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A spectral method for a nonpreemptive priority BMAP/G/1 queue. (English) Zbl 1069.60081

Summary: We consider a nonpreemptive priority queue with two priority classes of customers. Customers arrive according to a batch Markovian arrival process (BMAP). In order to calculate the boundary vectors we propose a spectral method based on zeros of the determinant of a matrix function and the corresponding eigenvectors. It is proved that there are \(M\) zeros in a set \(\Omega\), where \(M\) is the size of the state space of the underlying Markov process. The zeros are calculated by the Durand-Kerner method, and the stationary joint probability of the numbers of customers of classes 1 and 2 at departures is derived by the inversion of the two-dimensional Fourier transform. For a numerical example, the stationary probability is calculated.

MSC:

60K25 Queueing theory (aspects of probability theory)
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
90B22 Queues and service in operations research
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