Transient Analysis of an M/M/1 Queue with Sleep Modes, Startup Time, Disaster, Repair and Its Application to Wireless Sensor Networks

Abstract

An M/M/1 queueing system with vacation, threshold policy, start up time, waiting server, system disaster and repair is considered. This work is motivated by the energy management of Wireless Sensor Networks (WSNs). In this model, the system switches to various states namely busy state, idle state, shutdown state, inactive state, wake-up state and failure state.   The disaster can occur at state state of the system except at failure state and subsequent repair is considered. The disaster can be considered as a jamming signal is WSNs. For this investigated system, a closed form of expression is obtained for both transient and steady- state probabilities. Furthermore, performance measures such as mean, variance and probability that the server is in various stages of power management modes are computed. Finally, graphical illustrations are made to understand the effect of the parameters on the performance of the system.