In this paper, an analytic model of a sleep mode operation in the IEEE 802.16e is investigated. A mobile subscriber station(MSS) goes to sleep mode after negotiations with the base station(BS) and wakes up periodically for a short interval to check whether there is downlink traffic to it. If the arrival of traffic is notified, an MSS returns to wake mode. Otherwise, it again enters increased sleep interval which is double as the previous one. In order to consider the situation more practically, we propose the sleep mode starting threshold, during which MSS should await packets before it enters the sleep mode. By modifying the M/G/l with multiple vacations model, energy consumption ratio(ECR) and average packet response time are calculated. Our analytic model provides potential guidance in determining the optimal parameters values such as sleep mode starting threshold, minimal sleep and maximal sleep window.