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A generic linear mathematical model is proposed to represent the dynamics of bandwidth usage, network topology, and host processing power in large scale Peer-to-Peer (P2P) networks. Feedback control theory is employed to analyze system stability and query controllability, as well as deriving an explicit solution for the bandwidth usage. The proposed model and analysis methods can be applied to various P2P networks, such as broadcast based P2P network, super-peer based unstructured P2P network, and distributed hash table based structured P2P network. The synthesis of the model is also presented, which adaptively adjusts query rate in order to properly control the bandwidth usage.
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