The well-posedness of an M/G/1M/G/1 queue with second optional service and server breakdown

In this paper, the solution of an M/G/1M/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 C0C0 semigroup theory on Banach space, we prove the well-posedness of the system, and show the existence of a positive solution.