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