An evaluation of sampling algorithms for estimating the size of a Chord network

Abstract

Due to the decentralized nature of structured P2P systems, there is no a direct way for a single node of getting aggregate statistics about the whole network, such as its current size. In this paper we focus on the problem of estimating the size of one of the most popular structured P2P networks, Chord, using a sampling-based approach. With this approach, a node calculates an estimate of the network size after having queried a small number of its successors about some of their properties. We formally define three sampling-based algorithms that exploit well-known structural properties of a Chord network to derive an estimate of its size. An experimental evaluation was carried out through simulations to evaluate the accuracy of the three algorithms in different network scenarios. The evaluation allowed us to identify, among the three algorithms, a Ring Density Estimation (RDE) technique that was able to estimate the size of all the Chord networks considered with an average error of 2% or less, using only a few tens of sample nodes. Moreover, the simulation results showed that the RDE accuracy is not affected by dynamic network conditions, even in the presence of high nodes failure rates.