Statistical Modeling and Analysis of P2P Replication to Support Vod Service

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

2. Background • VoD: Video-on-Demand • http://www.xunlei.com/ • http://movie.youku.com/ • 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. Model • For a P2P VoD system • Average server bandwidth utilization(B) • Average number of movie copies(M) • Peers(N),movies(K) • Each peer: • Upload capacity(Ui) • movies stored(L) • movie set stored on peer i(Qi) • average requests received by peer i(λi) • Each movie: • relative popularity of movie j(ηj) • peer set replicating movie j(Sj)

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

8. Replication Algorithm • Random with Load Balancing Assignment • for j=1 to K do • Bj=0 • end for • for i=1 to N do • Peer i randomly select L movies from the movie set and puts the id of each movie into Qi; • for do • Bj=Bj+Ui/λi,for homogeneous,Ui=1 • if Bj≥1 then • Never select movie j any more • end if • end for • end for

9. Replication Algorithm • In this algorithm Bj 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 Xj 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/λi appears exactly L times.

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

16. Analysis • EQ.6: • rj(i,k)=1,means peers who store movie j have the same movie set,then λi=λk. • From EQ.4 we can get |sj|=λi.

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

18. Analysis • EQ.8:

19. Analysis Stationary demand and heterogeneous peers • The upload capacity of peer i be Ui. • 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 Bj 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(ηj=1/K). • Homogeneous peer uplink capacity(Ui=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!