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On a finite-buffer bulk-service queue with disasters

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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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
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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