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Large-scale and dynamically changing distributed systems such as the Grid, peer-to-peer overlays, etc., need to collect several kinds of global statistics in a decentralized manner. In this paper, we tackle a specific statistic collection problem called Group Size Estimation, for estimating the number of non-faulty processes present in the global group at any given point of time. We present two new decentralized algorithms for estimation in dynamic groups, analyze the algorithms, and experimentally evaluate them using real-life traces. One scheme is active: it spreads a gossip into the overlay first, and then samples the receipt times of this gossip at different processes. The second scheme is passive: it measures the density of processes when their identifiers are hashed into a real interval. Both schemes have low latency, scalable perprocess overheads, and provide high levels of probabilistic accuracy for the estimate. They are implemented as part of a size estimation utility called PeerCounter that can be incorporated modularly into standard peer-to-peer overlays. We present experimental results from both the simulations and PeerCounter, running on a cluster of 33 Linux servers.

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