A single-server queue with server vacations and a Batch Markovian Arrival Process

The paper considers a single server infinite queueing system where the arrival process is a Batch Markovian Arrival Process, which as special cases includes the Markovian Arrival Process and many batch arrival processes with correlated batch sizes. The server applies a general exhaustive service vacation policy. The service times are i.i.d. random variables, independent of the interarrival times and the inactive phase durations. Computational results are given for the queue length at service completion or inactive phase termination epochs, at service completion epochs, and at an arbitrary epoch. Finally, some specific types of vacations policies are considered.