1. EUROCONTROL EXPERIMENTAL CENTRE1 1st ICRAT Zilina 04/11/22-24 Frédéric Ferchaud EEC INO/LaBRI Vu Duong EEC INO Cyril Gavoille, Mohamed Mosbah LaBRI, University of Bordeaux 1 Reducing Disturbances by Using Absorption Areas

2. EUROCONTROL EXPERIMENTAL CENTRE2 1st ICRAT Zilina 04/11/22-24 Plan  Problem Presentation  Theoretical Results  Future work

3. EUROCONTROL EXPERIMENTAL CENTRE3 1st ICRAT Zilina 04/11/22-24  Airspace  Sectors  Air Traffic Controllers  Conflict Detection  Coordination across sectors  Conflict Resolution  « Capacity » Airspace Sectorization

4. EUROCONTROL EXPERIMENTAL CENTRE4 1st ICRAT Zilina 04/11/22-24 Slot Allocation ETO 01h 0 Number of aircraft in one hour = n Sector Capacity = c Regulated demand If n > c then the sector is regulated

5. EUROCONTROL EXPERIMENTAL CENTRE5 1st ICRAT Zilina 04/11/22-24 Absorption Areas  Sadly, the regulated demand is not respected. The uncertainty could perturb the planning.  In order to reduce disturbances due to uncertainty, we introduce the absorption areas. An absorption areas is defined as one or several slots let intentionally unfilled during the slot allocation in order to reallocate delayed aircraft without perturb the initial allocation.

6. EUROCONTROL EXPERIMENTAL CENTRE6 1st ICRAT Zilina 04/11/22-24 Slot Allocation Problem 0 1h Regulated demand More slots needed!

7. EUROCONTROL EXPERIMENTAL CENTRE7 1st ICRAT Zilina 04/11/22-24 Slot Allocation with Absorption Areas 0 1h Regulated demand

8. EUROCONTROL EXPERIMENTAL CENTRE8 1st ICRAT Zilina 04/11/22-24  ATFM Presentation  Theoretical Results  Future work

9. EUROCONTROL EXPERIMENTAL CENTRE9 1st ICRAT Zilina 04/11/22-24 Without slot reallocation Number of aircraft taking-off under safety conditions with high probability with 1000 slots.

10. EUROCONTROL EXPERIMENTAL CENTRE10 1st ICRAT Zilina 04/11/22-24 AA Distribution: Presentation Problems: Aircraft delayed more than one slot… Loadloss not minimized

11. EUROCONTROL EXPERIMENTAL CENTRE11 1st ICRAT Zilina 04/11/22-24 AA Distribution: First Idea Let X i be the random variable given the number of aircraft not finding a slot in the AA during the period i. Let (1-p i ) the rate of uncertainty on the period i.

12. EUROCONTROL EXPERIMENTAL CENTRE12 1st ICRAT Zilina 04/11/22-24 AA Distribution: Probabilistic Calculus (1) We obtain: We are interested by:

13. EUROCONTROL EXPERIMENTAL CENTRE13 1st ICRAT Zilina 04/11/22-24 AA Distribution: Probabilistic Calculus (2)

14. EUROCONTROL EXPERIMENTAL CENTRE14 1st ICRAT Zilina 04/11/22-24

15. EUROCONTROL EXPERIMENTAL CENTRE15 1st ICRAT Zilina 04/11/22-24  ATFM Presentation  SIVOR  Theoretical Results  Future Work

16. EUROCONTROL EXPERIMENTAL CENTRE16 1st ICRAT Zilina 04/11/22-24 White flights B A

17. EUROCONTROL EXPERIMENTAL CENTRE17 1st ICRAT Zilina 04/11/22-24 Conclusion  Traffic growth  AA interest.  Theoretical approach:  Amount of unfilled slot in one sector  Without reallocation  With reallocation  Take into account the distribution of the unfilled slot in one sector.  Take into account the space time dependencies.  Graph Theory.

18. EUROCONTROL EXPERIMENTAL CENTRE18 1st ICRAT Zilina 04/11/22-24 Thanks for your attention