Download presentation

Presentation is loading. Please wait.

Published byHadley Shirah Modified over 2 years ago

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

2
1 5 34 11678910 c1 c7c6 c2 c5 c9c10c11c8 c4c3 2 2 Broker c2 Local colony 2 c2c7c6 Extended colony associated to 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 i n at t=0 (brocker i n ancestor of brockers i n-1, …,i o ) X i (t) = membership of colony i at time t T(i) = set of nodes in tree rooted at i * Can be extented

5
1 5 34 11678910 c1 c7c6 c2 c5 c9c10c11c8 c4c3 2 T(2)={2,6,7} T(3)={3,8}T(4)={4,9,10} T(5)={5,11} T(1)={1,2, ….,11}

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

7
1 5 34 11678910 c1 c7c6 c2 c5 c9c10c11c8 c4c3 2 Success !

8
1 5 34 11678910 c1 c7c6 c2 c5 c9c10c11c8 c4c3 2

9
1 5 34 11678910 c1 c7c6 c2 c5 c9c10c11c8 c4c3 2 Success !

10
1 5 34 11678910 c1 c7c6 c2 c5 c9c10c11c8 c4c3 2 Success !

11
1 5 34 11678910 c1 c7c6 c2 c5 c9c10c11c8 c4c3 2 Failure!

12
N = # brokers/colonies (X 1, …, X N ) stationary version of membership process {X 1 (t), …,X N (t)} (X 1, …, X N ) 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) X i ~ Poisson rv with mean i = i. i P(X i =k) = ( i ) k exp(- i )/k!

14
Application 1 : probability of success/failure q(i n,i j ) = prob. R served at broker i j Q(i n ) = prob. R not served p i = probability member in colony i grants service (user availability) ; below p = p i 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 p f(l) in previous formulae:

17
Model extensions Compound requests R =(R 1, …, R M ) p i,m = Probability members in colony i grant service to sub-request R m Non-independent membership in different colonies Introduce workload, focus on execution time, network latency, … Introduce user mobility

Similar presentations

OK

Goal of Learning Algorithms The early learning algorithms were designed to find such an accurate fit to the data. A classifier is said to be consistent.

Goal of Learning Algorithms The early learning algorithms were designed to find such an accurate fit to the data. A classifier is said to be consistent.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on history of australia day Ppt on wireless network security Ppt on construction site safety Ppt on holographic technology hologram Ppt on afforestation and deforestation Converter doc em ppt online training Ppt on division for class 4 Ppt on different occupations images Ppt on wind energy in india 2012 Ppt on the topic online education