On Maximum Stability with Enhanced Scalability in High-Churn

DHT Deployment

Junfeng Xie, Nanjing University, ChinaZhenhua Li, Peking University, China

Guihai Chen, Nanjing University, ChinaJie Wu, Florida Atlantic University, USA

Outline

• A relaxation• Motivation• Related work• Grouping Strategy• Maximum Stability Problem• Performance Evaluation• Conclusion and Future Work

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A relaxation

• Vienna – so many famous places of interest • ICPP – so few audience

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A relaxation (cont.)

• Our paper has many formula• Steven Hawking: “One more formula, one half

audience”• So I add more pictures, reduce formula

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Motivation

• P2P, DHT – hot topics in the past 10 years• Why? – Utilization of Internet edge nodes

Internet edge nodes• Advantages: enormous – many many … so

scalability• Disadvantages: dynamic – join leave … so

stability5

Motivation (cont.)

• A fundamental problem of P2P and DHT-- efficient leverage of dynamic nodes (dwarfs)

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Related Work

• GiantOnly – OpenDHT : giants as DHT servers, dwarfs as clients

• Giant ≈ Dwarf – Chord, Pastry, Tapestry, Kademila, Cycloid

a giant = a DHT node, a dwarf = a DHT node

Problem? scalability vs. stability

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Grouping Strategy• Idea: 1) a giant = a DHT node 2) a group of dwarfs = a DHT node

• Inter-group: DHT• Intra-group: random,erasure-code or replicate

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Grouping Strategy (cont.)

• Grouping Strategy’s advantages:1)Enhanced scalability -- near Giant ≈ Dwarf2)Maximum stability -- near GiantOnlySweet spot between GiantOnly and Giant ≈ Dwarf

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Grouping Strategy (cont.)

• A simple example

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Grouping Strategy (cont.)

• Kernel problem: 1) how many groups? – N/logN2) how to group? – next section

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Maximum Stability Problem

• MSG problemto minimize

• And

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Maximum Stability Problem (cont.)

• 1) MSG problem is NP-hard (omitted here)• 2) MSG problem is infeasible – requires each

node’s join and leave time

• So restricted MSG problem 1) homogeneous grouping – nodes within the

similar dynamics are grouped 2) stochastic computation of ψ, σ and Var(ψ).

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Maximum Stability Problem (cont.)

• Homogeneous grouping

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ky0y 1y 2y 3y

Session length time (stl) intervals:

so Var(ψ) only depends on (y1, y2, …, yk, …)

ky0y 1y 2y 3y

Assume the nodes’ join and leave form a predictable stochastic process

Session length time (stl) intervals:

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Maximum Stability Problem (cont.)

Maximum Stability Problem (cont.)

• Therefore, the restricted MSG problem is in fact: how to design the intervals (y1, y2, …, ym-

1) so as to minimize Var(ψ)? -- Solution: Matlab function fminsearch(Var, y1, y2, …)

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Performance Evaluation

• Grouping snapshot (sorted by stl intervals)

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Performance Evaluation (cont.)

• Stability (churn rate)

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Performance Evaluation (cont.)

• Scalability (storage capacity)

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Conclusion and Future Work

• Conclusion: A homogeneous grouping strategy, which can

achieve maximum stability and enhanced scalability

• Problems: 1) Heterogeneous grouping? 2) Fast optimization algorithm

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The End

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