Performance analysis of a Queueing system based on vacation with fault repairable and spare servers in the MP2P network

Peer-to-Peer (P2P) network is a logical layer distributed network built on the physical network, and nowadays the communication of mobile P2P (MP2P) network in various wireless environments is also developing rapidly. However, the peer in the MP2P network needs to take on both server and client roles, resulting in poor network performance and high energy consumption. Combining this feature, improving network performance and reducing system energy consumption becomes a hot issue. In order to address the problem of wasted energy consumption caused by unnecessary online behavior of partially idle peers on the server side when there are few peers on the requesting side of the network, the mechanism of spare service peers online and standard service peers sleep is applied. In the meantime, considering physical damage, peer feedback and peer impatience, impatient customers and feedback strategies are introduced. Then an M/M/ c + d queueing model based on synchronous multiple vacation with fault repairable and spare servers, and variable service rates is built, which is subsequently used to simulate the performance of an MP2P network in various wireless environments, such as Wireless Mesh network (WMNs), wireless Local Area Network (WLAN), wireless Metropolitan Area network (WMAN), etc. The expressions for system performance indicators are obtained by employing quasi-birth-and-death process (QBD), matrix-geometric solution method and Gauss-Seidel iteration method. Through numerical experiments, the effects of system parameters on performance indicators of the MP2P system, such as online energy consumption, are studied. Moreover, through using Nash equilibrium and social optimal strategy, the value of the social maximum benefit under the social optimization is obtained, which provides a decision framework for the MP2P system to improve its network performance and reduce the online energy consumption.