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.