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

CUHK Outline Movie Replication Introduction Problem Formulation Analysis of Scheduling Algorithm Simulation Results Benefits of Coding for VoD Background Analysis Simulation Results Conclusion

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

CUHK 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 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

CUHK 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 N users continuously generate N viewing requests [D. Wu et al, Infocom ’ 09 best paper]  Relative popularity: for movie j and The peer population to view movie j follows Binomial Distribution.

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

CUHK The Chinese University of Hong Kong Formulation Q i is the set of movies replicated by peer i. L is the storage size of each peer. 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.

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

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

CUHK Request Scheduling Strategy Fixed BW allocation(FBA) Fair Sharing

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

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

CUHK 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.

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

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

CUHK PFS Worst Case 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. Cluster 1 store movie 1, 2,..L Cluster 1 store movie L+1,L+2,.. 2L Cluster L store movie K- L+1,..K

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

CUHK Random Load Balancing Algorithm Initialization To minimize correlation To balance bandwidth allocation B j = E[X j ]

CUHK 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 λ i = y [J. Wu et al, Infocom mini 2009] [K. Suh et al, JSAC 2007]

CUHK FSFD Worst Case 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. 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.

CUHK FBA, PFS vs FSFD Scheduling StrategyOptimal Replication Strategy FBAProportional PFSRLB FSFDProportional H = NL/K, which is the average storage resource.

CUHK 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. Balanced BW allocation, equivalent to E[X j ] = 1 N k is the expected peer population to view movie k.

CUHK 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. Type I An example with Y = 3 Type II

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

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

CUHK DAR Algorithm

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

CUHK Model Validation FBA Bound of PFS FSFD N=4000, K=400, L=4

CUHK FSBD DAR ARLB Proportional N=4000, K=400, L=4 Proportional

CUHK Outline Movie Replication Introduction Problem Formulation Analysis of Scheduling Algorithm Simulation Results Benefits of Coding for VoD Background Analysis Simulation Results Conclusion

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

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

CUHK 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

CUHK Model with d=1 For Greedy Strategy For FF Strategy Buffer mapX X playback FF SelectionGreedy Selection Performance depends on p(n). Streaming cost is 1-p(n) Helper Selection

CUHK 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 d 1 and d 2, if d 1 < d 2 and d 2 is divisible by d 1, the streaming cost for coding scheme d 2 is smaller than that for d 1. Main Result It is a tradeoff between streaming cost and movie replication cost.

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

CUHK Simulation Cont. A scenario with new movie. No helper replicates the new movie. Two ways for new movie replication: 1.Pushed from server. 2.Distributed among helpers.

CUHK We use a new approach to analyze 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. Conclusion

CUHK The end Thank you Q & A