A repairable queueing model with two-phase service, start-up times and retrial customers.

*(English)*Zbl 1178.90090Summary: A repairable queueing model with a two-phase service in succession, provided by a single server, is investigated. Customers arrive in a single ordinary queue and after the completion of the first phase service, either proceed to the second phase or join a retrial box from where they retry, after a random amount of time and independently of the other customers in orbit, to find a position for service in the second phase. Moreover, the server is subject to breakdowns and repairs in both phases, while a start-up time is needed in order to start serving a retrial customer. When the server, upon a service or a repair completion finds no customers waiting to be served, he departs for a single vacation of an arbitrarily distributed length. The arrival process is assumed to be Poisson and all service and repair times are arbitrarily distributed. For such a system the stability conditions and steady state analysis are investigated. Numerical results are finally obtained and used to investigate system performance.

##### MSC:

90B22 | Queues and service in operations research |

60K25 | Queueing theory (aspects of probability theory) |

##### Keywords:

Poisson arrivals; two-phase service; retrial queue; breakdowns; repairs; start-up time; vacation
PDF
BibTeX
XML
Cite

\textit{I. Dimitriou} and \textit{C. Langaris}, Comput. Oper. Res. 37, No. 7, 1181--1190 (2010; Zbl 1178.90090)

Full Text:
DOI

##### References:

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

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

[3] | Artalejo, J.R., A classified bibliography of research on retrial queues: progress in 1990-1999, Top, 7, 2, 187-211, (1999) · Zbl 1009.90001 |

[4] | Artalejo, J.R.; Choudhury, G., Steady state analysis of an M/G/1 queue with repeated attempts and two-phase service, Quality technology and quantitative management, 1, 189-199, (2004) |

[5] | Artalejo, J.R.; Gomez-Corral, A., Retrial queueing systems, a computational approach, (2008), Springer Berlin, Heidelberg · Zbl 1161.60033 |

[6] | Choi, D.I.; Kim, T., Analysis of a two phase queueing system with vacations and Bernoulli feedback, Stochastic analysis and applications, 21, 5, 1009-1019, (2003) · Zbl 1030.60082 |

[7] | Choudhury, G., Steady state analysis of a M/G/1 queue with linear retrial policy and two phase service under Bernoulli vacation schedule, Applied mathematical modelling, 32, 12, 2480-2489, (2008) · Zbl 1167.90444 |

[8] | Choudhury, G.; Deka, K., An M/G/1 retrial queueing system with two phases of service subject to the server breakdown and repair, Performance evaluation, 65, 10, 714-724, (2008) |

[9] | Choudhury, G.; Madan, K.C., A two stage batch arrival queueing system with a modified Bernoulli schedule vacation under N-policy, Mathematical and computer modelling, 42, 71-85, (2005) · Zbl 1090.90037 |

[10] | Cinlar, E., Introduction to stochastic processes, (1975), Prentice-Hall Englewood Cliffs, NJ · Zbl 0341.60019 |

[11] | Dimitriou, I.; Langaris, C., Analysis of a retrial queue with two-phase service and server vacations, Queueing systems, 60, 1-2, 111-129, (2008) · Zbl 1158.60377 |

[12] | Doshi, B.T., Analysis of a two phase queueing system with general service times, Operation research letters, 10, 265-272, (1991) · Zbl 0738.60091 |

[13] | Falin, G.I.; Templeton, J.G.C., Retrial queues, (1997), Chapman & Hall London · Zbl 0944.60005 |

[14] | Katayama, T.; Kobayashi, K., Sojourn time analysis of a queueing system with two phase service and server vacations, Naval research logistics, 54, 1, 59-65, (2006) · Zbl 1114.60075 |

[15] | Krishna, C.M.; Lee, Y.H., A study of a two phase service, Operation research letters, 9, 91-97, (1990) · Zbl 0687.68014 |

[16] | Kulkarni, V.G.; Choi, B.D., Retrial queue with server subject to breakdowns and repairs, Queueing systems, 7, 2, 191-208, (1990) · Zbl 0727.60110 |

[17] | Kulkarni, V.G.; Liang, H.M., Retrial queues revisited, (), 19-34 · Zbl 0871.60074 |

[18] | Krishna Kumar, B.; Vijayakumar, A.; Arivudainambi, D., An M/G/1 retrial queueing system with two phase service and preemptive resume, Annals of operation research, 113, 61-79, (2002) · Zbl 1013.90032 |

[19] | Krishna Kumar, B.; Arivudainambi, D., The M/G/1 retrial queue with Bernoulli schedules and general retrial times, Computers and mathematics with applications, 43, 15-30, (2002) · Zbl 1008.90010 |

[20] | Krishna Kumar, B.; Pavai Madheswari, S., \(\operatorname{M}^{\operatorname{X}} / \operatorname{G} / 1\) retrial queue with multiple vacations and starting failures, Opsearch, 40, 2, 115-137, (2003) · Zbl 1246.90040 |

[21] | Langaris, C.; Katsaros, A., Time depended analysis of a queue with batch arrivals and N levels of non-preemptive priority, Queueing systems, 19, 269-288, (1995) · Zbl 0833.60092 |

[22] | Pakes, A.G., Some conditions of ergodicity and recurrence of Markov chains, Operation research, 17, 1058-1061, (1969) · Zbl 0183.46902 |

[23] | Takacs, L., Introduction to the theory of queues, (1962), Oxford University Press New York · Zbl 0118.13503 |

[24] | Wang, J., An M/G/1 queue with second optional service and service breakdowns, Computers and mathematics with applications, 47, 1713-1723, (2004) · Zbl 1061.60102 |

[25] | Wang, J.; Cao, J.; Li, J., Reliability analysis of the retrial queue with server breakdowns and repairs, Queueing systems, 38, 363-380, (2001) · Zbl 1028.90014 |

[26] | Wang, J.; Li, J., A repairable M/G/1 retrial queue with bernouli vacation and two-phase service, Quality technology and quantitative management, 5, 2, 179-192, (2008) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.