IEEE 802.16e is currently the latest broadband wireless access standard designed to support mobility. In mobile networks,how to control energy consumption is one of the most important issues for battery-powered mobile stations. The standard proposes an energy saving mechanism named’sleep mode’ for conserving the power of mobile stations. According to the operation principle of the sleep mode for downlink traffic in the type I power saving class,considering the self-similar nature of massive multimedia data in wireless networks,a discrete-time batch arrival GeomX/G/1 queuing model with a close-down time and multiple vacations is built. The batch size is supposed to be Pareto distributed. By employing an embedded Markov chain method,the average queue length and the average sojourn time of the system model are derived. Correspondingly,the performance measures are obtained of the energy saving rate and the average packet delay time for the sleep mode in the IEEE 802.16e. The numerical results demonstrate the dependency relationships between the system performance measures and the system parameters with different offered loads and different self-similar degrees. Furthermore,a cost model is developed to determine the optimum length of the close-down time for minimizing the total system cost. IEEE 802.16e is currently the latest broadband wireless access standard designed to support mobility. In mobile networks, how to control energy consumption is one of the most important issues for battery-powered mobile stations. ’for conserving the power of mobile stations. According to the operation principle of the sleep mode for downlink traffic in the type I power saving class, considering the self-similar nature of massive multimedia data in wireless networks, a discrete-time batch arrival GeomX / G / 1 queuing model with a close-down time and multiple vacations is built. The employing size is supposed to be Pareto distributed. By employing an embedded Markov chain method, the average queue length and the average sojourn time of the system model are derived. Correspondingly, the performance measures are obtained of energy saving rate and the average packet delay time for the sleep mode in the IEEE 802.16e. The numerical resu lts demonstrates the dependency relationships between the system performance measures and the system parameters with different system loads and different self-similar degrees.