The distribution of the first passage time for the markov processes ofGI/M/LType

Abstract

Using truncation of the Markov chain, we obtain an explicit expression for the Laplace-Stieltjes transform of the first passage time to level 0 for Markov processes of GI/M/l type. The result can be used to study the busy periods of some queueing systems and, in particular, to find explicit first moment expressions.

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