A BMAP/PH/N Queue with Negative Customers and Partial Protection of Service

A multi-server queueing system with finite and infinite buffers is considered. The input flow is described by the BMAP (Batch Markovian Arrival Process). The service time has the PH (Phase) type distribution. Besides ordinary (positive) customers, the MAP (Markovian Arrival Process) of negative customers arrives to the system. A negative customer can delete an ordinary customer in service if the state (phase) of its PH-service process does not belong to some given set of so-called protected phases. The stationary distribution of the system states and waiting time distribution are derived. The main performance measures of the queueing system considered are computed and numerically illustrated.

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