Abstract
A single-server preemptive priority queueing system consisting of two types of units, with unlimited Poisson input of high priority and limited Poisson input of low priority, and exponential service time distribution is studied. The higher-priority units are served in batches according to a general bulk service rule and they have preemptive priority over lower-priority units. The server will stop servicing a low-priority unit if the size of the queue of high-priority units reaches the minimum number of units required for the bulk service. The server will start servicing a low-priority unit if the size of the high-priority input queue is less than the minimum required for the general bulk service. The probabilities of the number of customers in the queue in steady state and the stability condition are obtained using the matrix-geometric algorithmic approach.
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