A preemptive priority queue as a model with server vacations

The paper derives the performance measures for non-priority customers in a priority single-server queue with two types of Markovian arrival processes (MAPs). One type of customers has preemptive resume (or repeat) priority over the other. The paper regards the model with two types of MAP arrivals as an MAP/SM/1 queue with only non-priority customers arrivals, semi-Markovian service times and some server vacations. Performance measures such as the waiting time distribution and the queue length distribution are represented by matrix exponential forms. The present model cannot assume i.i.d. services or i.i.d. server vacations and, in addition, the vacation length depends on the service process. Thus, the formulas give new insights on existing results concerning a MAP/SM/1 queue with i.i.d. multiple server vacations.