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The well-posedness of an \(M/G/1\) queue with second optional service and server breakdown. (English) Zbl 1186.90040

Summary: The solution of an \(M/G/1\) queue with second optional service and server breakdown is investigated. By using the method of functional analysis, especially, the linear operator theory and the \(C_{0}\) semigroup theory on Banach space, we prove the well-posedness of the system, and show the existence of a positive solution.

MSC:

90B22 Queues and service in operations research
34G10 Linear differential equations in abstract spaces
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