### Impacto

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

PDF
Restringido a Repository staff only hasta 31 December 2020. 301kB |

Official URL: http://www.tandfonline.com/doi/pdf/10.1080/07362990601139651

## 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 |

References: | Falin, G.I., and Templeton, J.G.C. 1997. Retrial Queues. Chapman and Hall, London. Kosten, L. 1973. Stochastic Theory of Service Systems. International Series of Monographs in Pure and Applied Mathematics. Vol. 103, Pergamon Press, Oxford. Neuts, M.F., and Rao, B.M. 1990. Numerical investigation of a multiserver retrial model. Queueing Systems 7:169–190. Choi, B.D., and Chang, Y. 1999. MAP1, MAP2/M/c with retrial queue with the retrial group of finite capacity and geometric loss. Mathematical and Computer Modelling 30:99–113. Diamond, J.E., and Alfa, A.S. 1999. Matrix-analytic methods for a multiserver retrial queue with buffer. Top 7:249–266. Breuer, L., Dudin, A.N., and Klimenok, V.I. 2002. A retrial BMAP/PH/N system. Queueing Systems 40:433–457. Chakravarthy, S.R., Krishnamoorthy, A., and Joshua, V.C. 2006. Analysis of a multi-server queue with search of customers from the orbit. Performance Evaluation 63:776–798. Gomez-Corral, A. 2006. A bibliographical guide to the analysis of retrial queues through matrix analytic techniques. Annals of Operations Research 141:163–191. Artalejo, J.R., Economou, A., and Lopez-Herrero, M.J. 2005. Algorithmic analysis for the number of customers served in a busy period of the M/M/c retrial queue. In Proceedings of the National Conference on Mathematical and Computational Models, December 15–16, Coimbatore, India. Arumugnathan, R., and Nadarajan, R. (Eds.), Allied Publishers, New Delhi, 3–15. Artalejo, J.R., and Gomez-Corral, A. 2005. Waiting time in the M/M/c queue with finite retrial group. Bulletin of Kerala Mathematics Association 2:1–17. Artalejo, J.R., Economou, A., and Lopez-Herrero, M.J. 2007. Algorithmic approximations for the busy period of the M/M/c retrial queue. European Journal of Operational Research 176:1687–1702. Artalejo, J.R., and Lopez-Herrero, M.J. 2007. On the distribution of the number of retrials. Applied Mathematical Modelling 31:478–489. Artalejo, J.R., and Chakravarthy, S.R. 2006. Computational analysis of the maximal queue length in the MAP/M/c retrial queue. Applied Mathematics and Computation 183:1399–1409. Marcus, M., and Minc, H. 1964. A Survey of Matrix Theory and Matrix Inequalities. Allyn and Bacon, Boston, MA. Lucantoni, D.M. 1991. New results on the single server queue with a batch Markovian arrival process. Stochastic Models 7:1–46. Downloaded by [Biblioteca Universidad Complutense de Madrid] at 02:17 14 March 2012 Neuts, M.F. 1992. Models based on the Markovian arrival process. IEICE Transactions on Communications E75B:1255–1265. Chakravarthy, S.R. 2001. The batch Markovian arrival process: A review and future work. In Advances in Probability Theory and Stochastic Processes. Krishnamoorthy, A., et al. (Eds.), Notable Publications Inc., New Jersey, 21–39. |

Deposited On: | 04 Jun 2012 08:24 |

Last Modified: | 06 Feb 2014 10:25 |

Repository Staff Only: item control page