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While the legacy power-saving mechanism in wireless networks usually uses a predetermined and fixed sleep interval to enhance the energy conservation of mobile stations, the IEEE 802.16e Mobile WiMAX system adopts a power-saving mechanism with a binary truncated exponent (BTE) algorithm for determining sleep intervals. Although the BTE algorithm allows more flexibility in determining sleep intervals, it still does not consider the delay of the response packet. Thus, in this paper, we suggest a new power-saving mechanism, which is the probabilistic sleep interval decision (PSID) algorithm, in the context of an IEEE 802.16e Mobile WiMAX system. While the length of sleep interval is restricted by the upper and lower bounds, irrespective of response packet's arrival time under the BTE algorithm, the PSID algorithm determines sleep interval placement by using the distribution function of the response packet's arrival time so that the response packet may arrive at the base station during each sleep interval with the same probability. To compare the two algorithms, the main properties of the BTE algorithm and the proposed PSID algorithm are discussed, and a theoretical framework for analyzing its performance is provided. Analytical and simulation results show that under the BTE algorithm, energy consumption and buffering delay converge to a saturation point, and a short buffering delay can be obtained at the expense of sacrificing energy consumption. Meanwhile, the PSID algorithm performs better with respect to energy consumption and buffering delay than the BTE algorithm.