queueing models for p2p systems. extend classical queuing theory for p2p systems. develop taxonomy...
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Extend classical queuing theory for P2P systems.
Develop taxonomy for different variations of these queuing models.
Derive stability conditions for these models.
Contents
Jobs and service stations both arrive randomly,possibly correlated .
Following questions can be answered : 1.Necessary and sufficient conditions for
stability2.Performance of given workload and
service parameters
Introduction
Stability• A p2p system is stable if its corresponding job-server process {nc(t),ns(t)} is positive recurrent
•Transition rates for M/M/(M/M)/FCFS systems( nc, ns ) to ( nc + 1, ns ) = ƛc( nc, ns ) to ( nc - 1, ns ) = nsµc
( nc, ns ) to ( nc , ns + 1 ) = ƛs( nc, ns ) to ( nc , ns - 1 ) = nsµc
Quasi Birth Death Process Quasi birth death process is CTMC
that satisfies that : 1.It has a two dimensional state
space union of l(n) where l(n) is called level.
2.A transition from (n1,i) to (n2,j) is not possible if | n1- n2| >= 2
It is called homogeneous if transition rates are independent of n
• M/M/(M/M)/FCFS system is homogeneous QBD process.• Applying results from QBD process , stability condition for M/M/(M/M)/FCFS is
ρc < ρv
Stability for M/M/(M/M)/PS(k) system•M/M/(M/M)/PS(k) system is nonhomogeneous QBD•It is stable if and only if
ρc < ρv
M/M/(-/-) system : It is one dimensional birth-death
process exactly similar to M/M/∞ system which
is always stable M/M/(-/+G) system : Number of servers > Number of jobs,
hence always stable. As long as every peer brings in some
service capability , system is always stable
Modelling P2P storage system : Wuala• In Wuala,there are storage peers and downloading peers.• File is divided into fragments and fragments are stored at different storage peers.• Question : What type of online behavior of storage peers is necessary to satisfy download request rates ?•Notations : • ton – average online time of a storage peer• toff – average offline time of a storage peer• ru – upload bandwidth of each storage peer• rd – download bandwidth of downloading peer• L – average file length
Assumptions : Server ON-OFF times and file lengths are exponentially distributed.Arrival of file download requests to follow a Poisson process then such a P2P system can be modeled by an M/M/(M/M)/PS(k) modelHere
ƛs = 1/toff , µs = 1/ton
ƛ = ɣ , µc = ru / L and k = rd / ru
Discussion and Future Work : Here classical queuing theory is extended to
represent P2P service systems Future work directions include
1.Study of M/G/M/M systems with general service time
2.System with different classes of service policy
3.System with different type of job/server correlation
4.System with heterogenous servers
5.More analytical results than just stability e.g average queue length , applying little’s law average service time can be obtained
Contents
Infinite server queuing network model
Considers two P2P streaming designs :
a) Isolated channel design b) View – upload decoupling Calculates critical performance
measures for both designs.
Introduction
Peers enter and leave video application on longer time scale,peers change channels on slower time scale
Isolated channel : Peers viewing same channel are organized into a swarm , with peers in the same swarm distributing to each other
View-Upload Decoupling : it decouples what it uploads from what it views.
Closed Queuing Network Model Model for always on or slow churn Notations : 1.N – set of all peers , n – total no of
peers2.ui – upload rate of peer i3.J – no of channels4. rj - streaming rate of channel j5.vj - server rate of channel j6.1/µj – expected amount of time a peer
views channel j7.pij – probablity of peer switching from i to j
• Let Mj be random variable denoting number of peers viewing channel j• System can be viewed as closed Jackson network
Performance Metrics
1. Universal Streaming occurs when every peer is receiving channel it is viewing at the streaming rate of channel
2. Expexted no of Happy ChannelsResource Index : бj(Mj) = bj –oj / dj(Mj)
Viewing-Uploading Decoupling Here each stream is divided into
substreams Probability of universal streaming is
calculated for each substream from which PS and HC are calculated
Optimal Streaming : For given allocation Nj for channel j,to
maximize probability of universal streaming, channel is divided into equal rate
substreams
Asymptotic analysis : Determine under what conditions
PS, probability of universal streaming goes to 1 , for large number of peers
They propose a simple scheme to dimension the group sizes
Similarly for ISO design , expressions of probability of universal streaming and expected number of happy channels are derived and asymptotic analysis done
Peer Churn and Channel Churn To include peer churn in the model,
infinite server open jackson network model is used
Conclusion
Performance of multichannel P2P systems is studied using jackson networks
Model captures essential aspects multichannel video systems such as peers churn,channel switching,b/w heterogeneity
VUD performs better than ISO Model can be extended to capture
heterogeneous peer channel switching patterns
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