Energy efficiency plays vital roles in wireless communication system due to the "Energy limited battery service" of a Mobile Station (MS). To ensure longer battery life in WiMAX, a new protocol has been introduced in its IEEE802.16m version. This new sleep mode has extended listening window and adjustable sleep cycle length. In this paper, they analyze the probability of attaining at three states: serving state, state of timer inactivity and silent state in a simplified statistical model using traffic parameters of arrival rate, pdf (probability density function) of inter arrival time and its threshold value. Finally they developed a new state transition chain of the above three states of a MS of IEEE802.16m and solved the chain in closed form.