Discretization of Markovian Queueing Systems

Recently it turned out, that discretizing the time in a markovian queueing model makes it possible to apply powerfull combinatorid methods which often yield surprisingly simple answeres to complicated questions. In this paper we show that the continuous time solution of a markovian queueing model may be obtain from the solution of its discrete time analogue by a simple limiting procedure. Under mild regularity conditions these limiting forms can be shown to be the unique solutions of Kolmogorov's backward differential equations. Furthermore some additional methodological results concerning taboo probabilities and first passage densities are obtained. In a final section some examples are given. (author's abstract)