  In this paper we present an analytical study of dynamic membership (aka
churn) in structured peer-to-peer networks. We use a fluid model approach to
describe steady-state or transient phenomena, and apply it to the Chord system.
For any rate of churn and stabilization rates, and any system size, we
accurately account for the functional form of the probability of network
disconnection as well as the fraction of failed or incorrect successor and
finger pointers. We show how we can use these quantities to predict both the
performance and consistency of lookups under churn. All theoretical predictions
match simulation results. The analysis includes both features that are generic
to structured overlays deploying a ring as well as Chord-specific details, and
opens the door to a systematic comparative analysis of, at least, ring-based
structured overlay systems under churn.
