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This paper presents an energy conservation scheme, Maximum Unavailability Interval (MUI), to improve the energy efficiency for the Power Saving Class of Type II in IEEE 802.16e. By applying the Chinese Remainder Theorem, the proposed MUI is guaranteed to find the maximum Unavailability Interval, during which the transceiver can be powered down. We also propose new mathematical techniques to reduce the computational complexity when solving the Chinese Remainder Theorem problem. Because the computational complexity is reduced significantly, the proposed MUI can be practically implemented in real systems. The proposed MUI is fully compatible with the 802.16e standard. It provides a systematic way to determine the start frame number, one of the important parameters defined in the standard. In addition to analyzing the computational complexity, simulations and experiments are conducted to evaluate the performance of the proposed algorithms.