FIRST-PASSAGE PERCOLATION ON THE RANDOM GRAPH
Probability in the Engineering and Informational Sciences
Performance Analysis of Communications Networks and Systems
Performance Analysis of Communications Networks and Systems
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Data Communications Networking
Data Communications Networking
The weight and hopcount of the shortest path in the complete graph with exponential weights
Combinatorics, Probability and Computing
The effect of peer selection with hopcount or delay constraint on peer-to-peer networking
NETWORKING'08 Proceedings of the 7th international IFIP-TC6 networking conference on AdHoc and sensor networks, wireless networks, next generation internet
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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).