### Impacto

Artalejo, Jesús R. and Economou, A. and Lopez-Herrero, M. J.
(2007)
*Algorithmic analysis of the maximum queue length in a busy period for the M/M/c retrial queue.*
INFORMS Journal on Computing , 19
(1).
pp. 121-126.
ISSN 1091-9856

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## Abstract

This paper deals with the maximum number of customers in orbit (and in the system) during a busy period for the M/M/c retrial queue. Determining the distribution for the maximum number of customers in orbit is reduced to computation of certain absorption probabilities. By reducing to the single-server case we arrive at a closed analytic formula. For the multi-server case we develop an efficient algorithmic procedure for computation of this distribution by exploiting the special block-tridiagonal structure of the system. Numerical results illustrate the efficiency of the method and reveal interesting facts concerning the behavior of the M/M/c retrial queue.

Item Type: | Article |
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Uncontrolled Keywords: | M/M/c retrial queue; maximum orbit size; busy period; continuous-time Markov chain; tridiagonal; linear system; Extreme values |

Subjects: | Sciences > Mathematics > Operations research |

ID Code: | 15270 |

References: | Artalejo, J. R. 1999a. Accessible bibliography on retrial queues. Math. Comput. Model. 30 1-6. Artalejo, J. R. 1999b. A classified bibliography of research on retrial queues: Progress in 1990-1999, Top 7 187-211. Artalejo, J. R., G. L Falin, 2002, Standard and retrial queueing systems: A comparative analysis, Revista Matematica Complutense 15 101-129. Choo, Q. H., B. Conolly, 1979, New results in the theory of repeated orders queueing systems, J. Appl. Probab. 16 631-640. Chung, K. L. 1967. Markov Chains with Stationary Transition Probabilities, 2nd ed. Springer-Verlag, New York. Ciarlet, P, G. 1989, Introduction to Numerical Linear Algebra and Optimization. Cambridge University Press, Cambridge, UK. Cooper, R. B. 1981, Introduction to Queueing Theory, 2nd ed, Edward Arnold, London, UK. Falin, G. I., J. G. C. Templeton, 1997, Retrial Queues. Chapman and Hall, London, UK. Gomez-Corral, A. 2001. On extreme values of orbit lengths in M/G/1 queues with constant retrial rate, OR Spectrum 23 395^09. Lopez-Herrero, M. J. 2002, Distribution of the number of customers served in an M/G/1 retrial queue, J. Appl. Probab. 39 407-412. Lopez-Herrero, M. J., M. F. Neuts, 2002, The distribution of the maximum orbit size of an M/G/1 retrial queue during the busy period. J, R, Artalejo, A. Krishnamoorthy, eds. Advances in Stochastic Modelling. Notable Publications Inc, Chennai, India, 219-231. Serfozo, R. R 1988, Extreme values of birth and death processes and queues. Stochastic Process. Appl. 27 291-306. |

Deposited On: | 18 May 2012 09:06 |

Last Modified: | 06 Feb 2014 10:20 |

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