N I ] 2 4 Ja n 20 05 A Statistical Theory of Chord under Churn ∗

Most earlier studies of DHTs under churn have either depended on simulations as the primary investigatio n tool, or on establishing bounds for DHTs to function. In this paper, we present a complete analytical study of churn using a master-equation-based approach, used traditionally in n o equilibrium statistical mechanics to describe steady-sta te or transient phenomena. Simulations are used to verify all the oretical predictions. We demonstrate the application of ou r methodology to the Chord system. For any rate of churn and stabilization rates, and any system size, we accurately pre dict the fraction of failed or incorrect successor and finger poin ters and show how we can use these quantities to predict the performance and consistency of lookups under churn. We also discuss briefly how churn may actually be of different ’types ’ and the implications this will have for the functioning of DH Ts