1 / 17

Simple stochastic models for Arigatoni overlay networks

Simple stochastic models for Arigatoni overlay networks. Philippe Nain INRIA ARIGATONI on WHEELS Kickoff meeting, Sophia Antipolis, February 26-27, 2007. c1. 1. c5. c2. c3. c4. 5. 2. 3. 4. 6. 7. 8. 9. 10. 11. c6. c7. c8. c9. c10. c11. Broker. Extended colony

zyta
Download Presentation

Simple stochastic models for Arigatoni overlay networks

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Simple stochastic models for Arigatonioverlay networks Philippe Nain INRIA ARIGATONI on WHEELS Kickoff meeting, Sophia Antipolis, February 26-27, 2007

  2. c1 1 c5 c2 c3 c4 5 2 3 4 6 7 8 9 10 11 c6 c7 c8 c9 c10 c11 Broker Extended colony associated to 2 Local colony 2 c2 c2 c6 c7 2

  3. N Brockers always active : always able to handle a request (i.e. serve or forward a request to its predecessor) whether it is « local » or not • Members are dynamics : join a local colony, stay connected for a while and then leave (temporarily or permanently)

  4. Focus on single, atomic*, request R issued at brocker in at t=0 (brocker in ancestor of brockers in-1, …,io ) Xi(t) = membership of colony i at time t T(i) = set of nodes in tree rooted at i * Can be extented

  5. c1 T(1)={1,2, ….,11} 1 c5 c2 c3 c4 5 2 3 4 6 7 8 9 10 11 c6 c7 c8 c9 c10 c11 T(5)={5,11} T(2)={2,6,7} T(3)={3,8} T(4)={4,9,10}

  6. Focus on single, atomic*, request R issued at brocker in at t=0 (brocker in ancestor of brockers in-1, …,io ) Xi(t) = membership of colony i at time t T(i) = set of nodes in tree rooted at i With probability • pn (Xm(0), m T(in)), R served by extended colony in • 1- pn (Xm(0), m T(in)), R forwarded to brocker in-1 ; if so, with prob. pn (Xm(0), m  T(in-1)-T(in)), R served by colonies in T(in-1)-T(in)); otherwise, R forwarded to in-2, etc. * Can be extented

  7. c1 Success! 1 c5 c2 c3 c4 5 2 3 4 6 7 8 9 10 11 c6 c7 c8 c9 c10 c11

  8. c1 1 c5 c2 c3 c4 5 2 3 4 6 7 8 9 10 11 c6 c7 c8 c9 c10 c11

  9. c1 Success ! 1 c5 c2 c3 c4 5 2 3 4 6 7 8 9 10 11 c6 c7 c8 c9 c10 c11

  10. c1 Success ! 1 c5 c2 c3 c4 5 2 3 4 6 7 8 9 10 11 c6 c7 c8 c9 c10 c11

  11. c1 Failure! 1 c5 c2 c3 c4 5 2 3 4 6 7 8 9 10 11 c6 c7 c8 c9 c10 c11

  12. N = # brokers/colonies (X1, …, XN) stationary version of membership process {X1(t), …,XN(t)} (X1, …, XN) iid rvs

  13. Members join each colony according to independent Poisson processes (reasonnable assumption) • Intensity i for colony i Each member stays connected for a random time with an arbitrary distribution • i= Mean connection duration in colony i Proposition (membership distribution in colony i) Xi ~ Poisson rv with mean i= i . i P(Xi=k) = (i)k exp(-i)/k!

  14. Application 1 : probability of success/failure q(in,ij) = prob. R served at broker ij Q(in) = prob. R not served pi = probability member in colony i grants service (user availability) ; below p = pii

  15. No need to know maximal number of members in a colony; only need to know average membership Few input parameters

  16. Application 2 : same as #1 but with fixed membership i = membership in colony i Replace e-(1-p)f(l) by pf(l) in previous formulae:

  17. Model extensions • Compound requests R =(R1, …, RM) pi,m = Probability members in colony i grant service to sub-request Rm • Non-independent membership in different colonies • Introduce workload, focus on execution time, network latency, … • Introduce user mobility

More Related