Performance measures of variant working vacations on batch arrival queue with server breakdowns

This paper analyzes an M-x/M/1 variant working vacation queue with server breakdowns and repair. The server takes working vacations as soon as the system becomes empty. The service times during regular busy period, working vacation period, vacation times, breakdown times and repair times are all assumed to be exponentially distributed and are mutually independent. We have used the probability generating functions to derive the steady-state probabilities and obtain the closed form expressions of the system size. In addition, we obtain some other performance measures and their monotonicity with respect to variant working vacations.