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ICRAT Budapest, Hungary June, 2010

ICRAT Budapest, Hungary June, 2010. Throughput/Complexity Tradeoffs for Routing Traffic in the Presence of Dynamic Weather. Presented by: Valentin Polishchuk, Ph.D. Team of Collaborators. Jimmy Krozel, Ph.D., Metron Aviation, Inc., USA

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ICRAT Budapest, Hungary June, 2010

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  1. ICRATBudapest, HungaryJune, 2010 Throughput/Complexity Tradeoffs for Routing Traffic in the Presence of Dynamic Weather Presented by: Valentin Polishchuk, Ph.D.

  2. Team of Collaborators • Jimmy Krozel, Ph.D., Metron Aviation, Inc., USA • Joseph S.B. Mitchell, Ph.D., Applied Math, Stony Brook University, USA • Valentin Polishchuk, Ph.D., and Anne Pääkkö, Computer Science, University of Helsinki, Finland • Funding provided by: Academy of Finland, NASA and NSF ICRAT ’10 Budapest, Hungary

  3. Algorithmic Problem • Given weather-impacted airspace • Find weather-avoiding trajectories for aircraft • Assumptions en-route fixed flight level (2D, xy) generally unidirectional (e.g., East-to-West) flow ICRAT ’10 Budapest, Hungary

  4. Airspace Sector ICRAT ’10 Budapest, Hungary

  5. Airspace Center ICRAT ’10 Budapest, Hungary

  6. Airspace FCA FCA ICRAT ’10 Budapest, Hungary

  7. Generic Model • Polygonal domain • outer boundary • source and sink edges • obstacles • weather, no-fly zones Source Sink ICRAT ’10 Budapest, Hungary

  8. Aircraft: Disk • Radius = RNP = 5nmi ICRAT ’10 Budapest, Hungary

  9. Airlane: “thick path” • Thickness = 2*RNP= 10nmi MIT = 10nmi ICRAT ’10 Budapest, Hungary

  10. Algorithmic Problem • Given weather-impacted airspace • Find weather-avoiding trajectories for aircraft ICRAT ’10 Budapest, Hungary

  11. Model • Given polygonal domain with obstacles, source and sink • Find thick paths pairwise-disjoint avoiding obstacles ICRAT ’10 Budapest, Hungary

  12. Solution: Search Underlying Grid ICRAT ’10 Budapest, Hungary

  13. Hexagonal disk packing in free space ICRAT ’10 Budapest, Hungary

  14. Graph • Nodes: disks • Edges between touching disks • Source, sink • Every node has capacity 1 ICRAT ’10 Budapest, Hungary

  15. Source-Sink Flow • Decomposes into disjoint paths ICRAT ’10 Budapest, Hungary

  16. Source-Sink Flow MaxFlow → Max # of paths MinCost Flow → Shortest paths • Decomposes into disjoint paths • Inflate thepaths ICRAT ’10 Budapest, Hungary

  17. Examples ICRAT ’10 Budapest, Hungary

  18. ICRAT ’10 Budapest, Hungary

  19. Additional constraints: Sector boundaries crossing Communication between ATCs ICRAT ’10 Budapest, Hungary

  20. Higher cost for crossing edges in the graph ICRAT ’10 Budapest, Hungary

  21. Conforming flow ICRAT ’10 Budapest, Hungary

  22. Theoretical guarantee: Max # of paths Maximum Flow Rates for Capacity Estimation in Level Flight with Convective Weather Constraints Krozel, Mitchell, P, Prete Air Traffic Control Quarterly 15(3):209-238, 2007 Capacity = length of shortest B-T path in “critical graph” ℓij = floor(dij/w) ICRAT ’10 Budapest, Hungary

  23. Moving obstacles? • Paths become infeasible ICRAT ’10 Budapest, Hungary

  24. FreeFlight ICRAT ’10 Budapest, Hungary

  25. Solution: Search Time-Expanded Grid ICRAT ’10 Budapest, Hungary

  26. Lifting to (x,y,t) ICRAT ’10 Budapest, Hungary

  27. Obstacles ICRAT ’10 Budapest, Hungary

  28. Time Slicing ICRAT ’10 Budapest, Hungary

  29. Disk Packings ICRAT ’10 Budapest, Hungary

  30. Edges ICRAT ’10 Budapest, Hungary

  31. Node Capacity = 1 ICRAT ’10 Budapest, Hungary

  32. Supersource, supersink ICRAT ’10 Budapest, Hungary

  33. Supersource-supersink flow ICRAT ’10 Budapest, Hungary

  34. Examples ICRAT ’10 Budapest, Hungary

  35. ICRAT ’10 Budapest, Hungary

  36. ICRAT ’10 Budapest, Hungary

  37. ICRAT ’10 Budapest, Hungary

  38. ICRAT ’10 Budapest, Hungary

  39. ICRAT ’10 Budapest, Hungary

  40. Holding ICRAT ’10 Budapest, Hungary

  41. ICRAT ’10 Budapest, Hungary

  42. ICRAT ’10 Budapest, Hungary

  43. Holding ICRAT ’10 Budapest, Hungary

  44. ICRAT ’10 Budapest, Hungary

  45. The two extremes • Static airlanes • coherent traffic • not adjustable to dynamic constraints • Flexible flow corridors • paths, morphing with obstacles motion • keep threading amidst obstacles • FreeFlight • fully dynamic • “ATC nightmare” ICRAT ’10 Budapest, Hungary

  46. ICRAT ’10 Budapest, Hungary

  47. ICRAT ’10 Budapest, Hungary

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