The abstract Cauchy problem for the non-stationary bulk queue M(t)|M[k, B]|1

Abstract

We derived state probability equations describing the queue M(t)|M[k, B]|1 and formulated as an abstract Cauchy problem to investigate by means of the semi-group theory of bounded linear operators in functional analysis. For the abstract Cauchy problem of this queue, we determined the eigenfunctions of maximal operator and showed some properties of the Dirichlet operator.