On the Degree Distribution of Faulty Peer-to-Peer Overlay Networks

This paper presents an analytical approach to model fault-tolerance in P2P overlays, represented as complex networks. We define a distributed protocol for managing the overlay and reacting to node faults; peers try to maintain a desired degree and make (accept) requests for creating links only if their actual degree is lower than their desired degree. Based on the protocol, evolution equations are defined and manipulated by resorting to generating functions. Obtained outcomes provide insights on the nodes' degree probability distribution. We study different networks, characterized by three specific desired degree distributions, i.e.~fixed desired degree, random graphs and power law. All these networks are assessed via the analytical tool and simulation as well. Results show that based on the provided mathematical model, it is possible to properly tune the average attachment rate at peers so as they are enabled to maintain their own desired degree.