  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 the vacation trigger duration.
Once the system enters in vacation mode, it may continue for several
consecutive vacations. At the end of a vacation, the server goes on another
vacation, possibly with a 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 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.
