1 statistical modeling and analysis of p2p replication to support vod service zyp infocom, 2011,...
TRANSCRIPT
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
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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
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• 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)
Model
K
jj
1
1
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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)
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• 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
Model
iQj ji N
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• Random with Load Balancing Assignment1. for j=1 to K do2. Bj=03. end for4. 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 Qi;6. 7. for do8. Bj=Bj+Ui/λi,for homogeneous,Ui=19. if Bj≥1 then10. Never select movie j any more11. end if12. end for13.end for
Replication Algorithm
iQj ji N
jQj
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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
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Analysis
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)(RePr
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
jj SiiX ),(
3
1)]([,
1)]([
ij
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11
Analysis
• EQ.1:
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11
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Analysis
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• Aggregate bandwidth that peers watching movie j get from other peers:
• We need variance of Xj to describe B:– EQ.2
)1),(1.()1
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),(2)]([])([
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Analysis
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,,11
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• Weighted average variance of all movies:– EQ.3
• Constraints to restrict the allocation:– EQ.4
– EQ.5
– The RLB algorithm satisfying both conditions.
L
KN
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Analysis• EQ.5:
– Each peer stores exactly L movies,means 1/λi appears exactly L times.
L
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j Si i
K
j Sij
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Analysis
NL
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2
• 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
2
12
1
2 )()1
(1
NL
K
N
N
i i
K
jjj
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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.
NL
K
SS
NSS
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iXSVariXVar
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Analysis
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1)Pr(1
2
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1 1
M
N
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NKB
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1
• 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 M
N
L
KB
2
1
2
1
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Analysis• EQ.8:
M
N
L
NKN
XXX
XXX
XXB
K
jjj
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)Pr()1()Pr(2
1
)Pr()Pr(12
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)Pr(12
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1 1
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AnalysisStationary 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
3
2
)]([,)]([i
ij
i
ij
UiXVar
UiXE
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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).
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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.
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Simulation• A.Stationary demand and static replicati
on assignment– Model validation under homogeneous setti
ngs:• 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.
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Simulation• Sever load
decreases when L is increased.
• Server load of RLB is strictly bounded.
• L=1 achieved lower-bound.
Fig.1
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Simulation– Sensitivity analysis on configuration parameters:
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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
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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.
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Simulation
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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
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Thank you!