The paper establishes a general approach for analyzing queueing models with repeated inhomogeneous vacations. The server goes on for a vacation if the inactivity prolongs more than the vacation trigger duration. Once the system enters in vacation mode, it may continue for several consecutive vacations, possibly with a {\em different} probability distribution. We study a simple $M/G/1$ queue, which has the advantage of being tractable analytically. The theoretical model is applied to the problem of power saving for mobile devices in which the sleep durations of a device correspond to the server vacations. Various system performance metrics such as the frame response time and the economy of energy are derived. A constrained optimization problem is formulated to maximize the economy of energy in power save mode with QoS constraints. An illustration of the proposed methods is shown with a WiMAX system scenario to obtain design parameters for better performance. Our analysis allows us not only to optimize the system parameters for a given traffic intensity but also to propose parameters that provide the best performance under worst case conditions.