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In Mobile World Interoperability for Microwave Access (WiMAX), the power-saving mechanism (PSM), which operates alternately in sleep and awake modes, works to extend the lifetime of mobile stations (MSs), although it concurrently induces a medium access control (MAC) service data unit (SDU) response delay. In this study, the authors derive the analytical models for two of the most important performance metrics: the average power consumption and the average MAC SDU response delay of an MS in sleep mode. These metrics are given as a function of the sleep mode system parameters: initial sleep window Tmin and final sleep window Tmax. Based on these models, the authors show that a tradeoff relationship exists between them. The authors then propose an optimised power-saving mechanism (OPSM) that jointly determines the optimal Tmin and Tmax to minimise the power consumption under a given MAC SDU response delay constraint. Through both numerical analyses and subsequent simulations, the authors show that the OPSM effectively minimises the power consumption of an MS in its sleep mode while guaranteeing the MAC SDU response delay constraint.