Abstract
We derive 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. We regard 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. Our 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, our formulas give new insights on existing results concerning an MAP/SM/1 queue with i.i.d. multiple server vacations.
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