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

Towards Simplified Optimal Sector Splitting Billy Josefsson - LFV Valentin Polishchuk, Leonid Sedov - Linköping University

dynamic Demand Capacity Balancing (dCDB) Traffic density - changing Sectors - static 9:00 AM Controller A - A Controller B - B Everyone is happy! For how long? 2

dynamic Demand Capacity Balancing (dCDB) Traffic density - changing Sectors - static 12:00 Controller A - A Controller B - B Solution? 3

dynamic Demand Capacity Balancing (dCDB) Traffic density - changing Sectors - static 12:00 Controller A - A Controller B - Controller C - C B Everyone is happy again 4

dynamic Demand Capacity Balancing (dCDB) Traffic density - changing Sectors - static 14:00 Controller A - A Controller B - Controller C - C B $$$ Do we need sector C? 5

dynamic Demand Capacity Balancing (dCDB) Traffic density - changing Sectors - static 14:00 Controller A - A Controller B - Controller C - C B Do we need sector C? 6

dynamic Demand Capacity Balancing (dCDB) Traffic density - changing Sectors - static 14:00 Controller A - A Controller B - B 7

Gluing [Kjellin ‘14] [Yousefi and Donohue ‘04] 8

Cutting [Gerdes et al., SID’16] 9

Binary split Split airspace into 2 parts Need more sectors? - Do recursive split. 10

Convex boundaries Line segment intersects convex region at most once 11

Straightline cuts Chord joins two points on boundary 12

KPIs Maximum imbalance - peak complexity Average imbalance - total complexity Maximum imbalance 13

KPIs Maximum imbalance - peak complexity Average imbalance - total complexity Balance max or avg? Average imbalance - We can both! 14

Input ● Region P ● Set S of straightline flight segments ○ Segment start and end coordinates ○ Times when aircraft enters and leaves segment 15

Сritical points 16

Сritical points 17

Сritical points 18

Сritical points 19

Сritical points 20

Сritical points 21

Сritical points 22

Ham sandwich theorem 23 http://www.etudes.ru/en/etudes/ham-sandwich-theorem/

Proof: avg = 0 split exists for each point 24

Proof: avg = 0 split exists for each point 1 0 25

Proof: avg = 0 split exists for each point 1 0 26

Proof: avg = 0 split exists for each point 1 0 27

Proof: avg = 0 split exists for each point 0.9 0.1 28

Proof: avg = 0 split exists for each point 0.6 0.4 29

Proof: avg = 0 split exists for each point 0.5 0.5 30

Proof: exists max & avg = 0 split 31

Proof: exists max & avg = 0 split B avg = 0 max > 0 ML(AB) = 3 MR(AB) = 2 A 32

Proof: exists max & avg = 0 split B avg = 0 max > 0 ML(AB) = 3 MR(AB) = 2 A 33

Proof: exists max & avg = 0 split avg = 0 B max > 0 ML(AB) = 4 MR(AB) = 2 A 34

Proof: exists max & avg = 0 split A avg = 0 max < 0 ML(AB) = 2 MR(AB) = 3 B 35

Proof: exists max & avg = 0 split B avg = 0 max > 0 ML(AB) = 3 MR(AB) = 2 A 36

1: Find critical points 37

2: Lines through all pairs of critical points 38

2: Lines through all pairs of critical points 39

2: Lines through all pairs of critical points 40

3: Find pairs of intervals with 0 M-imbalance 41

3: Find pairs of intervals with 0 M-imbalance 42

3: Find pairs of intervals with 0 M-imbalance 43

3: Find pairs of intervals with 0 M-imbalance 44

3: Find pairs of intervals with 0 M-imbalance 45

4: Look for avg-balanced splits 46

4: Look for avg-balanced splits 47

Artificial example 48

M-imbalance changes 49

Rectangular boundary 50

Straightline flight segments 51

Optimal cut 52

All optimal cuts 53

Second cut 54

Second cut 55

Further research ● Multiple sectors ● Directions of flights ● Interaction between flights and boundaries ● Choose between optimal cuts (KPI?) 56

Further research ● Multiple sectors ● Directions of flights ● Interaction between flights and boundaries ● Choose between optimal cuts (KPI?) THANK YOU! 57