On Lifetime-Based Node Failure and Stochastic Resilience of Decentralized Peer-to-Peer Networks

摘要

To model P2P networks that are commonly faced with high rates of churn and random departure decisions by end-users, this paper investigates the resilience of random graphs to lifetime-based node failure and derives the expected delay before a user is forcefully isolated from the graph and the probability that this occurs within his/her lifetime. Using these metrics, we show that systems with heavy-tailed lifetime distributions are more resilient than those with light-tailed (e.g., exponential) distributions and that for a given average degree, $k$-regular graphs exhibit the highest level of fault tolerance. As a practical illustration of our results, each user in a system with $n=100$ billion peers, 30-minute average lifetime, and 1-minute node-replacement delay can stay connected to the graph with probability $1-1$ using only 9 neighbors. This is in contrast to 37 neighbors required under previous modeling efforts. We finish the paper by observing that many P2P networks are almost surely (i.e., with probability $1-o(1)$ ) connected if they have no isolated nodes and derive a simple model for the probability that a P2P system partitions under churn.