In this article, a model of the operation of a wireless sensor network (WSN) node with an energy saving mechanism based on a threshold-controlled multiple vacation policy is considered. When the queue of packets directed to the node becomes empty, a multiple vacation period is started during which the receiving/transmitting of packets is blocked. In such a period, successive vacations of a fixed constant duration are taken until a predetermined number of N packets accumulated in the queue is detected. Then, at the completion epoch of this vacation, the processing restarts normally. The analytic approach is based on the conception of an embedded Markov chain; integral equations and renewal theory are applied to study the queue-size transient behaviour. The representations for the Laplace transforms of the queue-size distribution at an arbitrary fixed time t and on the idle and processing periods are obtained. The compact-form formulae for the distributions of the idle and processing period duration are derived. Numerical examples are attached as well.
Keywords: energy saving; multiple vacation policy; queue-size distribution; threshold policy; transient state.