On lifetime-based node failure and stochastic resilience of decentralized peer-to-peer networks

It is shown 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.

Abstract

To understand how high rates of churn and random departure decisions of end-users affect connectivity of P2P networks, this paper investigates 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. Our results indicate 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 resilience. 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 n using only 9 neighbors. This is in contrast to 37 neighbors required under previous modeling efforts. We finish the paper by showing 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.