Towards Simplified Optimal Sector Splitting Billy Josefsson - LFV - - PowerPoint PPT Presentation

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Towards Simplified Optimal Sector Splitting Billy Josefsson - LFV - - PowerPoint PPT Presentation

Dec 18, 2022 425 likes •1k views

Towards Simplified Optimal Sector Splitting Billy Josefsson - LFV Valentin Polishchuk, Leonid Sedov - Linkping University dynamic Demand Capacity Balancing (dCDB) Traffic density - changing Sectors - static 9:00 AM Controller A - A

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Towards Simplified Optimal Sector Splitting

Billy Josefsson - LFV Valentin Polishchuk, Leonid Sedov - Linköping University

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dynamic Demand Capacity Balancing (dCDB)

Traffic density - changing Sectors - static A B Controller A - Controller B - 9:00 AM Everyone is happy! For how long?

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dynamic Demand Capacity Balancing (dCDB)

Traffic density - changing Sectors - static A B Controller A - Controller B - 12:00 Solution?

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dynamic Demand Capacity Balancing (dCDB)

Traffic density - changing Sectors - static A B Controller A - Controller B - Controller C - 12:00 C Everyone is happy again

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dynamic Demand Capacity Balancing (dCDB)

Traffic density - changing Sectors - static A B Controller A - Controller B - Controller C - 14:00 C Do we need sector C?

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$$$

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dynamic Demand Capacity Balancing (dCDB)

Traffic density - changing Sectors - static A B Controller A - Controller B - Controller C - 14:00 C Do we need sector C?

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dynamic Demand Capacity Balancing (dCDB)

Traffic density - changing Sectors - static A B Controller A - Controller B - 14:00

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Gluing

[Kjellin ‘14] [Yousefi and Donohue ‘04]

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Cutting

[Gerdes et al., SID’16]

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Binary split

Split airspace into 2 parts Need more sectors? - Do recursive split.

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Convex boundaries

Line segment intersects convex region at most once

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Straightline cuts

Chord joins two points on boundary

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KPIs

Maximum imbalance - peak complexity Average imbalance - total complexity Maximum imbalance

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KPIs

Maximum imbalance - peak complexity Average imbalance - total complexity Average imbalance Balance max or avg?

  • We can both!

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Input

  • Region P
  • Set S of straightline flight segments

○ Segment start and end coordinates ○ Times when aircraft enters and leaves segment

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Сritical points

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Сritical points

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Сritical points

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Сritical points

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Сritical points

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Сritical points

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Сritical points

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Ham sandwich theorem

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http://www.etudes.ru/en/etudes/ham-sandwich-theorem/

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Proof: avg = 0 split exists for each point

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Proof: avg = 0 split exists for each point

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1

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Proof: avg = 0 split exists for each point

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1

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Proof: avg = 0 split exists for each point

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1

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Proof: avg = 0 split exists for each point

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0.1 0.9

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Proof: avg = 0 split exists for each point

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0.6 0.4

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Proof: avg = 0 split exists for each point

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0.5 0.5

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Proof: exists max & avg = 0 split

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Proof: exists max & avg = 0 split

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avg = 0 max > 0

B A

ML(AB) = 3 MR(AB) = 2

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Proof: exists max & avg = 0 split

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B A

avg = 0 max > 0 ML(AB) = 3 MR(AB) = 2

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Proof: exists max & avg = 0 split

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avg = 0 max > 0

B A

ML(AB) = 4 MR(AB) = 2

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Proof: exists max & avg = 0 split

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A B

avg = 0 max < 0 ML(AB) = 2 MR(AB) = 3

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Proof: exists max & avg = 0 split

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avg = 0 max > 0

B A

ML(AB) = 3 MR(AB) = 2

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1: Find critical points

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2: Lines through all pairs of critical points

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2: Lines through all pairs of critical points

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2: Lines through all pairs of critical points

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3: Find pairs of intervals with 0 M-imbalance

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3: Find pairs of intervals with 0 M-imbalance

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3: Find pairs of intervals with 0 M-imbalance

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3: Find pairs of intervals with 0 M-imbalance

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3: Find pairs of intervals with 0 M-imbalance

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4: Look for avg-balanced splits

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4: Look for avg-balanced splits

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Artificial example

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M-imbalance changes

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Rectangular boundary

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Straightline flight segments

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Optimal cut

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All optimal cuts

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Second cut

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Second cut

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Further research

  • Multiple sectors
  • Directions of flights
  • Interaction between flights and boundaries
  • Choose between optimal cuts (KPI?)

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Further research

  • Multiple sectors
  • Directions of flights
  • Interaction between flights and boundaries
  • Choose between optimal cuts (KPI?)

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THANK YOU!