A discrete-time gated vacation queue with a bulk service

This paper investigates a discrete-time gated vacation queue with a general bulk service rule (L, K) subject to a single- vacation policy. There are two queues separated by a gate. Arriving packets first join the secondary queue located before the gate in order of arrival and move at the end of the last slot of a single-vacation period in batches of minimum size L packets and maximum size K to the primary queue which is spaced after the gate, whenever the gate opens. Using a probability generating function approach, the steady state analysis is carried out under the assumption that service times of batches are independent of the number of packets in any batch.