### Impacto

Gómez Corral, Antonio
(2005)
*On a finite-buffer bulk-service queue with disasters.*
Mathematical Methods of Operations Research, 61
(1).
pp. 57-84.
ISSN 1432-2994

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Official URL: http://www.springerlink.com/content/th2mh8al9tl0x511/fulltext.pdf

## 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.

Item Type: | Article |
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Uncontrolled Keywords: | Bulk-service, Censored Markov chain, Clearing, Disasters, Finite-buffer queue, Markovian arrival process (MAP), Quasi-birth-and-death process (QBD |

Subjects: | Sciences > Mathematics > Operations research |

ID Code: | 15622 |

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Deposited On: | 14 Jun 2012 09:38 |

Last Modified: | 06 Feb 2014 10:28 |

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