Analysis of a Priority Retrial Queue with Dependent Vacation Scheme and Application to Power Saving in Wireless Communication Systems

In this paper, we analyse a priority retrial queue with repeated inhomogeneous vacations. Two types of customers arrive at the system and if they find the server unavailable, the first type join an ordinary queue, while the second have to reattempt after a random period. The server departs for a vacation when the ordinary queue is empty upon a service completion. Under this scheme, when a vacation period expires, the server wakes up. If the priority queue is non-empty, it starts serving it exhaustively. Otherwise, it remains awake for a limited time period, waiting for a possible request. If no customers arrive during this period, it goes for another vacation with a different probability distribution from the previous one. The theoretical model has application to the power-saving mechanism in wireless communication systems in which the sleep duration of the device corresponds to the vacation of the server and the listening duration to the time-limited idle period. Various system performance and energy metrics are derived. Moreover, we compare the proposed policy with other vacation schemes. Optimization problems are formulated for finding best values for the critical parameters of the model which maximize the economy of energy achieved in the power save mode, subject to performance constraints.