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, -regular graphs exhibit the highest level of fault tolerance. As a practical illustration of our results, each user in a system with = 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 (1)) connected if they have no isolated nodes and derive a simple model for the probability that a P2P system partitions under churn.Index Terms-Lifetime node failure, network disconnection, peer-to-peer networks, stochastic resilience, user isolation.

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This paper examines graph-theoretic properties of existing peer-to-peer architectures and proposes a new infrastructure based on optimal-diameter de Bruijn graphs. Since generalized de Bruijn graphs possess very short average routing distances and high resilience to node failure, they are well suited for structured peer-to-peer networks. Using the example of Chord, CAN, and de Bruijn, we first study routing performance, graph expansion, and clustering properties of each graph. We then examine bisection width, path overlap, and several other properties that affect routing and resilience of peer-to-peer networks. Having confirmed that de Bruijn graphs offer the best diameter and highest connectivity among the existing peer-to-peer structures, we offer a very simple incremental building process that preserves optimal properties of de Bruijn graphs under uniform user joins/departures. We call the combined peer-to-peer architecture ODRI -Optimal Diameter Routing Infrastructure.

Abstract. BitTorrent users and consumer ISPs are often pictured as having opposite interests, with end-users aggressively trying to improve their download times, while ISPs throttle this traffic to reduce their costs. However, inefficiencies in both download time and quantity of long-distance traffic originate in BitTorrent randomly selecting peers to interact with. We show that biasing the link selection allows one to reduce both median download times by up to 32% and long-distance traffic by up to 16%. This optimization can be deployed by modifying only the BitTorrent trackers. No external infrastructure nor specialized client-side software deployment is necessary, thereby facilitating the adoption of our technique.