Energy efficiency plays vital roles in wireless communication system due to the ââ?¬Å?energy limited\nbattery serviceââ?¬Â of a mobile station (MS). To ensure longer battery life in WiMAX, a new protocol\nhas been introduced in its IEEE802.16m version. This new sleep mode has extended listening\nwindow and adjustable sleep cycle length. In this paper, we analyze the probability of attaining at\nthree states: serving state, state of timer inactivity and silent state in a simplified statistical model\nusing traffic parameters of arrival rate, pdf (probability density function) of interarrival time and\nits threshold value. Finally we developed a new state transition chain of the above three states of a\nMS of IEEE802.16m and solved the chain in closed for
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