Analysis of Batch Arrival Single and Bulk Service Queue with Multiple Vacation Closedown and Repair

In this paper, we analyze batch arrival single and bulk service queueing model with multiple vacation, closedown and repair. The single server provides single service if the queue size is ‘\u3c a’ and bulk service if the queue size is ‘ ≥ a’. After completing the service (single or bulk), the server may breakdown with probability ξ and then it will be sent for repair. When the system becomes empty or the server is ready to serve after the repair but no one is waiting, the server resumes closedown and then goes for a multiple vacation of random length. Using supplementary variable technique, the steady-state probability generating function (PGF) of the queue size at an arbitrary time is obtained. The performance measures and cost model are also derived. Numerical illustrations are presented to visualize the effect of system parameters