ICRAT Budapest, Hungary June, 2010

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


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


Airspace

Sector


Airspace

Center


Airspace

FCA

FCA


Generic Model

Sin

k

Sou

rce

• Polygonal domain– outer boundary

• source and sink edges

– obstacles • weather, no-fly zones


Aircraft: Disk

• Radius = RNP = 5nmi


Airlane: “thick path”

• Thickness = 2*RNP = 10nmi

MIT = 10nmi


Algorithmic Problem

• Givenweather-impacted airspace

• Findweather-avoiding trajectories for aircraft


Model

• Givenpolygonal domain with obstacles, source and sink

• Findthick paths

pairwise-disjoint

avoiding obstacles


Solution: Search Underlying Grid


Hexagonal disk packing in free space


• Nodes: disks• Edges between

touching disks• Source, sink

• Every node has capacity 1

Graph


Source-Sink Flow

• Decomposes into disjoint paths


Source-Sink Flow

• Decomposes into disjoint paths

• Inflate thepaths

MaxFlow → Max # of paths MinCost Flow → Shortest paths


Examples


June, 2010


Additional constraints: Sector boundaries crossing

Communication between ATCs


Higher cost for crossing edges in the graph


Conforming flow

June, 2010

June, 2010


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)


Moving obstacles?

• Paths become infeasible


FreeFlight


Solution: Search Time-Expanded Grid


Lifting to (x,y,t)


Obstacles


Time Slicing


Disk Packings


Edges


Node Capacity = 1


Supersource, supersink


Supersource-supersink flow


Examples







Holding




Holding



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”




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


Experiments


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


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


100 instances for each WSI

• Static • FreeFlight • Corridors

speed = 420 knots

Compute trajectories


Traffic Complexity

• Average over time and tiles• In a tile, at a time

– # of aircraft– Var(velocites)


Complexity (100 instances / WSI)


Throughput (100 instances / WSI), aircraft / .5 hr


• 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


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




Documents

ICRAT Budapest, Hungary June, 2010