Probabilistic Estimation of Network Size and Diameter

Abstract

Determining the size of a network and its diameter are important functions in distributed systems, as there are a number of algorithms which rely on such parameters, or at least on estimates of those values. Although important, determining the size of a network, in a distributed manner, is not trivial. Algorithms that do this should be fast, to cope with high churn; fault-tolerant, to cope with link and node failures; and use a small number of messages, in order not to impose a high overhead in network bandwidth. The Extrema Propagation technique presented in Baquero et al., 2007 allows the estimation of the size of a network in a fast, distributed and fault tolerant manner. The technique was studied in a simulation setting where rounds advance synchronously and where there is no message loss. This work presents two main contributions. The first, is the study of the Extrema Propagation technique under asynchronous rounds and integrated in the Network Friendly Epidemic Multicast (NeEM) framework. The second, is the evaluation of a diameter estimation technique associated with the Extrema Propagation. This study also presents a small enhancement to the Extrema Propagation in terms of communication cost and points out some other possible enhancements. Results show that there is a clear trade-off between time and communication that must be considered when configuring the protocola faster convergence time implies a higher communication cost. Results also show that its possible to reduce the total communication cost by more the 18% using a simple approach. The diameter estimation technique is shown to have a relative error of less than 10% even when using a small sample. The Extrema Propagation technique was partly integrated into the NeEM framework. Full integration would simply be a matter of feeding the estimated values back into the gossip and overlay layers which could use the estimated values for a better configuration of the fanout and time-to-live parameters.

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