On Maximum Stability with Enhanced Scalability in High- Churn DHT Deployment Junfeng Xie, Nanjing University, China Zhenhua Li, Peking University, China Guihai Chen, Nanjing University, China Jie Wu, Florida Atlantic University, USA
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
2
A relaxation
• Vienna – so many famous places of interest • ICPP – so few audience
3
A relaxation (cont.)
• Our paper has many formula• Steven Hawking: “One more formula, one half
audience”• So I add more pictures, reduce formula
4
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)
6
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
7
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
8
Grouping Strategy (cont.)
• Grouping Strategy’s advantages:1)Enhanced scalability -- near Giant ≈ Dwarf2)Maximum stability -- near GiantOnlySweet spot between GiantOnly and Giant ≈ Dwarf
9
Grouping Strategy (cont.)
• A simple example
10
Grouping Strategy (cont.)
• Kernel problem: 1) how many groups? – N/logN2) how to group? – next section
11
Maximum Stability Problem
• MSG problemto minimize
• And
12
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).
13
Maximum Stability Problem (cont.)
• Homogeneous grouping
14
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:
15
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, …)
16
Performance Evaluation
• Grouping snapshot (sorted by stl intervals)
17
Performance Evaluation (cont.)
• Stability (churn rate)
18
Performance Evaluation (cont.)
• Scalability (storage capacity)
19
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
20
The End
21