icrat budapest, hungary june, 2010
Post on 02-Feb-2016
24 Views
Preview:
DESCRIPTION
TRANSCRIPT
June, 2010
ICRATBudapest, HungaryJune, 2010
Presented by:
Valentin Polishchuk, Ph.D.
Throughput/Complexity Tradeoffs for Routing Traffic
in the Presence of Dynamic Weather
June, 2010ICRAT ’10 Budapest, Hungary
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
June, 2010ICRAT ’10 Budapest, Hungary
Algorithmic Problem
• Givenweather-impacted airspace
• Findweather-avoiding trajectories for aircraft
• Assumptionsen-route
fixed flight level (2D, xy)
generally unidirectional (e.g., East-to-West) flow
June, 2010ICRAT ’10 Budapest, Hungary
Airspace
Sector
June, 2010ICRAT ’10 Budapest, Hungary
Airspace
Center
June, 2010ICRAT ’10 Budapest, Hungary
Airspace
FCA
FCA
June, 2010ICRAT ’10 Budapest, Hungary
Generic Model
Sin
k
Sou
rce
• Polygonal domain– outer boundary
• source and sink edges
– obstacles • weather, no-fly zones
June, 2010ICRAT ’10 Budapest, Hungary
Aircraft: Disk
• Radius = RNP = 5nmi
June, 2010ICRAT ’10 Budapest, Hungary
Airlane: “thick path”
• Thickness = 2*RNP = 10nmi
MIT = 10nmi
June, 2010ICRAT ’10 Budapest, Hungary
Algorithmic Problem
• Givenweather-impacted airspace
• Findweather-avoiding trajectories for aircraft
June, 2010ICRAT ’10 Budapest, Hungary
Model
• Givenpolygonal domain with obstacles, source and sink
• Findthick paths
pairwise-disjoint
avoiding obstacles
June, 2010ICRAT ’10 Budapest, Hungary
Solution: Search Underlying Grid
June, 2010ICRAT ’10 Budapest, Hungary
Hexagonal disk packing in free space
June, 2010ICRAT ’10 Budapest, Hungary
• Nodes: disks• Edges between
touching disks• Source, sink
• Every node has capacity 1
Graph
June, 2010ICRAT ’10 Budapest, Hungary
Source-Sink Flow
• Decomposes into disjoint paths
June, 2010ICRAT ’10 Budapest, Hungary
Source-Sink Flow
• Decomposes into disjoint paths
• Inflate thepaths
MaxFlow → Max # of paths MinCost Flow → Shortest paths
June, 2010ICRAT ’10 Budapest, Hungary
Examples
June, 2010ICRAT ’10 Budapest, Hungary
June, 2010
June, 2010ICRAT ’10 Budapest, Hungary
Additional constraints: Sector boundaries crossing
Communication between ATCs
June, 2010ICRAT ’10 Budapest, Hungary
Higher cost for crossing edges in the graph
June, 2010ICRAT ’10 Budapest, Hungary
Conforming flow
June, 2010
June, 2010
June, 2010ICRAT ’10 Budapest, Hungary
Capacity = length of shortest B-T path in “critical graph”
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
Theoretical guarantee: Max # of paths
ℓij = floor(dij/w)
June, 2010ICRAT ’10 Budapest, Hungary
Moving obstacles?
• Paths become infeasible
June, 2010ICRAT ’10 Budapest, Hungary
FreeFlight
June, 2010ICRAT ’10 Budapest, Hungary
Solution: Search Time-Expanded Grid
June, 2010ICRAT ’10 Budapest, Hungary
Lifting to (x,y,t)
June, 2010ICRAT ’10 Budapest, Hungary
Obstacles
June, 2010ICRAT ’10 Budapest, Hungary
Time Slicing
June, 2010ICRAT ’10 Budapest, Hungary
Disk Packings
June, 2010ICRAT ’10 Budapest, Hungary
Edges
June, 2010ICRAT ’10 Budapest, Hungary
Node Capacity = 1
June, 2010ICRAT ’10 Budapest, Hungary
Supersource, supersink
June, 2010ICRAT ’10 Budapest, Hungary
Supersource-supersink flow
June, 2010ICRAT ’10 Budapest, Hungary
Examples
June, 2010ICRAT ’10 Budapest, Hungary
June, 2010ICRAT ’10 Budapest, Hungary
June, 2010ICRAT ’10 Budapest, Hungary
June, 2010ICRAT ’10 Budapest, Hungary
June, 2010ICRAT ’10 Budapest, Hungary
June, 2010ICRAT ’10 Budapest, Hungary
Holding
June, 2010ICRAT ’10 Budapest, Hungary
June, 2010ICRAT ’10 Budapest, Hungary
June, 2010ICRAT ’10 Budapest, Hungary
Holding
June, 2010ICRAT ’10 Budapest, Hungary
June, 2010ICRAT ’10 Budapest, Hungary
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”
June, 2010ICRAT ’10 Budapest, Hungary
June, 2010ICRAT ’10 Budapest, Hungary
June, 2010ICRAT ’10 Budapest, Hungary
Computing the Corridors
• Decide– how many are possible– threading amidst obstacles
• At every time slice– route paths– with given threadings
– Shortest paths • “pulled taut” against obstacles →
• morph slowly
June, 2010ICRAT ’10 Budapest, Hungary
Experiments
June, 2010ICRAT ’10 Budapest, Hungary
Airspace• 300 x 210 nmi rectangle• Weather Severity Index (WSI)
– percentage of space covered with obstacles
• Weather organizations– Popcorn Convection (PC)
• scattered obstacles
– Squall Line (SL)• aligned obstacles
June, 2010ICRAT ’10 Budapest, Hungary
Setup
• For WSI = 0,10,…,60– until reaching WSI
• generate random obstacle
• place it randomly in the airspace
• Random velocity
• Squall Line– WSI = 0,5,…,35
June, 2010ICRAT ’10 Budapest, Hungary
100 instances for each WSI
• Static • FreeFlight • Corridors
speed = 420 knots
Compute trajectories
June, 2010ICRAT ’10 Budapest, Hungary
Traffic Complexity
• Average over time and tiles• In a tile, at a time
– # of aircraft– Var(velocites)
June, 2010ICRAT ’10 Budapest, Hungary
Complexity (100 instances / WSI)
June, 2010ICRAT ’10 Budapest, Hungary
Throughput (100 instances / WSI), aircraft / .5 hr
June, 2010ICRAT ’10 Budapest, Hungary
• Airspace capacity estimationFundamental research question: can study either theoretically or empirically
At the root of Traffic Flow Management (TFM):
How do you know that you have a TFM problem, Demand > Airspace Capacity, unless you have a good way of estimating the airspace capacity?
Capacity ≠ function( airspace )
• Different paradigms → different capacity → different complexity
• Operational requirements
– e.g., conforming flows
• Temporal component
– e.g., holding
Help in quantifying tradeoffs
Summary
June, 2010ICRAT ’10 Budapest, Hungary
Future Research
• Sensitivity to complexity parameters• Route Planning in Terminal or Transition Airspace
– Trees (e.g., STARS)• static
• “free”?
• flexible
• Further Dimensions– Multiple Altitudes, Directions of Flows– 4D Space-Time Constraints (flow and weather constraints)– Different route types
• Real Weather
June, 2010ICRAT ’10 Budapest, Hungary
June, 2010ICRAT ’10 Budapest, Hungary
June, 2010ICRAT ’10 Budapest, Hungary
top related