Abstract
A retrial queueing system with the batch Markovian arrival process and semi-Markovian service is investigated. We suppose that the intensity of retrials linearly depends on the number of repeated calls. The distribution of the number of calls in the system is the subject of research. Asymptotically quasi-Toeplitz 2-dimensional Markov chains are introduced into consideration and applied for solving the problem.
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Dudin, A., Klimenok, V. A retrial BMAP/SM/1 system with linear repeated requests. Queueing Systems 34, 47–66 (2000). https://doi.org/10.1023/A:1019196701000
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DOI: https://doi.org/10.1023/A:1019196701000