The distribution of the first passage time for the markov processes of<i>GI/M/L</i>Type

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.