Numerical Algebra, Control and Optimization (NACO)

Load distribution performance of super-node based peer-to-peer communication networks: A nonstationary Markov chain approach

Pages: 593 - 610, Volume 1, Issue 4, December 2011      doi:10.3934/naco.2011.1.593

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Kazuhiko Kuraya - Graduate School of Informatics, Kyoto University, Yoshida Honmachi, Sakyo-ku, Kyoto 606-8501, Japan (email)
Hiroyuki Masuyama - Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan (email)
Shoji Kasahara - Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan (email)

Abstract: Voice over Internet protocol (VoIP) services using peer-to-peer (P2P) technology have become popular in recent years. In P2P-based VoIP networks such as Skype and P2P session initiation protocol (P2PSIP), super nodes are chosen from among all ordinary end-user nodes and handle particular tasks such as the management of user information, call establishment, and traffic relay. Future communication networks based on P2P technology must support a huge number of user nodes. A fundamental analysis of the load distribution in decentralized user-information management is needed to develop efficient and robust communication networks. In this paper, we analyze the performance of the P2P-based dynamic load distribution. In our analytical model, new nodes join the network according to a nonstationary Poisson process, and the stochastic behavior of the number of online nodes is analyzed approximately with an M($t$)/M/$\infty$ queue. We focus on two performance measures that significantly affect the quality of service (QoS) provided to the users: the churn rate and the load of super nodes. Numerical examples show that the performance of the P2P-based VoIP networks is sensitive to the sojourn time of super nodes and the maximum number of nodes managed by a super node.

Keywords:  Decentralized user information management system, nonstationary Poisson process, nonstationary queue, nonstationary Markov chain, online node process, P2P, QoS, VoIP.
Mathematics Subject Classification:  Primary: 68M20; Secondary: 60K25, 68M20.

Received: May 2011;      Revised: August 2011;      Available Online: November 2011.