A vacation queueing model with service breakdowns. (English) Zbl 0966.90024

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.


90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
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