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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!
    View slide
  • 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
    View slide
  • 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