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heterogeneity-hotp2p.. - Playing with the Bandwidth Conservation Law

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    heterogeneity-hotp2p.. - Playing with the Bandwidth Conservation Law heterogeneity-hotp2p.. - Playing with the Bandwidth Conservation Law Presentation Transcript

    • Heterogeneity in Data-DrivenLive Streaming:Blessing or Curse?
      Fabien Mathieu
      Hot-P2P, 04/23/2010
    • Roadmap
      Problemstatement
      Model
      Motivation
      Optimal broadcasting of a single chunk
      Many-to-one
      One-to-one
      One-to-c
      Towardsfastbroadcasting of a stream of chunks
      Curses
      Blessings
      2/22
    • 3/22
      The Live Streaming Problem
      A live stream (streamrates) to watch…
      Injected by a server of capacity
      Watched by a set of N peers…
      Goal #1: make it work!
      Goal #2: make it fast!
    • 4/22
      Chunk-based (aka data-driven) diffusion
      Chunk-based: the streamis split intochunks of equal size;
      Integrity-rule: onlyforwardfullyreceivedchunks;
      Upload-constrained: delaycomesfromuploadbandwidth
      u1¸…¸uN;
      Bandwidth are expressed in chunks per second
      No overlay constraints
      !Oversimplified model to focus on heterogeneity
    • 5/22
      Optimal delay in the homogeneous case
      Homogeneity allows to work in slotted time
      The best way to broadcast one chunk takes
      Extends to a stream of chunks by permutation of the single chunk tree
    • 6/22
      Optimal delay in the heterogeneous case
      Nice formula for the optimal single chunk transmission: failed
      Direct link single chunk / stream of chunks: failed
      Intuition: shouldbefaster (centralizationis the extreme case)
      In practice:
      (Bonald et al., Sigmetrics, 2208)
      Summary: heterogeneityis a b….
    • 7/22
      Model extension: forwarding policies
      Authorize collaborations, or force parallelism:
      Many-to-one: any set of peerswith a chunkcanforwardthatchunk in time 1/iui.
      Not realisticat all, but soeasier to compute;
      Will help understand the othermodels.
      One-to-one (mono-source): a peeriwith a chunkcanforwardit in time 1/ui.
      the genuine model;
      slowerthanmany-to-one, but more realistic.
      One-to-c (parallelism): a peerineedsat least c/ui to forward a chunk, up to c peerssimultaneously.
      Extend the classical model;
      parallelismcanavoidbandwidthwaste, but itslower.
    • 8/22
      Delays under the model
    • 9/22
      Example
      3 peers, s=1, n0=u1=1, u2=u3=1/2
      Exactly the bandwidthrequiredaccording to Bandwidth Conservation Law (BCL)
      Equivalent homogeneous system: n0=1, u=2/3
      Streaming is the issue
    • Single CHUNK
      10/22
    • 11/22
      Results for the single chunk transmission
      Dm is given by a simple greedy algorithm:
      Gives
      Absolute, tight, lower bound for chunk transmission.
      Homogeneous case:
    • 12/22
      Results for the single chunk transmission
      D1 is also given by a simple greedy algorithm.
      No simple, closed formula.
      Theorem:
      Conjecture (sigh!):
      Price of atomicity is
      Extension to parallelism:
      Price of parallelism is
    • STREAM OF CHUNKS
      13/22
    • 14/22
      Streaming case: feasibility
    • 15/22
      Bad case scenario
      In the one-to-one model, poorpeermay affect the delay if you have to use thematsome time
      This canhappeneven in overprovisionnedscenarios
    • 16/22
      Good case 1: emulating homogeneity
      Assume wecanfindu suchthat
      (BCL of the emulated system)
      (emulation condition)
      Thenwe have
      Poorpeers (ui<u) are neverused
      Sufficient condition for u to exist: factor 2 BW provisioning for quantification
    • 17/22
      Good case 2: avoiding competition
    • 18/22
      Good case 2: avoiding competition
      Idea: protect the early diffusion to emulate the Dr· 1 case.
      Recipe:
      Split the peers into E equal subsets, (E¼ Dr)
      All subsets should have roughly the original BW distribution.
      Round-robin the chunk injection among the subsets.
      Primary goal: intra-diffusion of the chunk.
      Secondary goal (when idle): broadcast to other subsets
    • 19/22
      Good case 2: avoiding competition
      Proper validation of the ideastill on-going
      Quantification effectscanmakesome BW useless
      The subset must be as similar as possible(one monsterpeer in a single subsetis hard to handle)
      Lead to condition u¸ r(1+1/E)+cst, with E¼ log(N/n_0).
      CorrespondingdelayalmostlikeD
      For someslightlyoverprovisionnedsystems, the streamdelayisalmostlike the chunkdelay
    • 20/22
      Chunk-based model and delay: summary
      For homogeneoussystems, single delay=streamdelay
      Collaboration for one chunktransferis not thatuseful
      Parallelismis not thatscary
      Heterogeneityspeeds up single delay
      Somebandwidthoverprovisioningseems to berequired in the general case
    • 21/22
      And then? Limits of the chunk-based model
      ChunkscomesfromBitTorrent’s world
      Integritypurpose
      Great for unstructuredapproaches
      Bigchunkreduceoverhead
      Good for theory
      Quantification
      Delay expressed as bandwidth
      But when streaming isconcerned…
      Need to go down to latencytimescales
      Limits of the model validity
      A possible lead for future work
      Do wereallyneedstrongintegritymechanisms?
      Try to learnfrom the stripe world
    • Thankyouverymany!
      No interactive questions, but youcan
      • Have a look at the paper
      • Email me (fabien.mathieu@orange-ftgroup.com)
      22/22