The MAP/G/1 G‐Queue with Unreliable Server and Multiple Vacations

Abstract

In this paper, we consider a MAP/G/1 G‐queues with unreliable server and multiple vacations . The arrival of a negative customer not only removes the customer being in service, but also makes the server under repair. The server leaves for a vacation as soon as the system empties and is allowed to take repeated (multiple) vacations. By using the supplementary variables method and the censoring technique, we obtain the queue length distributions. We derive the mean of the busy period based on the renewal theory. Furthermore, we analyze some main reliability indexes and investigate some important special cases.