidade Federal Fluminense-UFF, Brazil.

Extended abstract submitted for presentation at the 11th Triennial Symposium onTransportation Analysis conference (TRISTAN XI)
June 19-25, 2022, Mauritius Island

January 26, 2022
Keywords: Air traffic management, networks, clustering, traffic assignment, traffic complexity.

1 INTRODUCTION
In recent decades, free-flight has been adopted by airlines where aircraft are freed from flying
along a network of airways and waypoints to follow a more direct optimized trajectory. At the stageof carrying out these free-flights, the blind superposition of such types of trajectories leads to thegeneration of a large number of potential conflicts which need the intervention of traffic control toprevent their realization, de-characterizing the computed free-flight trajectories (Bucuroiu, 2015).
This situation contributes to increase the complexity of air traffic and limit its performance(diminished capacity, new delays, extra costs, and increased risk). Then the recently introduced
concept of airstream which can concentrate safely large volumes of traffic appears of interest to
diminish the demand for free flight and reducing the resulting traffic complexity. In an airstream, theflow of traffic will be organized in different lanes according to aircraft performances and traffic
volume, while the aircraft will present new enhanced guidance, anticollision and navigation functions(Ab-Wahid, et al., 2014).
In this paper, after presenting broadly the concept of airstream, a method based on ad-hoc clustering
techniques is proposed to build a structure of airstreams to efficiently channel a large part of the air
traffic of a given region. Then the problem of assigning air traffic to airstreams is considered. The
proposed approach to perform traffic assignment to the airstream network introduces a new tacticalparameter for air traffic management, the airstream distance discount factor to enforce, and regulate
in the case of saturation, the use of sections of airstreams instead of direct flights. This paper is basedon the recent European project Flight Centric Air Traffic Control with Airstreams (FC2A), fundedby SESAR in 2020 (Dohy, et al., 2020).

2 AIR LINK CLUSTERING
A possible first step for generating, from a given prediction of air traffic demand, an airstream
network is to perform a bundling of the air-links which are the pairs of airports connected by flights.
The goal of the bundling mechanism is to partition the traffic into groups/aggregates geometrically

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as close as possible with respect to and separated one to another as much as possible. Two classesof traffic demand are then generated: bundled air-links associated to a bundle and outliers. The flightaggregates, or bundles, define the backbone (main flows) of the airstream network. Each cluster isallocated to an airstream which is built using the intrinsic characteristics of the aggregated traffic.
Figure 1 describes the stages of the design process.

Figure 1 _ Airstream Generation Process
The proposed approach considers that the ultimate desire of airlines would be to deliver more directflights between departure and arrival airports so that travel distances and durations are minimum,
optimizing the transportation service offered to costumers, contributing to the minimization ofoperational costs and to a more efficient aircraft fleet management. Considering that from the pointof view of Air Traffic Management, there is no difference of treatment between flights of different
airlines realized between the same airports, the focus is given here on air-links between each pair ofconsidered airports, rather than in individual flights. An air-link will be characterized by the pair ofarrival and destination airports (no order), the free flight trajectory between them and its length, thenumber of flights using this air-link during a day period. Then, the number of air-links is muchsmaller than the number of flights, limiting already the computational burden. A perfect direct flighttrajectory is associated to the orthodromic curve between the two airports defining an air-link, it ischaracterized by two parameters, its route angle and root position. The clustering approach which
progressively builds each cluster by inspection of the air-link list and on-line adaptation is described
below. This method applied to the air-link set in a sequential way should reduce the computationalburden compared with optimizing approaches or global approaches. Two parameters can be tuned
for generating the clustering: the Maximum route deviation and the Maximum root deviation.

Figure 1_ Air-link and flight in a cluster
The steps of the heuristic are: Rank air-links by traffic volume and select the first one as a seed forthe first cluster and airstream, compare routes then roots and gather or not in the current cluster
according to the size of their differences; update the current cluster and check the next air-link; if all
air-links have been checked and no more air-links, the search ends; otherwise initialize a new clusterand start again the process with the remaining air-links.

3 FLIGHT ASSIGNMENT TO AIRSTREAMS
Once a set of airstreams has been defined to cover a large proportion of flights, it is necessary topredict the way in which the flights will use these airstreams. How to design for each flight a best
trajectory using portions of the airstreams? Here the main considered objectives are: to ease thetraffic control workload by minimizing cross conflicts through the use of airstreams, a simple way

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to contribute to this objective is to minimize the portions of flights which are not flown inside
airstreams where traffic control acquires an automatic character, and to minimize the length offlights, this second objective is related to the operational costs supported by airlines and the travel
time of passengers. It is obvious that the minimum distance flight between a departure airport D andan arrival airport A is the portion of the great circle linking them and assimilated here to a straightsegment. So, to force traffic to deviate and use the airstreams, some attractiveness must be given tothem. This can be done through the adoption of a discount factor to each airstream where theequivalent distance used in the computation of the flight path in airstream i is given by: 𝑑𝑖𝑒 = 𝑖 𝑑𝑖where di is the real flown distance in the airstream and 𝑖 is the discount factor associated toairstream i. The adoption of this discount factor to compute flight paths may be turned mandatory
by ATM but may also correspond to a reduction of air traffic control fees in airstreams. The discountfactor can be associated to a given flight, to a given air-link, to a given bundle or to the whole traffic
demand. Here two cases should be considered: the case in which a flight is part of the bundle
associated to an airstream and the case of an outlier flight. Only the first case will be developed here,
the second case can be tackled using a Dynamic Programming approach. Figure 3 represents therelative position of an air-link with respect to an airstream and a possible flight path using part ofthis airstream.

Figure 3 _ Airstream section of a bundled air-link
The pseudo-length of the flight path is given by:𝑙(𝑑𝐷 , 𝑑𝐴 , ) = √ℎ𝐷2 + 𝑑𝐷2 + (𝑠𝐴 − 𝑠𝐷 − (𝑑𝐷 + 𝑑𝐴 )) + √ℎ𝐴2 + 𝑑𝐴2(1)This is a convex function of dD and dA and its minimum is given by:1−𝑙𝑚𝑖𝑛 () = 𝑠𝐴 − 𝑠𝐷 + √1+ (|ℎ𝐷 | + |ℎ𝐴 |) with
and20    𝑚𝑎𝑥 where 𝑚𝑎𝑥 = 𝜎𝐷𝐴 /√1 + 𝜎𝐷𝐴𝑑𝐷∗ =√1−2with|ℎ𝐷 |and 𝑑𝐴∗ =√1−2|ℎ𝐴 | (2)𝜎𝐷𝐴 = |𝑠𝐴 − 𝑠𝐷 |/(|ℎ𝐷 | + |ℎ𝐴 |) (3)If 𝑚𝑎𝑥 ≤  < 1 the airstream is not used by the considered air-link and the direct flight between
airports D and A minimizes the above pseudo length. Possible KPIs associated with the chosen pathand parametrized by  with 0    𝑚𝑎𝑥 are the ratio 𝑝𝐷𝐴 of the flight lengths associated to that
air-link which will be outside the airstream, the ratio 𝜋𝐷𝐴 between these outside sections of flightand the length of the direct flight, the path length increase ratio DA , all given by analyticalexpressions depending of . It can be seen easily that when  increases, 𝑝𝐷𝐴 and 𝜋𝐷𝐴 increase while𝜌𝐷𝐴 decreases. If a performance level is attached to these KPIs, those air-links which do not comply
with the required performance can be reclassified as outliers. If the number of these new outliers issignificant, they can be excluded from the computation of the corresponding airstream. Mean ratios
can also be computed for the whole air-links associated to a given bundle and airstream. If the flightpath design process is performed centrally on a chronological basis (planned departure time of aflight), assigning momentarily a value equal or superior to one to the discount factor will avoid
considering an airstream which is currently saturated. The proposed approach has been applied to amedium size hypothetical case displayed in Figure 4 where on the left is the original demand with

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three airstreams and on the right is the resulting assignment of traffic to these airstreams in the casein which =0.5. Only four air-links (13%) do not use the three available airstreams.

Figure 4 _Assignment of flights to airstreams

4 4 CONCLUSION
In this communication, the problem of designing airstream networks to efficiently channel a largepart of the air traffic of a given geographic area has been considered. The proposed design techniques
have avoided unnecessary complexity so that real size problems can be quickly processed. The
proposed approach to perform traffic assignment to the airstream networks introduces a new tacticalparameter for air traffic management, the airstream distance discount factor. From the obtained
results it appears that there is an increased concentration of flight sections connecting airports andairstreams. So, it is of interest, with the objective of reducing further traffic complexity, to extent
the airstream concept to departing and arriving traffic at airports. Then it will be possible to assign
each aircraft to a unique dynamic slot leading it safely and efficiently through airstreams from thedeparture airport to the arrival airport of the considered flight. The introduced discount factor should
be an input for the computation of air traffic control charges so that airlines comply with the proposed
traffic assignment. Then it is possible to compute for different values of this discount factor theresulting traffic complexity and the environmental impact of the resulting traffic pattern for a given
demand of traffic during a day over a given region. It is expected that, whatever the adopted
complexity metric (Zhou, et al., 2017), a drastic diminution of the complexity of the resulting traffic
pattern will be observed.

References
Ab Wahid,Mastura, Mora-Camino, F., Bouadi, H., Cerqueira Revoredo,T. & Roux de Oliveira ,T.,2014. “Design of aircraft space indexed guidance along an airstream”, Digital Avionics Systems
Conference (DASC), 2014 IEEE/AIAA 33rd, pages 7B1–1. IEEE.
Bucuroiu, R., 2015. Free route airspace deployed in europe, available at:https://www.eurocontrol.int/news/free-route-airspace-deployed-europe.
Dohy, Didier, Mykoniatis, G., Raoul J.L. & and Mora-Camino, F.,2020. “Flight Centric ATC with
Airstreams (FC2A): initial approach on adaptative airspace & flow monitoring”, poster session,SESAR Innovation Days 2020.
Zhu, Xi, Cao, Xianbin & Cai, Kaiquan, 2017. “Measuring air traffic complexity based on smallsamples”, Chinese Journal of Aeronautics, Volume 30, Issue 4, August 2017, Pages 1493-1505.

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