Observations on the Dynamic Evolution of Peer-to-Peer Networks
A fundamental theoretical challenge in peer-to-peer systems is proving statements about the evolution of the system while nodes are continuously joining and leaving. Because the system will operate for an infinite time, performance measures based on runtime are uninformative; instead, we must study the rate at which nodes consume resources in order to maintain the system state.This "maintenance bandwidth" depends on the rate at which nodes tend to enter and leave the system. In this paper, we formalize this dependence. Having done so, we analyze the Chord peer-to-peer protocol. We show that Chord's maintenance bandwidth to handle concurrent node arrivals and departures is near optimal, exceeding the lower bound by only a logarithmic factor. We also outline and analyze an algorithm that converges to a correct routing state from an arbitrary initial condition.