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This paper introduces a novel Medium Access Control (MAC) strategy for energy efficient wireless data transmissions which reduces energy consumption while minimizing the negative impact on network Quality of Service (QoS). This strategy adaptively adjusts the sleeping window of the mobile devices' wireless transceiver. The proposed mechanism - the Slow sTart Exponential and Linear Algorithm (STELA) - consists of three sleeping window adaptation phases, each phase employing a different duty cycle management function. Based on analyzing historic data regarding traffic arrival patterns, traffic modeling is used to estimate future patterns. Consequently, the specific adaptation phases are scheduled and tuned to improve energy efficiency without compromising data delivery performance. Simulation-based testing results show significant energy savings with reduced impact on network QoS achieved when STELA is used, as opposed to other existing MAC layer protocols (IEEE 802.11 and IEEE 802.16) considered in this paper for performance comparisons.