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The 802.16e power management helps to increase the lifetime of Mobile Subscriber Stations (MSSs) by reducing their energy consumption, but this reduction results in Medium Access Control (MAC) Service Data Unit (SDU) response delay. Hence, both energy consumption and MAC SDU response delay are important performance metrics; however, they have a trade-off relationship. To guarantee the delay constraints of delay-sensitive applications, operating parameters in sleep-mode operation such as minimum sleep interval, Tmin, and maximum sleep interval, Tmax, should be considered seriously. Especially, large Tmax, results in high MAC SDU response delay. However, in the IEEE 802.16e standard, this point is not given enough attention. In this paper, we first propose a numerical model to determine Tmax based on MAC SDU response delay. Then, we propose a Delay -Guaranteed Energy Saving (DGES) algorithm to minimize energy consumption with a given MAC SDU response delay by finding the optimal Tmax under a fixed Tmin. Our proposed numerical model and DGES algorithm are verified by simulation results. [ABSTRACT FROM AUTHOR]