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The IEEE 802.16e mobile WiMAX technology aims to provide with an energy efficient communication platform for various mobile applications. In the standard, the sleep mode feature with three Power Saving Classes (PSCs) is designed to compensate for the power saving as the target. Prior work has shown that the proposed Markov Decision Process (MDP) approach can achieve the optimal performance in terms of energy consumption and packet delay through the optimal PSC selection. In this paper, we further consider the design of when to sleep and how to sleep in the system to achieve better tradeoffs between the switching frequency during idle mode and mean power consumption in overall. First, we present our optimal timeout scheme designed based on the previous proposed MDP approach, which can help the system determine when to sleep as well as how to sleep optimally with less switching frequency intuitively. To guarantee the optimality, we show the equivalency of the MDP approach and our optimal timeout scheme that both can achieve the optimal performance in terms of energy consumption level. Also, we demonstrate the performance of our proposed scheme through numerical analysis and validate it with simulation experiments using ns-2 compared with the MDP approach. Finally, we evaluate the impact of Poisson and non-Poisson traffic on our proposed optimal scheme.