Much research has been devoted to optimizing the power saving mechanism in wireless mobile devices. Recent advances in wireless radio technology facilitate the implementation of various possible sleep policies. One basic question that arises, which policy performs best under a certain condition. Furthermore, what are the optimal parameters for a given policy. To answer these questions, we provide a formulation of an optimization problem, which entails cost minimization for a given parameterized policy and selection of the best policy among a class. We propose a cost function which captures the inherent tradeoff of delay and energy saving. This takes into account the cost of response time due to extra sleep, the energy saving during the sleep, and the cost for periodic waking up (for listening). As an application, we consider IEEE 802.16e sleep power saving mechanism. We derive various practical policies and check their performances. We show that, %for a class of identical sleep policies, constant duration policy is optimal for exponentially distributed inactive durations. We also show that this structure is not optimal for hyper-exponentially distributed inactive periods. Several extra structural and numerical results are obtained for analytically intractable policies. Our framework allows us to compare the performance of several optimal and suboptimal practical policies with the proposed Standard for WiMAX policy.
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