Core Persistence in Peer-to-Peer Systems Relating Size to Lifetime
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Transcript of Core Persistence in Peer-to-Peer Systems Relating Size to Lifetime
Core Persistence in Peer-to-Peer SystemsRelating Size to Lifetime
V. Gramoli, A-M. Kermarrec, A. Mostefaoui, M. Raynal, B. Sericola
OTM RDDS’06October, 30th
Gramoli, Kermarrec, Mostefaoui, Raynal, Sericola
Context
Large-Scale Dynamic Systems Nodes join and leave the System Rejoining nodes might not hold the data Nodes maintain no global information
Data Persistence Problem For a data, if all its owners leave, it becomes lost
Observations on Peer-to-Peer (P2P) Systems Highly dynamic Never empty
OTM RDDS’06October, 30th
Gramoli, Kermarrec, Mostefaoui, Raynal, Sericola
Goal
Guaranteeing Persistence despite Dynamics
Major Challenge Providing
• Required probability, p, and• The system churn, c,
…data must be replicated • Adjusting replication period, δ,• Adjusting replication size, q.
OTM RDDS’06October, 30th
Gramoli, Kermarrec, Mostefaoui, Raynal, Sericola
System Churn
Large-Scale Distributed System n interconnected nodes each w/ unique ID w/o global knowledge
Dynamic System Nodes join/leave the system A joining node is new
Data Data is initially replicated at a subset of
nodes, called a core.
OTM RDDS’06October, 30th
Gramoli, Kermarrec, Mostefaoui, Raynal, Sericola
Churn Model, c
Churn: System dynamism intensity.
It represents: Rate of arrival and departure by node by unit of
time.
We observe the system at two instants Let Q be the initial core, and q its size, Let A be the set of replaced nodes, α its size, Let Q’ be the resulting core (after replacement).
OTM RDDS’06October, 30th
Gramoli, Kermarrec, Mostefaoui, Raynal, Sericola
Churn Model
timet
Nodes w/ data.
Nodes w/o data
OTM RDDS’06October, 30th
Gramoli, Kermarrec, Mostefaoui, Raynal, Sericola
Churn Model
timet
Nodes w/ data.
Nodes w/o data
Core Q at time t,|Q| = q
OTM RDDS’06October, 30th
Gramoli, Kermarrec, Mostefaoui, Raynal, Sericola
Churn Model
timet t + δ
Nodes w/ data.
Nodes w/o data
After period δ = 2
and with churn c = 0,2
Core Q at time t,|Q| = q
OTM RDDS’06October, 30th
Gramoli, Kermarrec, Mostefaoui, Raynal, Sericola
Churn Model
timet t + δ
Nodes w/ data.
Nodes w/o data
Replaced nodes A,|A| = α
After period δ = 2
and with churn c = 0,2
Core Q at time t,|Q| = q
OTM RDDS’06October, 30th
Gramoli, Kermarrec, Mostefaoui, Raynal, Sericola
Churn Model
timet t + δ
Nodes w/ data.
Nodes w/o data
Core Q’ at time t+δ,
|Q’| = q
After period δ = 2
and with churn c = 0,2
Core Q at time t,|Q| = q
Replaced nodes A,|A| = α
OTM RDDS’06October, 30th
Gramoli, Kermarrec, Mostefaoui, Raynal, Sericola
Churn Model
Evolution of the amount of initial nodes t0 n initial nodes t1 n-nv = n(1-v) initial nodes
... ti n(1-v)i initial nodes ti+1 n(1-v)i - n(1-v)iv = n(1-v)i+1 initial nodes
We choose α = ┌n-n(1-v)δ
┐ the number of
nodes replaced after δ time units
OTM RDDS’06October, 30th
Gramoli, Kermarrec, Mostefaoui, Raynal, Sericola
Data Availability
Initially, q nodes own the data (replicas)
α nodes are replaced uniformly at random
How many data replicas remain after δ time
units in a system w/ churn c ?
OTM RDDS’06October, 30th
Gramoli, Kermarrec, Mostefaoui, Raynal, Sericola
Data Availability
Preliminary Observation Number β = |Q’ ∩ A| of nodes that owned the
data and leave the system is bounded:
max(0, α + q - n) ≤ β ≤ min(α, q)
a b
OTM RDDS’06October, 30th
Gramoli, Kermarrec, Mostefaoui, Raynal, Sericola
Data Availability
Probability of β = k replicas have been replaced?
OTM RDDS’06October, 30th
Gramoli, Kermarrec, Mostefaoui, Raynal, Sericola
Looking for the data
Initially, q replicas.
δ time units later, q system nodes are uniformly drawn at random.
What is the probability of finding the data after this
δ time units in a system w/ churn c ?
OTM RDDS’06October, 30th
Gramoli, Kermarrec, Mostefaoui, Raynal, Sericola
Looking for the data
Probability of missing the data Random drawing, at uniform, and w/o replacement of q nodes.
Let E = Q’ \ A.
(disjoint events)
OTM RDDS’06October, 30th
Gramoli, Kermarrec, Mostefaoui, Raynal, Sericola
Looking for the data
Probability of missing the data
OTM RDDS’06October, 30th
Gramoli, Kermarrec, Mostefaoui, Raynal, Sericola
Core size for n = 104
α/n =
the core size
prob
abili
ty o
f m
issi
ng t
he d
ata
OTM RDDS’06October, 30th
Gramoli, Kermarrec, Mostefaoui, Raynal, Sericola
Probability, Dynamism, and Core Lifetime
Varying churn, size, and probabilityProba of
finding data α/n Core size for
OTM RDDS’06October, 30th
Gramoli, Kermarrec, Mostefaoui, Raynal, Sericola
Conclusion
Retrieving a data is paradoxally easy!
Storage Applications Modifying the data at q nodes Accessing the up-to-date data by contacting q nodes Cores are probabilistic quorums
Future Research Modeling the churn using a more realistic model
(Markovian continu). Specifying a protocol for probabilistic data
consistency/persistence in dynamic system.
OTM RDDS’06October, 30th
Gramoli, Kermarrec, Mostefaoui, Raynal, Sericola
Some References
A Quorum based protocol for searching objects in P2P ntwks.K. Miura, T. Tagawa, and H. Kakugawa. IEEE Trans. on Parallel and Distributed Systems, 17(1):25–37, 2006.
Probabilistic quorums for dynamic systems.I. Abraham and D. Malkhi. Distributed Computing, 18(2):113–124, 2005.
Reconfigurable distributed storage for dynamic ntwks. G. Chockler, S. Gilbert, V. Gramoli, P. M. Musial, and A. A. Shvartsman. In Proc. of 9th Int’l Conf. on Principles of Distributed Systems, 2005.