The goal of this paper is to establish a general approach for analyzing queueing models with repeated inhomogeneous vacations. The server goes on for a vacation if the inactivity prolongs more than a vacation trigger duration. Once the system enters in vacation mode, it may continue for several consecutive vacation. At the end of a vacation, the server goes on another vacation, possibly with a {\em different} probability distribution, if during the previous vacation there have been no arrivals. However the system enters in vacation mode only if the inactivity is persisted beyond a defined trigger duration. In order to get an insight on the influence of parameters on the performance, we choose to study a simple $M/G/1$ queue (Poisson arrivals and general independent service times) 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 vacations of the server. 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 achieved in power save mode, with constraints as QoS conditions to be met. 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.