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The Busy Period and the Waiting Time Analysis of a MAP/M/c Queue with Finite Retrial Group |
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| Authors: | J R Artalejo S R Chakravarthy M J Lopez-Herrero |
| Institution: | 1. Department of Statistics and Operations Research , Faculty of Mathematics, Complutense University of Madrid , Madrid, Spain jesus_artalejo@mat.ucm.es;3. Department of Industrial and Manufacturing Engineering , Kettering University , Flint, Michigan, USA;4. School of Statistics , Complutense University of Madrid , Madrid, Spain |
| Abstract: | 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. |
| Keywords: | Busy period Markovian arrival process Multi-server queue Retrials Waiting time |