Recently, Skype has been receiving considerable attention as a peer-to-peer (P2P) Internet telephony. In Skype, a voice connection is established via super nodes chosen from among ordinary end-user nodes. User information such as an IP address and port number of an on-line Skype node is managed by super nodes in a decentralized manner where the number of super nodes changes dynamically according to the number of online Skype nodes. In this paper, we analyze the performance of this decentralized management system of user information. In our analytical model, new nodes join the system according to a nonstationary Poisson process, and the online-node process associated with the number of super nodes is analyzed with a nonstationary Markov chain. We derive the system of difference-differential equations for the probability distribution of the number of online nodes to compute performance measures using the stationary peakedness approximation method. Numerical examples show that the user-information management system based on P2P can keep the quality of service (QoS) more stable than a client-server system with a high-performance centralized server.