Weight of the Shortest Path to the First Encountered Peer in a Peer Group of Size m

Journal article
Department
Network Architectures and Services Group (EEMCS) (TU Delft)
Copyright: © 2008 Van Mieghem, P.; Tang, S.
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Source:

Linear Algebra and its Applications, Vol. 429, No. 2-3, July 2008

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Network Architectures and Services Group

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 i.i.d. 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 to estimate the minimal number of peers to offer an acceptable quality (delay or latency).

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