Analysis of a discrete-time queueing system with timed vacations

We consider a discrete-time GI-GI-1 queueing system with server vacations. Vacations occur whenever the queue becomes empty or whenever a timer expires. When the timer expires one of the following four actions is considered: the server completes transmission of the present packet before leaving for a vacation, the server immediately leaves for a vacation and the interrupted packet's service is either continued, repeated or resampled and repeated after the vacation. Using a probability generating functions approach, we derive various performance measures such as moments of the buffer contents at various time epochs in equilibrium and moments of the packet delay in equilibrium. By means of an example, we then compare the operation modes under consideration.