Abstract
This paper is aimed at investigating the transient losses in the M/M/1/1 Erlang loss system. We evaluate the explicit form of the probability distribution of the number of losses in the time interval [0, t) and provide two alternative representations: one based on the iterated derivatives of hyperbolic sinus and cosine and the other on the spherical modified Bessel function of the second kind. The mathematical structures of the transient loss rate and of the transient probability of losing all customers are described and several analytical properties are derived.
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Ferrante, P. Detailing Losses in the M/M/1/1 Transient Loss System. Acta Math. Appl. Sin. Engl. Ser. 34, 373–385 (2018). https://doi.org/10.1007/s10255-018-0747-9
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DOI: https://doi.org/10.1007/s10255-018-0747-9