Modeling The Population of File-Sharing Peer-to-Peer Networks With Branching Processes

In this paper we develop a simple but effective mathematical model to capture the file population dynamics of file-sharing peer-to-peer systems. Our modeling framework is based on the theory of branching processes. We describe analytically the behavior of the proposed model. The precise characterization of the necessary and sufficient conditions of population extinction or explosion is given based on the system parameters. We also present the expected ratio of active, passive and dead peers for the long-term regime. We validate and demonstrate our results in several simulation studies. Based on our results we propose a number of engineering guidelines to the design and control of file-sharing P2P systems.