Abstract.
We deal with a finite-buffer bulk-service queue with disasters. The arrival streams of units and disasters are Markovian arrival processes (MAPs). We study the stationary distribution of the embedded Markov chain at post-departure epochs. The block structure allows us to derive a general approach amenable to numerical calculation following results of the theory for censored Markov chains and level-dependent quasi-birth-and-death processes. We give tractable analytical formulas for the departure process and the stationary distributions of the system state at arbitrary and pre-arrival epochs. The effect of the disaster stream on certain probabilistic descriptors is graphically illustrated.
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Acknowledgments.
The research of the author was supported by the DGINV through project BFM2002-02189. The author wishes to thank the anonymous reviewer and the associate editor for their helpful comments.
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Manuscript received: October 2002/Final version received: March 2004
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Gómez-Corral, A. On a finite-buffer bulk-service queue with disasters. Math Meth Oper Res 61, 57–84 (2005). https://doi.org/10.1007/s001860400387
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DOI: https://doi.org/10.1007/s001860400387