Artalejo, Jesús R. and Economou, A. and Gómez-Corral, Antonio
(2008)
*Algorithmic analysis of the Geo/Geo/c retrial queue.*
European journal of operational research, 189
(3).
pp. 1042-1056.
ISSN 0377-2217

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Official URL: http://www.sciencedirect.com/science/article/pii/S037722170700519X

## Abstract

In this paper, we consider a discrete-time queue of Geo/Geo/c type with geometric repeated attempts. It is known that its continuous counterpart, namely the M/M/c queue with exponential retrials, is analytically intractable due to the spatial heterogeneity of the underlying Markov chain, caused from the retrial feature. In discrete-time, the occurrence of multiple events at each slot increases the complexity of the model and raises further computational difficulties. We propose several algorithmic procedures for the efficient computation of the main performance measures of this system. More specifically, we investigate the stationary distribution of the system state, the busy period and the waiting time. Several numerical examples illustrate the analysis.

Item Type: | Article |
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Uncontrolled Keywords: | Discrete-time; Size distribution; Queueing; Geo/Geo/c queue; Retrials; Stationary Distribution; Busy period; Waiting time; Matrix-analytic methods |

Subjects: | Sciences > Mathematics > Operations research |

ID Code: | 15225 |

References: | J.R. Artalejo. Accessible bibliography on retrial queues. Mathematical and Computer Modelling, 30 (1999), pp. 1–6 J.R. Artalejo, A. Gómez-Corral. Waiting time in the M/M/c queue with finite retrial group. Bulletin of Kerala Mathematics Association, 2(2005), pp. 1–17 Artalejo, J.R., Lopez-Herrero, M.J., 2005. A discrete-time multiserver retrial queue: Performance analysis and simulation. In: Ermakov, S.M., Melas, V.B., Pepelyshev, A.N. (Eds.), Proceedings of the 5th Workshop on Simulation, St. Petersburg, pp. 85–90. J.R. Artalejo, M. Pozo. Numerical calculation of the stationary distribution of the main multiserver retrial queue. Annals of Operations Research, 116 (2002), pp. 41–56 J.R. Artalejo, I. Atencia, P. Moreno. A discrete-time Geo[X]/G/1 retrial queue with control of admission. Applied Mathematical Modelling, 29 (2005), pp. 1100–1120. J.R. Artalejo, A. Economou, M.J. Lopez-Herrero. Algorithmic approximations for the busy period distribution of the M/M/c retrial queue. European Journal of Operational Research, 176 (2007), pp. 1687–1702 I. Atencia, P. Moreno. A discrete-time Geo/G/1 retrial queue with general retrial times. Queueing Systems, 48 (2004), pp. 5–21 I. Atencia, P. Moreno. A discrete-time Geo/G/1 retrial queue with the server subject to starting failures. Annals of Operations Research, 141 (2006), pp. 85–107 H. Bruneel, B.G. Kim. Discrete-Time Models for Communications Systems including ATM. Kluwer Academic Publishers, Boston (1993) M.L. Chaudhry. On numerical computations of some discrete-time queues. W.K. Grassmann (Ed.),Computational Probability, Kluwer, Boston (2000) B.D. Choi, J.W. Kim. Discrete-time Geo1, Geo2/G/1 retrial queueing system with two types of calls. Computers and Mathematics with Applications, 33 (1997), pp. 79–88 G.I. Falin, J.G.C. Templeton Retrial Queues, Monographs on Statistics and Applied Probability, vol. 75Chapman and Hall, London (1997) A. Gómez-Corral. A bibliographical guide to the analysis of retrial queues through matrix analytic techniques. Annals of Operations Research, 141 (2006), pp. 163–191 J.J. Hunter. Mathematical Techniques of Applied Probability, Discrete Time Models: Basic Theory, vol. 1 Academic Press, New York (1983) G. Latouche, V. Ramaswami. Introduction to Matrix Analytic Methods in Stochastic Modeling, ASA-SIAM Series on Statistics and Applied Probability. SIAM, Philadelphia (1999) H. Li, T. Yang. Geo/G/1 discrete time retrial queue with Bernoulli schedule. European Journal of Operational Research, 111 (1998), pp. 629–649 H. Li, T. Yang. Steady-state queue size distribution of discrete-time PH/Geo/1 retrial queues. Mathematical and Computer Modelling, 30 (1999), pp. 51–63 M.F. Neuts. Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. The Johns Hopkins University Press, Baltimore, Maryland (1981) M.F. Neuts, B.M. Rao. Numerical investigation of a multiserver retrial model. Queueing Systems, 7 (1990), pp. 169–190 W.J. Stewart. Introduction to the Numerical Solution of Markov Chains. Princeton University Press, New Jersey (1994) H. Takagi. Queueing Analysis: A Foundation of Performance Evaluation, Discrete-Time Systems, vol. 3North-Holland, Amsterdam (1993) M. Takahashi, H. Osawa, T. Fujisawa Geo[X]/G/1 retrial queue with non-preemptive priority. Asia-Pacific Journal of Operational Research, 16 (1999), pp. 215–234 M.E. Woodward. Communication and Computer Networks: Modelling with Discrete-Time Queues. IEEE Computer Society Press, Los Alamitos (1994) T. Yang, H. Li. On the steady-state queue size distribution of the discrete-time Geo/G/1 queue with repeated attempts.Queueing Systems, 21 (1995), pp. 199–215 |

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Last Modified: | 06 Feb 2014 10:19 |

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