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1st ICRATZilina04/11/22-24

Frédéric Ferchaud EEC INO/LaBRIVu Duong EEC INO

Cyril Gavoille, Mohamed Mosbah LaBRI, University of Bordeaux 1

Reducing Disturbances by Using Absorption Areas

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1st ICRATZilina04/11/22-24 Plan

Problem Presentation Theoretical Results Future work

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1st ICRATZilina04/11/22-24

Airspace Sectors

Air Traffic Controllers

Conflict Detection

Coordination across sectors

Conflict Resolution

« Capacity »

Airspace Sectorization

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1st ICRATZilina04/11/22-24 Slot Allocation

ETO0 1h

0 1h

Number of aircraft in one hour = n Sector Capacity = c

Regulated demand

If n > c then the sector is regulated

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1st ICRATZilina04/11/22-24 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.

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1st ICRATZilina04/11/22-24 Slot Allocation Problem

0 1hRegulated demand

More slots needed!

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1st ICRATZilina04/11/22-24 Slot Allocation with Absorption Areas

0 1hRegulated demand

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1st ICRATZilina04/11/22-24

ATFM Presentation Theoretical Results Future work

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1st ICRATZilina04/11/22-24 Without slot reallocation

Number of aircraft taking-off under safety conditions with high probability with 1000 slots.

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1st ICRATZilina04/11/22-24 AA Distribution: Presentation

rd 1

rd 2

rd 3

•Problems:•Aircraft delayed more than one slot…•Loadloss not minimized

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1st ICRATZilina04/11/22-24 AA Distribution: First Idea

1r 1z

n

1X

2r 2z mr mz

2X mX

Let Xi be the random variable given the number of aircraft not finding a slot in the AA during the period i.Let (1-pi) the rate of uncertainty on the period i.

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1st ICRATZilina04/11/22-24 AA Distribution: Probabilistic Calculus (1)

We obtain:

We are interested by:

else

rzjifppCjX

ppCX

iizjr

ijz

ijz

ri

z

j

jrii

jri

iiii

i

ii

i

0

)1()Pr(

)1()0Pr(0

m

iiXjX

1

)Pr(

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1st ICRATZilina04/11/22-24 AA Distribution: Probabilistic Calculus (2)

...)2Pr(

)1Pr(...)0Pr()0Pr(

...

)0Pr(...)1Pr()0Pr(

)0Pr(...)0Pr()1Pr()1Pr(

)1()0Pr(

21

21

21

0 0

X

XXX

XXX

XXXX

ppCX

m

m

m

m

i

z

j

jrjj

jr

i

i

i

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1st ICRATZilina04/11/22-24

m

i

r

j

jrjjr ppCX

0

2

0

)1()0Pr(

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1st ICRATZilina04/11/22-24

ATFM Presentation SIVOR Theoretical Results Future Work

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1st ICRATZilina04/11/22-24 White flights

B

A

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1st ICRATZilina04/11/22-24 Conclusion

Traffic growth AA interest. Theoretical approach:

Amount of unfilled slot in one sectorWithout reallocationWith reallocation

Take into account the distribution of the unfilled slot in one sector.

Take into account the space time dependencies. Graph Theory.

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1st ICRATZilina04/11/22-24

Thanks for your attention