Gómez Corral, Antonio
(1999)
*Stochastic analysis of a single server retrial queue with general retrial times.*
Naval Research Logistics (NRL), 46
(5).
pp. 561-581.
ISSN 0894-069X

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Official URL: http://onlinelibrary.wiley.com/doi/10.1002/(SICI)1520-6750(199908)46:5%3C561::AID-NAV7%3E3.0.CO;2-G/pdf

## Abstract

Retrial queueing systems are widely used in teletraffic theory and computer and communication networks. Although there has been a rapid growth in the literature on retrial queueing systems, the research on retrial queues with nonexponential retrial times is very limited. This paper is concerned with the analytical treatment of an M/G/1 retrial queue with general retrial times. Our queueing model is different from most single server retrial queueing models in several respectives. First, customers who find the server busy are queued in the orbit in accordance with an FCFS (first-come-first-served) discipline and only the customer at the head of the queue is allowed for access to the server. Besides, a retrial time begins (if applicable) only when the server completes a service rather upon a sen ice attempt failure. We carry out an extensive analysis of the queue, including a necessary and sufficient condition for the system to be stable, the steady state distribution of the server state and the orbit length, the waiting time distribution, the busy period, and other related quantities. Finally, we study the joint distribution of the server state and the orbit length in non-stationary regime.

Item Type: | Article |
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Uncontrolled Keywords: | retrial queueing systems; single server retrial queue; nonexponential distribution; waiting time; busy period; steady state distribution; orbit length |

Subjects: | Sciences > Mathematics > Stochastic processes |

ID Code: | 15875 |

References: | J. Abate and W. Whitt, The Fourier-series method for inverting transforms of probability distributions,Queueing Syst 10 (1992), 5–88. J.R. Artalejo and G.I. Falin, On the orbit characteristics of the M/G/1 retrial queue, Nav Res Logistics 43 (1996), 1147–1161. J.R. Artalejo and A. Go´mez-Corral, Steady state solution of a single-server queue with linear request repeated, J Appl Probab 34 (1997), 223–233. B.D. Choi, K.K. Park, and C.E.M. Pearce, An M/M/1 retrial queue with control policy and general retrial times, Queueing Syst 14 (1993), 275–292. G.L. Choudhury, D.M. Lucantoni, and W. Whitt, Multidimensional transform inversion with applications to the transient M/G/1 queue, Ann Appl Probab 4 (1994), 719–740. R.B. Cooper, Introduction to queueing theory, Edward Arnold, 1981. G.I. Falin, Single-line repeated orders queueing systems, Optimization 17 (1986), 649–677. G.I. Falin, A survey of retrial queues, Queueing Syst 7 (1990), 127–168. G.I. Falin and J.G.C. Templeton, Retrial queues, Chapman and Hall, New York, 1997. G. Fayolle, “A simple telephone exchange with delayed feedbacks,” Teletraffic analysis and computer performance evaluation, O.J. Boxma, J.W. Cohen, and H.C. Tijms (Editors), Elsevier, Amsterdam,1986, pp. 245–253. S.W. Fuhrmann and R.B. Cooper, Stochastic decomposition in the M/G/1 queue with generalized vacations, Oper Res 33 (1985), 1117–1129. V.A. Kapyrin, A study of the stationary characteristics of a queueing system with recurring demands,Cybernetics 13 (1977), 584–590. J. Keilson, J. Cozzolino, and H. Young, A service system with unfilled requests repeated, Oper Res 16 (1986), 1126–1137. L. Kleinrock, Queueing systems, vol. I: Theory, Wiley-Interscience, New York, 1975. V.G. Kulkarni and H.M. Liang, “Retrial queues revisited,” Frontiers in queueing. Models and applications in science and engineering, J.H. Dshalalow (Editor), CRC Press, Boca Raton, FL, 1997,pp. 19–34. M. Martin and J.R. Artalejo, Analysis of an M/G/1 queue with two types of impatient units, Adv Appl Probab 27 (1995), 840–861. M.F. Neuts and M.F. Ramalhoto, A service model in which the server is required to search for customers, J Appl Probab 21 (1984), 157–166. B. Pourbabai, A note on a D/G/K loss system with retrials, J Appl Probab 27 (1990), 385–392. L.I. Sennot, P.A. Humblet, and R.L. Tweedie, Mean drifts and the non-ergodicity of Markov chains,Oper Res 31 (1983), 783–789. L. Taka´cs, Introduction to the theory of queues, Oxford University Press, Oxford, 1962. T. Yang and J.G.C. Templeton, A survey on retrial queues, Queueing Syst 2 (1987), 201–233. T. Yang, M.J.M. Posner, J.G.C. Templeton, and H. Li, An approximation method for the M/G/1 retrial queue with general retrial times, Eur J Oper Res 76 (1994), 552–562. |

Deposited On: | 10 Jul 2012 08:15 |

Last Modified: | 06 Feb 2014 10:33 |

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