On the M/G/1 retrial queue subjected to breakdowns
RAIRO - Operations Research - Recherche Opérationnelle, Tome 36 (2002) no. 4, pp. 299-310.

Retrial queueing systems are characterized by the requirement that customers finding the service area busy must join the retrial group and reapply for service at random intervals. This paper deals with the M/G/1 retrial queue subjected to breakdowns. We use its stochastic decomposition property to approximate the model performance in the case of general retrial times.

DOI : https://doi.org/10.1051/ro:2003007
Classification : 60K25,  90B22,  68M20
Mots clés : retrial queue, breakdown, stochastic decomposition, approximation
@article{RO_2002__36_4_299_0,
author = {Djellab, Natalia V.},
title = {On the M/G/1 retrial queue subjected to breakdowns},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {299--310},
publisher = {EDP-Sciences},
volume = {36},
number = {4},
year = {2002},
doi = {10.1051/ro:2003007},
zbl = {1037.90005},
mrnumber = {1997927},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro:2003007/}
}
Djellab, Natalia V. On the M/G/1 retrial queue subjected to breakdowns. RAIRO - Operations Research - Recherche Opérationnelle, Tome 36 (2002) no. 4, pp. 299-310. doi : 10.1051/ro:2003007. http://www.numdam.org/articles/10.1051/ro:2003007/

[1] A. Aissani, A retrial queue with redundancy and unreliable server. Queueing Systems 17 (1994) 431-449. | MR 1298601 | Zbl 0817.60093

[2] A. Aissani and J.R. Artalejo, On the single server retrial queue subject to breakdowns. Queueing Systems 30 (1998) 309-321. | MR 1672139 | Zbl 0918.90073

[3] V.V. Anisimov, Averaging methods for transient regimes in overloading retrial queueing system. Math. Comput. Modelling 30 (1999) 65-78. | MR 1722592 | Zbl 1042.60528

[4] J.R. Artalejo, New results in retrial queueing systems with breakdown of the servers. Statist. Neerlandica 48 (1994) 23-36. | MR 1267054 | Zbl 0829.60087

[5] J.R. Artalejo, Retrial queues with a finite number of sources. A Korean Math. Soc. 35 (1998) 503-525. | MR 1660793 | Zbl 0930.60079

[6] J.R. Artalejo and A. Gomez-Coral, Unreliable retrial queues due to service interruptions arising from facsimile networks. Belg. J. Oper. Res. Statist. Comput. Sci. 38 (1998) 31-41. | Zbl 1010.90503

[7] G.I. Falin, A survey of retrial queues. Queueing Systems 7 (1990) 127-168. | MR 1079714 | Zbl 0709.60097

[8] G.I. Falin and J.G.C. Templeton, Retrial queues. Chapman and Hall (1997). | Zbl 0944.60005

[9] E. Gelenbe, On the optimum checkpoint interval. J. ACM 26 (1979) 259-270. | MR 528031 | Zbl 0395.68024

[10] E. Gelenbe and M. Hernandez, Optimum checkpoints with age dependent failures. Acta Inform. 27 (1990) 519-531. | MR 1060147 | Zbl 0673.68007

[11] E. Gelenbe and R. Iasnogorodski, A queue with server of walking type. Ann. Inst. H. Poincaré (B) 16 (1980) 63-73. | EuDML 77137 | Numdam | MR 575177 | Zbl 0433.60086

[12] A. Krishnamoorthy and P.V. Ushakumari, Reliability of a $k$-out-of-$n$ system with repair and retrial of failed units. Top 7 (1999) 293-304. | MR 1737650 | Zbl 0951.60087

[13] V.G. Kulkarni and B.D. Choi, Retrial queue with server subject to breakdowns and repairs. Queueing Systems 7 (1990) 191-208. | MR 1079715 | Zbl 0727.60110

[14] J.G.C. Templeton, Retrial queues. Top 7 (1999) 351-353. | Zbl 0949.90022

[15] T. Yang et al., An approximation method for the M/G/1 retrial queue with general retrial times. Eur. J. Oper. Res. 76 (1994) 552-562. | Zbl 0802.60089

[16] T. Yang and J.G.C. Templeton, A survey on retrial queues. Queueing Systems 2 (1987) 201-233. | MR 925180 | Zbl 0658.60124