1. BALANCING THROUGHPUT, ROBUSTNESS, AND IN- ORDER DELIVERY IN P2P VOD Bin Fan, David G. Andersen, Michael Kaminsky†, Konstantina Papagiannaki † Carnegie Mellon University, †Intel Labs Pittsburgh Presented by Haoming Fu

2. INDEX INTRODUCTION TRS TRADEOFF BALANCING THE TRADEOFF EVALUATION CONCLUSION

3. 1, INTRODUCTION P2P Background Important Metrics VOD Goals

4. P2P BACKGROUND P2P file transfer: Bit Torrent, Emule VoD(Video on Demand): PPLive Live Streaming: 中大网络电视 (no terminal software, centralized solution?) Features of VoD: Demand sequentiality for playback while downloading chunks. Desire short buffering time but not low downloading time. Less synchrony, permit longer buffering time(though not desired), jump & skip.

5. I MPORTANT M ETRICS (T)hroughtput: the number of bytes downloaded per second (R)obustness: the ability to maintain high throughput in face of network conditions such as node failure, arrival/departure and heterogeneity of users’ bandwidth. (S)equentiality: the order of chunk arrival. What we actually want is: high sequential throughput with tolerable robustness.

6. VOD GOALS Useful chunks : a subset of chunks in a contiguous sequence from the start of the file. Useful chunks

7. VOD GOALS Buffer time Out of buffer Slope: playback rate

8. 2, TRS TRADEOFF Model Assumptions and Metrics Definitions & Assumptions Throughput Robustness Sequentiality Three Basic Schemes Tradeoff Theorem

9. DEFINITIONS & ASSUMPTIONS Downlink capacity is not bottleneck. Leave once a node has all chunks. Steady state : #the rate of departures = #the rate of new arrivals, thus the population size of the swarm is stable. Bandwidth allocation : Seed and peers allocate their uplink bandwidth capacity uniformly among the chunks that they are serving. chunk 1348 chk 12457810 bandwidth

10. DEFINITIONS & ASSUMPTIONS Ci: the sum of the share of the uplink bandwidth allocated for chunk i from the seed and all other peers.

11. THROUGHPUT It’s safe to assume there is only one seed in the swarm since seeds are homogeneous( 同质的 ). g i : the seed allocates a fraction g i of its uplink bandwidth to chunk i. f i : on average a peer allocates fi.

12. THROUGHPUT Theorem 1: for a system in steady state, b: chunk size : maximal arrival rate Proof: Steady state: Q i (T)/T is the rate of replicating chunk i, which is bounded by the per-chunk capacity C i /b. Therefore < <=C i /b, for all i. num of chunk i’s copies peers go peers come

13. THROUGHPUT By eq.(1) and eq.(2), we have Chunk k is the bottleneck chunk. Apply a little law: to eq.(3), we have T is the average downloading time.

14. THROUGHPUT Applying Theorem 1, N= T, We get the lower bound for T,

15. ROBUSTNESS denotes the probability of a peer being “bad”(e.g. slow; failing) r i be the number of available sources that each peer can download chunk i from Intuitively, it is the probability of having at least one good source to download from.

16. ROBUSTNESS In steady state, the probability for a randomly selected peer to have x chunks is 1/M, for x = 0;1;…; M-1. the expected number of chunks that a random peer has downloaded is R’s upper bound: Total number of chunks

17. SEQUENTIALITY useful chunks Denote U(x) as the fraction of useful chunks given x downloaded chunks. 0 <= S <= 1 e.g U(400) = 300/400

18. 2, TRS TRADEOFF Model Assumptions and Metrics Three Basic Schemes Rarest Random Naive( 幼稚的 ) Sequential Cascading( 瀑布 ) Tradeoff Theorem

19. RAREST RANDOM The probability for a peer that has downloaded x chunks to have any particular chunk i is x/M. BT Throughput Apply theorem 1, we have Lower bound! Perfect throughput.

20. RAREST RANDOM Robustness Thus, Upper bound! Perfect robustness. Sequentiality Completely no sequentiality. #num of peers having x chunks #pro of having chunk i

21. NAIVE SEQUENTIAL Note, only peers with i, i+1, …, M chunks have chunk i. In steady state, the number of peers with 0, 1, …, M-1 chunks is N/M. Throughput C M is contributed only by seeds. C M is bottleneck, & Naive Sequential is unstable.

22. NAIVE SEQUENTIAL Robustness Sequentiality

23. CASCADING Highest throughput, if the seed is not the bottleneck, the downloading time is Lowest robustness, intuitively, when one link breaks down, the whole chain collapses. Fully sequentiality.

24. 2, TRS TRADEOFF Model Assumptions and Metrics Three Basic Schemes Tradeoff Theorem

25. TRADEOFF THEOREM Theorem 2. A P2P VoD system can not simultaneously maximize throughput, robustness and sequentiality. Proof Assume otherwise. Maximized T: Maximized S: a seed has i, then has i-1, …, 1 Maximized R: serve all the chunks it has i < j, then Ci < Cj, contradiction!

26. 3, BALANCING THE TRADEOFF Hybrid Strategy Segment Random Many More in the Space

27. HYBRID STRATEGY Combine rarest first and naive sequential. download a chunk according to naive sequential with pro, according to random with 1-s. higher s improves sequentiality but may reduce the system throughput. grey: x xs x(1-s)

28. HYBRID STRATEGY Discussion: bandwidth division 1. Downlink capacity d, playback rate q. d > q. Download sequentially at rate q, while randomly at d-q? When q/d  1, it degenerate to NS. 2. Dynamic scheme. With enough useful chunks buffered, s is low? Useful chunks buffered not enough  s increase  low throughput  further not enough  s increase  …

29. SEGMENT RANDOM The Segment random strategy groups all M chunks of the file into K segments, each of which consists of W chunks. Segments in order Chunks random chunk segment

30. SEGMENT RANDOM peers downloading chunks in the last segment can help upload this last segment. W large, RF K large, NS

31. 4, EVALUATION Experiment Setup TRS Tradeoff in Emulation Buffering Time

32. EXPERIMENT SETUP 1 seed, 50 peers 10 Mbps up, 20 Mbps down, 10 ms latency For robustness measurement, “bad” nodes: heterogeneous nodes (one third are significantly slower: 2 Mbps up and 5 Mbps down)

33. TRS TRADEOFF IN EMULATION high throughput 7.33, robust awful seq

34. BUFFERING TIME Only when sequential throughput is high, can the buffering time become low. beautiful aweful

35. 5, CONCLUSION TRS Tradeoff Theorem.

36. THANK YOU! Any questions, remarks or objections?

37. RAREST RANDOM The chunks are uniformly distributed among peers, thus the probability for a peer that has downloaded x chunks to have any particular chunk i is x/M. (BT) chunk i obtains 1/x of the uplink bandwidth if it has been downloaded already (with probability x/M) 0 with pro 1-x/M

38. RAREST RANDOM Throughput, we have Apply theorem 1, we have Lower bound! Perfect throughput.

39. RAREST RANDOM Robustness In steady state, peers are downloading equally rapidly so the number of peers having x chunks (x = 0;1;…;M-1) is N/M, we have Thus, Upper bound! Perfect robustness.

40. RAREST RANDOM Sequentiality We have, Completely no sequentiality.