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Analysis of Movie Replication and Benefits of Coding in P2P VoD

Analysis of Movie Replication and Benefits of Coding in P2P VoD. Yipeng Zhou Aug 29, 2012. Outline. Movie Replication Introduction Problem Formulation Analysis of Scheduling Algorithm Simulation Results Benefits of Coding for VoD Background Analysis Simulation Results

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Analysis of Movie Replication and Benefits of Coding in P2P VoD

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  1. Analysis of Movie Replication and Benefits of Coding in P2P VoD Yipeng Zhou Aug 29, 2012 CUHK

  2. Outline Movie Replication Introduction Problem Formulation Analysis of Scheduling Algorithm Simulation Results Benefits of Coding for VoD Background Analysis Simulation Results Conclusion 2014/9/23 CUHK

  3. Introduction Practical System: PPTV PPStream UUSee Challenge: How to organize peers share content? Scheduling How to place right content on peers? Replication Objective is to minimize server load by optimizing movies replicated by different peers. 2012-5-10 CUHK

  4. Related Work • Scheduling strategy and Movie Replication strategy are not analyzed separately. • Not covered • Topology: Any pair of peers can talk with each other. However, the number of simultaneously communicated peers is limited. • No Coding: Only a complete copy is replicated by a peer to simplify model complexity. CUHK

  5. To simplify analysis, we assume: Homogeneous movies. Homogeneous peers. (Same upload capacity & storage) Total peers’ uplink capacity is equal to total demand. View Upload Decoupling. No start-up delay, buffer is not considered Assumption 2014/9/23 CUHK

  6. Closed queuing network model N users, continuously watching movies. Select a movie, watch for a random period. After viewing a movie, select another movie based on transition probability matrix. By solving a fixed point equation, derive stationary popularity of movies. User Behavior Model  Relative popularity: for movie j and N users continuously generate N viewing requests The peer population to view movie j follows Binomial Distribution. [D. Wu et al, Infocom’09 best paper] 2014/9/23 CUHK

  7. Movie Popularity [N. Venkatasubramanian et al, ICDCS 97] is a parameter in the range [0.271, 1]. is a key parameter. Solution: Derive bound of server load to ignore the effect of Θ without considering long tail. Zipf distribution is used for movie popularity. All movies are ranked by descending order of popularity. 2014/9/23 CUHK

  8. Formulation Xj is the random variable to denote the bandwidth received by peers watching movie j from P2P system. Xj is determined by request scheduling strategy and replication strategy. Qiis the set of movies replicated by peer i. L is the storage size of each peer. 2014/9/23 CUHK The Chinese University of Hong Kong

  9. Formulation Cont. Balance BW Allocation It is still difficult to minimize the weighted variance. Fortunately, we can get the bound of average server load. 2014/9/23 CUHK The Chinese University of Hong Kong

  10. Xj Server load Playback Rate Fig. 2 Objective Xj Playback Rate time time Fig. 1 CUHK

  11. Request Scheduling Strategy Fixed BW allocation(FBA) • Fair Sharing 2014/9/23 CUHK

  12. FBA It is easy to calculate the bandwidth allocated to a particular movie. Replication strategy: Proportional (to popularity) in homogeneous network. [D. Wu et al, Infocom mini 09] A virtual super server can be used to derive average server load, as the figure shows. 2014/9/23 CUHK

  13. Proportional to movie popularity. Binomial Distribution FBA Cont. Server load is: CUHK

  14. PFS and FSFD Both of perfect fair sharing (PFS) and fair sharing with fixed degree (FSFD) are special cases of FS PFS When a peer wants to stream movie j, it sends out sub-requests to all peers storing movie j to fetch parts of that movie. When serving other peers, a peer treats all sub-requests the same. FSFD When a peer wants to stream a movie j, it sends out sub-requests to exactly y peers who store movie j. 2014/9/23 CUHK

  15. The distribution of Xj(i) is: PFS We use Poisson distribution as an approximation of Binomial distribution Received sub-requests by peer i in PFS is: Xj(i) is the random variable to denote the BW received by sending a sub-request to peer i for movie j. • We can derive the expected value and variance of Xj(i) CUHK

  16. The variance of Xj The correlation determines total variance. PFS Cont. It is very complicated to get the distribution of Xj The distribution of Xj(i) depends on the number of sub-requests received by peer i. The number of sub-requests received by peer i depends on Qi CUHK

  17. PFS Worst Case Cluster 1 store movie 1, 2,..L Cluster 1 store movie L+1,L+2,..2L Cluster L store movie K-L+1,..K Correlation is equal to 1 means that peers form K/L clusters. In each cluster, all peers store the same movie set. The movie set is random selected from the whole movie set. The received requests is the same for all peers in the same clusters. The behavior of a cluster is like a super server. The server load can be derived exactly. CUHK

  18. PFS Best Case The upper bound is achieved when all peers have the same load λi and the bandwidth from different peers is independent. Xj(i)s are independent identical distributed for different i. Normal distribution is used as approximation of Xj. The required server load to support one peer is: The total serever load is: CUHK

  19. Initialization To minimize correlation To balance bandwidth allocation Random Load Balancing Algorithm Bj = E[Xj] CUHK

  20. FSFD • Each peer sends out exactly y sub-requests to randomly selected peers replicating target movie. • Similar to PFS, the received BW from one sub-request is: Proportional replication strategy achieves the balanced bandwidth allocation since λi =y [J. Wu et al, Infocom mini 2009] [K. Suh et al, JSAC 2007] CUHK

  21. FSFD Worst Case Cluster 1 store movie 1, 2,..L Cluster 1 store movie L+1,L+2,..2L Cluster L store movie K-L+1,..K Here, the difference from PFS is that the each peer sends only y sub-requests instead of sending sub-requests to all peers. The received requests is perfect correlated for all peers in the same clusters. The behavior of a cluster is like a super server. The server load can be derived exactly. CUHK

  22. FBA, PFS vs FSFD H = NL/K, which is the average storage resource. CUHK

  23. Balanced BW allocation, equivalent to E[Xj] = 1 FSBD • When a peer wants to stream a movie j, it sends out at most Y sub-requests to random selected peers who store movie j. Nk is the expected peer population to view movie k. CUHK

  24. Type II Type II Type I FSBD Worst Case • The worst case is similar to the worst case of PFS. But there are two type clusters. • In type I cluster: y = Y, similar to FSFD. • In type II cluster: y = No. of Peers, similar to PFS. An example with Y = 3 CUHK

  25. Type II Type I FSBD Cont. Ri is the peer population of cluster i. B is maximized whenγ = 1 CUHK

  26. Performance comparison of FSBD with FSFD and PFS FSBD Cont. The next question: design a replication strategy to work no matter what the bound of out-degree, i.e. Y 2014/9/23 CUHK

  27. DAR Algorithm 2014/9/23 CUHK

  28. Bound Validation of PFS B = O(Sqrt(NK/L)) COV  1 COV  0 B = O(K/L) N = 10000, Fix ratio of K/L= 50, Homo. movie popularity and peer uplink bandwidth CUHK

  29. Model Validation N=4000, K=400, L=4 FBA FSFD Bound of PFS 2014/9/23 CUHK

  30. DAR ARLB Proportional FSBD N=4000, K=400, L=4 Proportional 2014/9/23 CUHK DAR

  31. Outline Movie Replication Introduction Problem Formulation Analysis of Scheduling Algorithm Simulation Results Benefits of Coding for VoD Background Analysis Simulation Results Conclusion 2014/9/23 CUHK

  32. Background For P2P, helper no. = peer no. CUHK

  33. Previous Work [F. Liu et al, Infocom’11] adopts RS Coding. [Y. Kao et al, TPDS’11] adopts Network Coding. CUHK

  34. To simplify analysis, we assume: Perfect View Upload Decoupling. Random Selected Enough Neighbors. Limited Downloading. No Encoding or Decoding Overhead. Discrete time slot. Model & Assumption 2014/9/23 2014/9/23 CUHK

  35. playback 1 2 3 4 5 6 7 8 Helper Selection Buffer map X X X X For Greedy Strategy FF Selection Greedy Selection For FF Strategy Model with d=1 Performance depends on p(n). Streaming cost is 1-p(n) CUHK

  36. Main Result Proposition 1: In a P2P system with perfect view-upload decoupling, the Greedy strategy is always the optimal strategy to maximize p(n, d). Proposition 2: For two coding schemes using Greedy strategy with block size d1and d2, if d1< d2and d2is divisible by d1, the streaming cost for coding scheme d2is smaller than that for d1. It is a tradeoff between streaming cost and movie replication cost. CUHK

  37. Simulation Helpers are assumed to have stored necessary encoded chunks. Streaming cost decreases with d CUHK

  38. Simulation Cont. A scenario with new movie. No helper replicates the new movie. • Two ways for new movie replication: • Pushed from server. • Distributed among helpers. CUHK

  39. Conclusion 2014/9/23 We use a new approach toanalyze three kinds of request scheduling strategies. Real-world systems is likely to be in between fair sharing (with some fixed degree) and perfect fair sharing. Therefore, we propose a novel FSBD model with varying out-degree. This allows us to illustrate the effect of out-degree in request scheduling. We use a simple mean field stochastic model to analyze the benefits by adopting coding for movie replication. CUHK

  40. The end Thank you Q & A 2014/9/23 CUHK

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