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In wireless communication networks, power saving is a critical issue. Sleep mode is usually applied to save power in mobile devices; when there is no data to transmit or receive, a mobile device can switch to sleep mode periodically. Evidently, there is a trade-off between power saving and response delay, and the performance of a power saving mechanism depends on user traffic characteristics and how well the power saving mechanism can predict the termination time of an idle period. In the literature, it is commonly accepted that traffic on a highspeed network is self-similar, resulting from heavy-tailed on-off periods. In this paper, we model the on-off durations by generalized Pareto distributions and apply the Xp inspection policy of operational research to power saving mechanism design for wireless communication devices. Numerical examples are provided to show the usefulness of the proposed scheme.