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

In this paper, an M/G/1 G-queue with server breakdowns, working vacations and vacation interruption is analyzed. A breakdown at busy server is represented by the arrival of a negative customer which causes the customer being in service to be lost. After repair the server is as good as new. Using the method of supplementary variable and the matrix-analytic method, the queue length distribution and the probability of service status at the arbitrary epoch under steady state conditions are obtained. Further, a special cases are presented. Finally, numerical illustrations are provided.