Gray, William J.; Wang, Pu Patrick; Scott, MecKinley A vacation queueing model with service breakdowns. (English) Zbl 0966.90024 Appl. Math. Modelling 24, No. 5-6, 391-400 (2000). Summary: The authors analyze a multiple-vacation queueing model, where the service station is subject to breakdown while in operation. Service resumes immediately after a repair process, and a vacation starts at the end of each busy period. Arrivals follow a Poisson process with rates depending upon the system state, namely, vacation, service, or breakdown state. The repair times, times to breakdown following a repair or vacation, uninterrupted service times, and length of each vacation follow exponential distributions. Some results are also obtained when vacation, service, and repair times follow phase-type distributions. Cited in 11 Documents MSC: 90B22 Queues and service in operations research 60K25 Queueing theory (aspects of probability theory) 60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.) Keywords:queueing model; Poisson process PDF BibTeX XML Cite \textit{W. J. Gray} et al., Appl. Math. Modelling 24, No. 5--6, 391--400 (2000; Zbl 0966.90024) Full Text: DOI References: [1] Avi-Itzhak, B.; Naor, P., On a problem of preemptive priority queueing, Oper. Res., 9, 664-672 (1961) · Zbl 0102.14203 [2] Mitrany, I. L.; Avi-Itzhak, B., A many-server queue with service interruptions, Oper. Res., 16, 628-638 (1968) · Zbl 0239.60094 [3] Ibe, O. C., Two queues with alternating service and server breakdowns, Queueing Syst., 7, 7, 253-268 (1990) · Zbl 0712.60101 [4] Doshi, B. T., Queueing systems with vacations – a survey, Queueing Syst., 1, 29-66 (1986) · Zbl 0655.60089 [6] Takagi, H., M/G/1/N queues with server vacations and exhaustive service, Oper. Res., 42, 926-939 (1994) · Zbl 0829.90063 [7] Machihara, F., A pre-emptive priority queue as a model with server vacations, J. Oper. Res., 39, 118-131 (1996) · Zbl 0849.90063 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.