1 Statistical Modeling and Analysis of P2P Replication to Support Vod Service zyp Infocom, 2011, Shanghai

2 Background VoD: Video-on-Demand – – Traditional VoD and P2P VoD –First one,client-server approach –Second one,P2P assisted VoD

3 Outline Introduction Model Replication algorithm Analysis Adaptive Algorithm Simulation Conclusion

4 Introduction P2P VoD –Storage to replicate content –Upload bandwidth P2P replication is a central design issue in P2P VoD system

5 For a P2P VoD system –Average server bandwidth utilization(B) –Average number of movie copies(M) –Peers(N),movies(K) Each peer: –Upload capacity(U i ) –movies stored(L) –movie set stored on peer i(Q i ) –average requests received by peer i(λ i ) Each movie: –relative popularity of movie j(η j ) –peer set replicating movie j(S j ) Model

6 Assumed: –movies are of the same size – have the same playback rate equal to 1(same as the average upload capacity) –Perfect Fair-Sharing Model How a peer select a movie: –Deterministic Demand –Stationary(random)

7 Stationary(random): –transition matrix -> stationary state –in stationary state,any peer watch movie j is a Binomial distribution with η j –average number requests for peer i Objective of the P2P VoD system This paper try to do: minimize B Model

8 Random with Load Balancing Assignment 1.for j=1 to K do 2. B j =0 3.end for 4.for i=1 to N do 5. Peer i randomly select L movies from the movie set and puts the id of each movie into Q i ; for do 8. B j =B j +U i /λ i,for homogeneous,U i =1 9. if B j ≥1 then 10. Never select movie j any more 11. end if 12. end for 13.end for Replication Algorithm

9 In this algorithm B j meaning the expected received bandwidth for peers watching movie j. For Homogeneous peer,their uplink capacity U=1. This algorithm wants to make the most movie's B≥1

10 Analysis Stationary Demand and Homogeneous( 同类的 ) Peers Requests at any peer i is a random variable of Binomial distribution( ) –For large N: Bandwidth form provider i allocated to a peer watching movie j( ) –EQ.1

11 Analysis EQ.1:

12 Analysis Aggregate bandwidth that peers watching movie j get from other peers: We need variance of X j to describe B: –EQ.2

13 Analysis Weighted average variance of all movies: –EQ.3 Constraints to restrict the allocation: –EQ.4 –EQ.5 –The RLB algorithm satisfying both conditions.

14 Analysis EQ.5: –Each peer stores exactly L movies,means 1/λ i appears exactly L times.

15 Analysis The performance of RLB algorithm is given by EQ.3 Correlation r j (i,k) is complicating factor. –r j (i,k)=1 EQ.3 becomes EQ.6 –r j (i,k)=0 EQ.3 becomes EQ.7

16 Analysis EQ.6: –r j (i,k)=1,means peers who store movie j have the same movie set,then λ i =λ k. –From EQ.4 we can get |s j |=λ i.

17 Analysis The sever load with eq.4 and eq.5: –EQ.8 The worst case r j (i,k)=1 –EQ.9 The best case r j (i,k)=0 –EQ.10

18 Analysis EQ.8:

19 Analysis Stationary demand and heterogeneous peers The upload capacity of peer i be U i. –EQ.1 is rewritten as EQ.11: Proposition 1:They share same lower bound Proposition 2:They share same upper bound

20 Adaptive Algorithm RLB is a centralized algorithm. ARLB is a distributed one –Do movie replication based on the watched movies. ARLB algorithm: –x + =x if x>0,else 0. –GAP means weighted gap between B j and required playback rate(1).

21 Adaptive Algorithm Step1-3:Check i's storage. Step4-5:Check movie j's bandwidth. Step7:Find out which movie to be replaced. Step8-19:Calculate the GAP before and after replace Step20-22:Decision.

22 Simulation A.Stationary demand and static replication assignment –Model validation under homogeneous settings: Evenly distributed movie popularity(η j =1/K). Homogeneous peer uplink capacity(U i =1). Simulation duration 1500 timeslots,viewing duration [20,40]. N=10000,each peer make independently selection. K/L=50,keep the bounds unchanged.

23 Simulation Sever load decreases when L is increased. Server load of RLB is strictly bounded. L=1 achieved lower- bound. Fig.1

24 Simulation –Sensitivity analysis on configuration parameters:

25 Simulation Fig.2 shows that all the six cases that RLB performs much better and RLB is strictly bounded. –(a) changing the popularity –(b) changing the peer uplink capacity –(c) changing N –(d) changing K –(e) changing L with N,K fixed –(f) changing L with K/L fixed

26 Simulation B.Evaluate adaptive replication algorithms –The simulation configuration parameters is similar to A. –Compare with four replacement algorithms. –Also, these simulations show that ARLB performs much better then others,and ARLB still bounded by upper- and lower-bounds.

27 Simulation

28 Conclusion This paper propose a service model and a stationary statistical demand model for P2P VoD. Design a replication algorithm(RLB) and give an adaptive version(ARLB). Simulation

29 Thank you!