An M/G/1 G-queue with server breakdown, working vacations and bernoulli vacation interruption

In this paper, an M/G/1 G-queue with server breakdown, working vacations and Bernoulli vacation interruption is considered. In the normal busy period, the arrival of a negative customer not only takes away the positive customer being in service, but also causes the server break down. During the repair time, the system is out of service until the repair is completed. And during the working vacation period, the vacation will be interrupted with probability p (0 ≤ p ≤ 1) or continues with probability p = 1 - p, if there are customers in the system at a service completion instant. By applying the matrix-analytic method and the supplementary variable technique, the probability generating functions of the queue length and the server state are obtained. Finally, the sensitivity analysis and cost analysis of the model are presented. © 2020 International Association of Engineers.