A Queueing System with Probabilistic Inhomogeneous Vacations for Modeling Power-Saving in Wireless Systems with Retransmissions

In this paper, we investigate the power management of mobile devices, using a variant of an M/G/1 queue with probabilistic inhomogeneous multiple vacations and generalized service process. Under the vacation scheme, at the end of a vacation the server goes on another vacation, with a different probability distribution, if during the previous vacation there have been no arrivals. The modified vacation policy depends on the initial vacation interval and the server selects randomly over M such vacation policies. The theoretical system can be applied for modeling the power saving mode of mobile devices in modern wireless systems. Moreover, the form of the service process properly describes the incremental redundancy retransmission scheme that provides different types of retransmissions in such systems. Steady state analysis is investigated, energy and performance metrics are obtained and used to provide numerical results that are also validated against simulations.