In IEEE 802.16 e/m mobile broadband wireless systems, mobile subscriber stations (MSSs) are encouraged to enter the sleep mode for energy saving when end users do not have downstream or upstream traffic. To avoid service disruption of an MSS which stays in the sleep mode, IEEE 802.16 e/m specifies a two-way handshake protocol between the base station (BS) and an MSS. After performing the handshake process, BS is aware of the sleep status of an MSS, and can thus buffer the downstream traffic which arrives when an MSS is asleep. However, the whole handshaking process takes at least four WiMAX frame durations, and the overhead involved may significantly impair the energy saving efficiency. In this paper, we propose a simple sleep control scheme to put an MSS into the sleep mode without performing the handshake between BS and MSSs. Our main idea is to let MSSs monitor and infer its downstream queue status based on the common information owned by both BS and MSSs, and make sleep decisions according to the inferred downstream queue information. We also let BS be aware of the sleep control scheme implemented at MSSs such that BS can accurately infer the status of MSSs without being explicitly notified. Simulation results show that significant power saving can be achieved without degrading the delay performances of MSSs.