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IEEE 802.16e standard currently supports mobile subscriber stations, which substantiates the need for energy-efficient communication. In this paper we analyze a novel sleep mode mechanism to be considered for the future IEEE 802.16m standard. We study the overall message delay in the downlink channel and explicitly account for the sleep mode power consumption. Simple expressions are given based on M/D/1 queueing system with multiple vacations. The analytical approach is verified by simulation.