A Retrial BMAP/PH/N System |
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| Authors: | Breuer Lothar Dudin Alexander Klimenok Valentina |
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| Institution: | (1) Department IV – Computer Science, University of Trier, 54286 Trier, Germany;(2) Department of Applied Mathematics and Computer Science, Belarus State University, 4 F. Skorina Ave, 220050 Minsk, Belarus |
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| Abstract: | A multi-server retrial queueing model with Batch Markovian Arrival Process and phase-type service time distribution is analyzed. The continuous-time multi-dimensional Markov chain describing the behavior of the system is investigated by means of reducing it to the corresponding discrete-time multi-dimensional Markov chain. The latter belongs to the class of multi-dimensional quasi-Toeplitz Markov chains in the case of a constant retrial rate and to the class of multi-dimensional asymptotically quasi-Toeplitz Markov chains in the case of an infinitely increasing retrial rate. It allows to obtain the existence conditions for the stationary distribution and to elaborate the algorithms for calculating the stationary state probabilities. |
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| Keywords: | BMAP/PH/N retrial model matrix analytic methods batch Markovian arrival process PH-distribution asymptotically quasi-Toeplitz Markov chains |
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