Abstract
An M / G / 1 retrial queue with a first-come-first-served (FCFS) orbit, general retrial time, two-phase service and server breakdown is investigated in this paper. Customers are allowed to balk and renege at particular times. Assume that the customers who find the server busy are queued in the orbit in accordance with an FCFS discipline. All customers demand the first “essential” service, whereas only some of them demand the second “optional” service, and the second service is multioptional. During the service, the server is subject to breakdown and repair. Assume that the retrial time, the service time, and the repair time of the server are all arbitrarily distributed. By using the supplementary variables method, the authors obtain the steady-state solutions for both queueing and reliability measures of interest.
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References
J. R. Artalejo, A classified bibliography of research on retrial queues: Progress in 1990–1999, Top, 1999, 7(2): 187–211.
J. R. Artalejo, Accessible bibliography on retrial queues, Mathematical Computer Modelling, 1999, 30(3–4): 1–6.
G. I. Falin and J. G. C. Templeton, Retrial Queues, Chapman & Hall, London, 1997.
K. Farahand, Single line queue with repeated demands, Qeueueing Systems, 1990, 6(1): 223–228.
A. Gómez-Corral, Stochastic analysis of single server retrial queue with the general retrial times, Naval Research Logistics, 1999, 46(5): 561–581.
J. Wang, Reliability analysis of M / G / 1 queues with general retrial times and server breakdowns, Progress in Natural Science, 2006, 16(5): 464–473.
K. C. Madan, An M / G / 1 queue with second optional service, Queueing Systems, 2000, 34(1–4): 37–46.
J. Medhi, A single server Poisson input queue with a second optional channel, Queueing Systems, 2002, 42(3): 239–242.
J. Wang, An M / G / 1 queue with second optional service and server breakdowns, Computers and Mathematics with Applications, 2004, 47(10–11): 1713–1723.
M. F. Neuts and M. F. Ramalhoto, A service model in which the server is required to search for customers, J. Appl. Probab., 1984, 21(1): 157–166.
J. Cao and K. Cheng, Analysis of M / G / 1 queueing system with repairable service station, Acta Math. Appl. Sinica, 1982, 5(2): 113–127.
J. Wang, J. Cao, and Q. Li, Reliability analysis of the retrial queue with server breakdowns and repairs, Queueing Systems, 2001, 38(4): 363–380.
D. H. Shi, A new method for calculation of the mean failure numbers of a repairable system during (0, t], Acta Math. Appl. Sinica, 1985, 8(1): 101–110.
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This research is supported by the National Natural Science Foundation of China under Grant No. 10871020.
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Wang, J., Li, J. A single server retrial queue with general retrial times and two-phase service. J Syst Sci Complex 22, 291–302 (2009). https://doi.org/10.1007/s11424-009-9164-8
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DOI: https://doi.org/10.1007/s11424-009-9164-8