1. Updates in Highly Unreliable, Replicated Peer-to-Peer Systems
Anwitaman Datta, Manfred Hauswirth, Karl Aberer
(EPFL)
Presented by Zhiyuan “Troy” Zhan
1/18/2019

2. Outline Motivation System Model & Algorithm
Analytical Model & Analysis
Related Work
Conclusion
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3. Motivation Peer-to-Peer System is not just about file sharing.
Data items can be added, deleted and updated frequently.
Peer commerce
Shared calendars/address books
Trust management
Medical information sharing
Replication is used to improve fault-tolerance and response time.
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4. Motivation – cont’d
How to disseminate updates to other peers is the target problem
Consistency guarantee
Scalability, underlying system assumption, resource consumption
Challenges:
Huge number of peers
Peers can go online/offline at any time
Often lack of global knowledge
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5. Motivation – cont’d Contributions
Address the update dissemination problem with low online probabilities of peers (<30%) and no global knowledge.
Present a “fully decentralized, efficient and robust communication scheme” based on rumor spreading.
A generic analytical model of combined push/pull technique.
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6. Motivation - Problem Statement
Assumptions:
Low percentage of online peers, impossible to achieve any kind of quorum.
Transactional consistency is not required, eventual consistency is desirable in most applications.
Update conflicts is very rare, the paper does not handle it.
Probabilistic guarantee of successful search are sufficient.
Total # of replicas is substantially lower than total # of peers (i.e vs 1000,000).
Consecutive updates can be distributed sparsely over time.
Communication overhead is the major performance measurement.
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7. Outline Motivation System Model & Algorithm
Analytical Model & Analysis
Related Work
Conclusion
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8. System Model A peer-to-peer overlay network.
Each peer has its own local knowledge, i.e. routing table, replica list, etc.
Peers can go offline at any time.
A communication channel can be established between any two online peers, otherwise, assume each other offline.
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9. Algorithm – Push Phase Executed when disseminating updates.
At replica “p”, upon receiving message Push(U,V,Rf,t):
IF Push(U,V,Rf,t) not processed THEN
Select a random subset Rp of replicas with |Rp|=R*fr;
With probability PF(t), send Push(U, V, Rf+Rp+{p}, t+1) to Rp-Rf;
Set Push(U,V,Rf,t) as processed;
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10. Algorithm – Push Phase,cont’d
U: actual update data item
V: version vector. Contains global version identifiers (GUID, can be computed locally), altered data items are treated as distinct coexist versions.
R, Rf, Rp: replicas.
PF(t): a function of t.
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11. Algorithm – Pull Phase
Executed when a peer recovers from failure, or reconnects, or receives no updates for a while, or receives pull message but not sure whether itself is in sync.
Contact online replicas;
Inquire for missed updates based on version vectors;
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12. Outline Motivation System Model & Algorithm
Analytical Model & Analysis
Related Work
Conclusion
1/18/2019

13. General Assumptions
Assume an update U is initiated for R online replicas.
In general, the online population in push round t:
Ron(t)=Ron(t-1)*x+[R-Ron(t-1)]*y
x=1-p, y=q
p: probability of an online peer going offline in one push round; q: probability of an offline peer coming online in one push round.
p,q are typically small and may vary in different rounds.
ASSUME p is constant and omit peers coming online:
Ron(t)=Ron(t-1)*x
ASSUME fr is constant.
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14. Analysis of Pull Phase – Round 0
Total number of messages: msg(0)=R*fr;
New replicas which receive the update: newreplicas(0)=Ron(0)*fr;
Online replicas that do not receive the update: Ron(0)*(1-fr);
Message length (size, denote U as the update message size): ML(0)=U+R*fr*B; (B: size of data required to describe one replica – meta data), only consider U and Rf;
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15. Analysis of Pull Phase – Round 1
# of messages in round 1: msg(1)=Ron(0)*fr*x*PF(1) * R*fr(1-fr)
# of replicas that newly pushed with updates after round 1: newreplicas(1)=Ron(0)*x*(1-fr) * [1-(1-fr)Ron(0)*fr*x*PF(1) ]
Length of message: ML(1)=U+R*B*(fr+fr*(1-fr)) =U+R*B*(1-(1-fr)2)
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16. Analysis of Pull Phase – Round t>=2
Define fd_aware(t) and faware(t)
fd_aware(t): Increment in fraction of online replicas which are aware of the update after round t
faware(t): Total fraction of online replicas which are aware of the update at the beginning of round t
faware(t)= faware(t-1)+ fd_aware(t-1)
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17. Analysis of Pull Phase – Round t>=2, cont’d
newreplicas(t)=Ron(t-1)*(1-faware(t-1))*x * [1 - (1-fr)Ron(t-1)*fd_aware(t-1)*x*PF(t) ] – in paper
newreplicas(t)=Ron(t-1)*(1-faware(t))*x * [1 - (1-fr)Ron(t-1)*fd_aware(t-1)*x*PF(t) ] – I think
Given fd_aware(t)=(1-faware(t))*[1-(1-fr)Ron(t-1)*fd_aware(t-1)*x*PF(t) ], we have:
faware(t)= faware(t-1)+ fd_aware(t-1)=1-(1-faware(t-1))*(1-fr)Ron(t-2)*fd_aware(t-2)*x*PF(t-1) =….;
faware(t) rapidly grows to 1;
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18. Analysis of Pull Phase – Round t>=2, cont’d
If the partial list is ignored:
msg(t)=Ron(t-1)* fd_aware(t-1)*x*RF(t) * R*fr;
If the partial list is considered:
msg(t)=Ron(t-1)* fd_aware(t-1)*x*RF(t) * R*fr*(1-fr)t; - (1)
ML(t)=U+R*B*(1-(1-fr)t+1); - (2)
Both (1) and (2) are proved in the paper by induction on t.
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19. Analysis of Pull Phase
Case1: a replica “p” comes online after a push phase is over
Trivial, assume other online replicas have got the update already.
Case2: “p” comes online during the push phase, suppose faware fraction of the replicas Ron are aware of the updates, the probability of “p” getting the update in m attempts is:
1-[1-(Ron* faware /R)]m -(3)
Query: similar to Pull, but may need majority logic, or version scheme, or hybrid of two, to identify the latest updates
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20. Analytical Results Varying initial online population Ron(0), 1%
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21. Analytical Results – cont’d
Varying initial online population Ron(0), >5%
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22. Analytical Results – cont’d
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23. Analytical Results – cont’d
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24. Analytical Results – cont’d, Parameter tuning
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25. Analytical Results – cont’d, scalability
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26. Discussions: Comparison with Gnutella
Parameter self-tuning (Optimization)
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27. Outline Motivation System Model & Algorithm
Analytical Model & Analysis
Related Work
Conclusion
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28. Related Work Replication and updates in DB:
iAnywhere Solutions: Server-based approach
Bayou: assumes significantly less replicas, less updates, disconnections are short
Some other approaches assume availability of resource and replicas in general
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29. Related Work – cont’d Group communication and lazy epidemic schemes:
Similar work: Bimodal multicast, epidemic updates
None has done “special case study of bimodal behavior and the utility of epidemic algorithms in a highly unreliable environment”
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30. Outline Motivation System Model & Algorithm
Analytical Model & Analysis
Related Work
Conclusion
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31. Conclusion
This paper provides “an analytical model to demonstrate the significant reduction of message overhead” using combined push and pull techniques.
Totally decentralized solution, no global knowledge is needed.
The paper is available at citeseer. Will appear in ICDCS 2003.
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