To provide energy conservation for the mobile devices. In this paper, the analytical models for sleep mode operations of both the IEEE 802:16e and IEEE 802:16m standards are proposed respectively. The effects of both downlink and uplink traffic are properly considered in the proposed models. Simulations are performed in order to validate the effectiveness of proposed system models. However, according to the performance evaluation for IEEE 802:16e/m system, inefficiency is observed which can be resulted from specific mechanisms within the sleep mode operations, such as frequent state transitions, under-utilized listening windows, and the adoption of binary-exponential growth of sleep window size. A POMDP-based sleep window determination (PSWD) approach is proposed in this paper, which stochastically determines the adequate length of each sleep window according to the traffic pattern. Based on the estimated traffic state, an energy cost-based sleep window determination policy is provided within the PSWD approach in consideration of tolerable network delays. Simulation results show that the proposed PSWD approach outperforms conventional IEEE 802:16e/m power saving mechanisms in terms of energy conservation while the delay constraints are also satisfied corresponding to various traffic demands.