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WEIGHT OF THE SHORTEST PATH TO THE FIRST ENCOUNTERED PEER IN A PEER GROUP OF SIZE m

Published online by Cambridge University Press:  18 December 2007

P. Van Mieghem  and
S. Tang
P. Van Mieghem
Affiliation:
Delft University of Technology, 2600 GA Delft, The Netherlands E-mail: P.F.A.VanMieghem@tudelft.nl; S.Tang@ewi.tudelft.nl
S. Tang
Affiliation:
Delft University of Technology, 2600 GA Delft, The Netherlands E-mail: P.F.A.VanMieghem@tudelft.nl; S.Tang@ewi.tudelft.nl
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Abstract

We model the weight (e.g., delay, distance, or cost) from an arbitrary node to the nearest (in weight) peer in a peer-to-peer (P2P) network. The exact probability generating function and an asymptotic analysis is presented for a random graph with independent and identically distributed exponential link weights. The asymptotic distribution function is a Fermi–Dirac distribution that frequently appears in statistical physics. The good agreement with simulation results for relatively small P2P networks makes the asymptotic formula for the probability density function useful for estimating the minimal number of peers to offer an acceptable quality (delay or latency).

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 22 , Issue 1 , January 2008 , pp. 37 - 52
Copyright
Copyright © Cambridge University Press 2008

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References

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