On a finite-buffer bulk-service queue with disasters

A. Gómez-Corral ()

Mathematical Methods of Operations Research, 2005, vol. 61, issue 1, 57-84

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. Copyright Springer-Verlag 2005

Keywords: Bulk-service; Censored Markov chain; Clearing; Disasters; Finite-buffer queue; Markovian arrival process (MAP); Quasi-birth-and-death process (QBD) (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:spr:mathme:v:61:y:2005:i:1:p:57-84

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DOI: 10.1007/s001860400387

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