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The busy period and the waiting time analysis of a MAP/M/c queue with finite retrial group

Artalejo, Jesús R. and Chakravarthy , S. R. and Lopez-Herrero, M. J. (2007) The busy period and the waiting time analysis of a MAP/M/c queue with finite retrial group. Stochastic Analysis and Applications, 25 (2). pp. 445-469. ISSN 0736-2994

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Abstract

We concentrate on the analysis of the busy period and the waiting time distribution of a multi-server retrial queue in which primary arrivals occur according to a Markovian arrival process (MAP). Since the study of a model with an infinite retrial group seems intractable, we deal with a system having a finite buffer for the retrial group. The system is analyzed in steady state by deriving expressions for (a) the Laplace–Stieltjes transforms of the busy period and the waiting time; (b) the probabiliy generating functions for the number of customers served during a busy period and the number of retrials made by a customer; and (c) various moments of quantites of interest. Some illustrative numerical examples are discussed.


Item Type:Article
Additional Information:

J. R. Artalejo and M. J. Lopez-Herrero thank the support received from the research project MTM2005-01248.

Uncontrolled Keywords:Busy period, Markovian arrival process, Multi-server queue, Retrials, Waiting time
Subjects:Sciences > Mathematics > Operations research
ID Code:15473
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Deposited On:04 Jun 2012 08:24
Last Modified:06 Feb 2014 10:25

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