The Variant Vacation Policy Geo/G/1 Queue with Server Breakdowns

摘要

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.