A Framework for Integrated Terminal Airspace Design Tobias Andersson Granberg, Ta0ana Polishchuk, Valen0n Polishchuk, Chris&ane Schmidt
• Traditionally: • 1. Routes, 2. Sectors • 1. Sectors, 2. Routes • Why? • Computational limits • Historical reasons • Here: two unified approaches to airspace design ➡ Simultaneous design of paths and sectors 2 14.11.2017 A Framework for Integrated Terminal Airspace Design
(I) MIP-based approach ❖ Combines two of our prior MIPs: one for TMA sectorization and one for STARs in the TMA ❖ Integrates constraints on the interaction between sector boundary and arrival routes (II) Voronoi-based approach ❖ Based on Voronoi diagram of “hotspots” of controller attention ❖ Can be used for any route design ❖ Idea: Computation of best possible routes more important than to optimise sector boundaries ❖ Routes determine how fast and with how much fuel aircraft can reach and leave the runway, and good design supports controllers to maintain safe separation. ❖ Sectors should guarantee that - Points of increased controller interest are not too close to sector boundary - Taskload of the different controllers is balanced ➡ Important: sector boundary as far away from “hotspots” as possible ➡ Exact location of remaining sector boundary not as important as exact run of routes. ➡ Goal: sectors that separated hotspots of routes as much as possible while balancing controller taskload 3 14.11.2017 A Framework for Integrated Terminal Airspace Design
Identification of Hotspots 4 14.11.2017 A Framework for Integrated Terminal Airspace Design
Goal: define the potential conflict points, the hotspots , of any route design ➡ Define important part of the interaction between routes and sectors Two-step process in interviews with ATCOs: 1. ATCOs identified hotspots for different SID and STAR combinations. 2. Discussed which type of hotspots any kind of design will induce (step to a general route-hotspot relation) Hotspots H : ๏ Runway ๏ Entry and exit points with high traffic load ๏ Intersection points of SIDs and STARs Second round: assign a weight ɷ η to each hotspot η ∈ H . 5 14.11.2017 A Framework for Integrated Terminal Airspace Design
Review Grid-based IP formulation for STARs 6 14.11.2017 A Framework for Integrated Terminal Airspace Design
Review Grid-based IP formulation for STARs ๏ Square grid in the TMA ๏ Snap locations of the entry points and the runway onto the grid ๏ EP : set of (snapped) entry points ๏ R: runway ๏ G = (V,E): ๏ Every grid node connected to its 8 neighbors ๏ length of an edge (i, j) ` i,j 1. No more than two routes merge at a point: in-degree ≤ 2 2. Merge point separation: distance threshold L 3. No sharp turns: angle threshold 𝛽 , minimum edge length L 4. Obstacle avoidance 5. STAR–SID separation: STAR–SID crossings far from the runway, where arriving and departing planes sufficiently separated vertically (difference of descend and climb slopes) 7 14.11.2017 A Framework for Integrated Terminal Airspace Design
Review Grid-based IP formulation for STARs decision variables: edge e participates in the STAR. x e f e flow variables: gives the flow on edge e = (i, j) (i.e., from i to j ) 8 P i = R Flow from all entry points reaches runway k ∈ EP κ k > < X X f ki − f ij = i ∈ EP (1) − κ i Flow of one leaves each entry point > k :( k,i ) ∈ E j :( i,j ) ∈ E 0 i ∈ V \ {EP ∪ R } Flow conservation : f e Edges with positive flow are in STAR (2) x e ≥ ∀ e ∈ E |EP| Flow non-negative f e ≥ 0 (3) ∀ e ∈ E Edge decision variables are binary x e ∈ { 0 , 1 } (4) ∀ e ∈ E X x ki ≤ 2 ∀ i ∈ V \ {EP ∪ R } Degree constraints: k :( k,i ) ∈ E outdegree of every vertex at most 1, (5) maximum indegree is 2. X x ij ≤ 1 ∀ i ∈ V \ {EP ∪ R } Runway only one ingoing, entry points only one outgoing edge. j :( i,j ) ∈ E (6) X x kR = 1 (7) k :( k,R ) ∈ E X x Rj ≤ 0 (8) j :( R,j ) ∈ E X x ki ≤ 0 ∀ i ∈ EP (9) a e = | A e | k :( k,i ) ∈ E X x ij = 1 ∀ i ∈ EP (10) j :( i,j ) ∈ E X a e x e + x f ≤ a e ∀ e ∈ E (11) If an edge x e the angle to the f ∈ A e consecutive segment of a route is never 8 14.11.2017 A Framework for Integrated Terminal Airspace Design
Review Grid-based IP formulation for STARs Objective functions: X min (1) ` e f e demand-weighted paths length e ∈ E X tree weight min (2) ` e x e e ∈ E 9 14.11.2017 A Framework for Integrated Terminal Airspace Design
Review Grid-based IP formulation for Sectorization 10 14.11.2017 A Framework for Integrated Terminal Airspace Design
Sectorization Problem: Given: The coordinates of the TMA, defining a polygon P , the number of sectors |S|, and a set C of constraints on the resulting sectors. Find: A sectorization of P with k = |S| , fulfilling C. Possible constraints for sectorization: (a) Balanced taskload (b) Connected sectors (c) Nice shape (smooth boundary and an easily memorable shape) (d) Convex sectors ((straight-line) flight cannot enter and leave a convex sector multiple times) (e) Interior conflict points ( Points that require increased attention from ATCOs should lie in the sector’s interior.) 11 14.11.2017 A Framework for Integrated Terminal Airspace Design
Review Grid-based IP formulation for Sectorization ๏ Square grid in the TMA ๏ G 2 = (V 2 ,E 2 ): ๏ Every grid node connected to its 8 neighbors ๏ N(i) = set of neighbors of i (including i) ๏ length of an edge (i, j) ` i,j Main idea: use an artificial sector, S 0 , that encompasses the complete boundary of P, using all counterclockwise (ccw) edges. o t s t p e c n o c y n a M s r Taskload? o t c e s n g i s s a d n a We use heat maps of the density of weighted clicks as a e r a t c e r r o c o t d n a an input. , d a o l k s a t x e v n o c BUT: we do not depend on specific maps. e c r o f n e s r o t c e s o t n i o g t o n o d e w ➜ s l i a t e d l l a r o f r e p a p [E. Zohrevandi, V. Polishchuk, J. Lundberg, Å. Svensson, J. Johansson, e e s ( and B. Josefsson. d e l i a t e Modeling and analysis of controller’s taskload in different predictability d conditions, 2016] ) n o i t p i r c s e d 12 14.11.2017 A Framework for Integrated Terminal Airspace Design
Review Grid-based IP formulation for Sectorization ⟹ Union of the |S| sectors completely covers the TMA. Assign sectors correct area (and balance it) Assign sectors correct taskload and balance it All sectors convex Objective Function: 13 14.11.2017 A Framework for Integrated Terminal Airspace Design
The Combined MIP 14 14.11.2017 A Framework for Integrated Terminal Airspace Design
• Compute sectors and routes simultaneously ➡ Variables for selecting routes ( and ) and for selecting boundary edges ( ) • Interaction (possibly achieve only close to orthogonal intersections) Grid for route edge selection Grid for sector boundary edge selection If edge (i,j) is used for sector boundary ➡ These edges are forbidden for routes (can be defined depending on goal) • Route vertices of different degree induce heat values at their location • These get split by the sectors ➡ Constraint that properly assign these heat values. • Computationally expensive to solve!! 15 14.11.2017 A Framework for Integrated Terminal Airspace Design
The Voronoi-based Approach 16 14.11.2017 A Framework for Integrated Terminal Airspace Design
REMINDER ❖ Idea: Computation of best possible routes more important than to optimise sector boundaries ❖ Routes determine how fast and with how much fuel aircraft can reach and leave the runway, and good design supports controllers to maintain safe separation. ❖ Sectors should guarantee that - Points of increased controller interest are not too close to sector boundary - Taskload of the different controllers is balanced ➡ Important: sector boundary as far away from “hotspots” as possible ➡ Exact location of remaining sector boundary not as important as exact run of routes. ➡ Goal: sectors that separated hotspots of routes as much as possible while balancing controller taskload • Also nice to have: simple shape and convex sectors • Convexity defined: - Geometrically (for any point of pairs in the sector the straight line connection is fully contained in the sector as well) - Trajectory-based (no route enters the same sector more than once) 17 14.11.2017 A Framework for Integrated Terminal Airspace Design
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