A Least-Resistance Path in Reasoning about Unstructured Overlay Networks

Unstructured overlay networks for peer-to-peer applications combined with stochastic algorithms for clustering and resource location are attractive due to low-maintenance costs and inherent fault-tolerance and self-organizing properties. Moreover, there is a relatively large volume of experimental evidence that these methods are efficiency-wise a good alternative to structured methods, which require more sophisticated algorithms for maintenance and fault tolerance. However, currently there is a very limited selection of appropriate tools to use in systematically evaluating performance and other properties of such non-trivial methods. Based on a well-known association between random walks and resistor networks, and building on a recently pointed-out connection with peer-to-peer networks, we tie-in a set of diverse techniques and metrics of both realms in a unifying framework. Furthermore, we present a basic set of tools to facilitate the analysis of overlay properties and the reasoning about algorithms for peer-to-peer networks. One of the key features of this framework is that it enables us to measure and contrast the local and global impact of algorithmic decisions in peer-to-peer networks. We provide example experimental studies that furthermore demonstrate its capabilities in the overlay network context