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Dimensional analysis of scalability of distributed systems

Dimensional analysis of scalability of distributed systems. Erik Aurell joint work with Sameh El-Ansary, Per Brand, Seif Haridi. Solution 1. Solution 2. Model Analytically. Simulate. What is this talk about?. Problem : We want to understand the behavior

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Dimensional analysis of scalability of distributed systems

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  1. Dimensional analysis of scalability of distributed systems Erik Aurell joint work with Sameh El-Ansary, Per Brand, Seif Haridi

  2. Solution 1 Solution 2 Model Analytically Simulate What is this talk about? Problem: We want to understand the behavior of self-properties of structured overlay networks Hard, Complex Prohibitive Dimensional analysis!!

  3. Sameh says 1: Self-organization • Without central coordination do: • A network graph with “good” properties: Logarithmic diameter & arity • Dynamic load balancing of storage among nodes • Chord , Pastry, Tapestry, P-grid, CAN, Viceroy, Koorde, Kademlia, Naor, Ulysses, DKS, Skipnet, HyperCup … • Studied deeply!!

  4. Sameh says 2: Self-Repair • How to maintain the graph? How to replicate data on the graph? • Current argument: “Just stabilize periodically and eventually everything will be OK, believe me!!”

  5. The research question Is it possible to find intensive variables that describe the characteristics of structured overlay networks that deploy self-organization and self-repair policies?

  6. Static properties of Chord

  7. Extra avg look-up length vs density

  8. A self-repair-related intensive variable •  is the typical time between perturbations to the network (leave/join),  is the time between corrective action (per node • =P/ is the dimensionless ratio perturbation to correction

  9. At given P, dependence on /

  10. Is  an intensive variable? (3/3)

  11. Average look-up length as fct of 

  12. Conclusion • [Done] Identified good candidates for intensive variables: • Self-organization-related: density • Self-repair-related: Perturbation/Stabilization • [To be done] • Find more intensive variables • Increase the accuracy through better statistics • Look for phase transitions • Start making use of the analysis in adaptive algorihms

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