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A repairable queueing model with two-phase service, start-up times and retrial customers. (English) Zbl 1178.90090
Summary: 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)
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[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)
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