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

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