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The paper explores the Kullback-Leibler divergence formalism (KLDF) applied to stable queue manifold. More potentially, both service time probability and cumulative functions, which make KLDF exact, are obtained. The credibility of KLDF is justified through consistency axioms. In other words, the current work provides a cutting-edge unification of information theory, combined with applied probability and divergence theory. Accordingly, this paper adds new knowledge, which extends a novel contemporary information theoretic link to some other different mathematical disciplines. The significance of Kullback-Leibler divergence (KLD) is highlighted through references to some potential applications of KLD to biometry. [ABSTRACT FROM AUTHOR]