Vacation policy optimization with application to IEEE 802.16e power saving mechanism

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 is: which policy performs best under a certain condition? Furthermore, what are the optimal parameters for a given policy? To answer these questions, we formulate 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 the 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's power saving mechanism. We study various practical policies and check their performance. We show that the constant duration policy is optimal for Poisson inactivity periods, but not for hyper-exponentially distributed inactivity periods. In the policy where vacations are i.i.d. exponential random variables, we derive analytically the optimal control as a function of the expected inactivity period. This result holds for general inactivity periods. Our framework allows us to compare the performance of several optimal and suboptimal practical policies with that of the IEEE 802.16e standard.