Performance analysis of a queueing system based on working vacation with repairable fault in the P2P network

Abstract Nowadays, P2P (Peer-to-Peer) absolutely d-\\ominates the Internet as a traffic in content distribution and sharing service, the issue of energy consumption has emerged as a hot issue. This paper combines the basic theoretical knowledge of queueing theory with the currently more popular hybrid P2P network structure model. In order to address the problem of wasted energy consumption generated by unnecessary online behavior of nodes, the working sleep mechanism for the serving nodes is introduced, and the synchronous multiple working vacation strategy is also adopted to decrease the system energy consumption. In the meantime, negative customer and feedback strategies are introduced. Then a queueing model with working vacation and repairable fault is built, which used to simulate the resource transmission process of P2P and to study the performance of P2P sharing system. The steady-state probability vector is derived by employing quasi-birth-and-death process (QBD) and matrix-geometric solution method. And the expressions for system performance indicators, such as the average delay, are obtained by employing Gauss-Seidel iteration method. Through numerical experiments, the performance indicators of the P2P resource sharing system are studied, which provides a theoretical basis to decrease online energy consumption of nodes in the P2P network system. And through employing Nash equilibrium and social optimal strategy, the value of the social maximum benefit under the social optimization is obtained.