the variant vacation policy geo/g/1 queue with server breakdowns
This study investigates a discrete-time Geo/G/1 queue, where the server operates a randomized vacation policy with at most J vacations, and may break down while working. After all messages have been served in the queue, the server immediately leaves for a vacation. Upon returning from the vacation, the server inspects the queue length. If the queue has some messages, then the server immediately serves the waiting messages; if no message is present in the queue, then the server takes another vacation with probability p or enters the idle state with a probability (1 - p ) until the next message arrives. The breakdown times of the server follow a geometric distribution and the server repair times follow a general distribution. Using the generating function technique, the probability generating functions of the various states are obtained. System characteristics of interest are also derived.
vacation breakdown idle period busy period waiting time