Well-Posedness of the Repairable M/G/1 Queueing System with Two Kinds of Breakdown States
We study the well-posedness of the repairable M/G/1 queueing system with two kinds of breakdown states by utilizing the linear operator semigroup theory.In this paper,it is assumed that the life termination of the the service station satisfy exponential distributions,the repair times and the vacation time of the repairman satisfy general continuous distribu-tions.By normalizing the system described by differential equations,we convert the system equations into an abstract Cauchy problem in the Banach space through introducing a state space,main operators and their domains.With the help of the Hille-Yosida theorem,Phillips theorem and Fattorini theorem in functional analysis,we prove that the parallel system has a umnique and positive time-dependent solution which satisfies probability condition.
the repairable M/G/1 queueing system with two kinds of breakdown statesdispersive operatorCo-semigroupquasi-compact operatortime-dependent solution
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