Tsung-Yin Wang
ABSTRACT
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.
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Index Terms
- The variant vacation policy Geo/G/1 queue with server breakdowns
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