A simple fluid model for the analysis of the squirrel peer-to-peer caching system

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Abstract
Peer-to-peer (P2P) systems are complex to analyze due to their large number of users who connect intermittently and to the frequency of requests for files or Web objects. In this paper we propose a mathematical model in which request streams are represented as fluid flows and then apply this model in an analysis of Squirrel: a recent P2P cooperative Web cache. Our fluid model provides a low-complexity means to estimate the performance of Squirrel (hit probability and latency) and ex- hibits the key qualitative properties of this system. The accuracy of our model is validated by a comparison with discrete-event simulation. results and at a low numerical complexity. Content distribu- tion networks appear to be good candidates to illustrate our approach as they typically involve a large number of users and many parameters. In turn, these characteristics imply large state spaces and a high numerical complexity when one uses detailed (microscopic) models (such as the Markovian) and simulations. In Section II we provide an overview of Squirrel. Our fluid model is introduced in Section III and we use it in Section IV to compute the main performance of Squirrel (hit probability, latency, etc.). In particular, we provide a simple expression for the hit probability, whose complexity is linear in the number of nodes in the Squirrel network. We show in Section V that our model provides substantial insight into performance issues of P2P cooperative Web caches such as Squirrel. Our analysis shows that two key parameters largely determine the performance of the system. In Section VI we compare results obtained with the fluid model to results obtained with a discrete-event simulation of Squirrel. We find that the fluid model is both qualitatively and quantitatively accurate. We conclude in Section VII with possible extensions of our fluid model.

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