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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 |
Deposited On: | 14 Jun 2012 09:38 |
Last Modified: | 26 Jun 2018 07:50 |
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