2019
Том 71
№ 1

# Stationary Mode and Binomial Moments for Networks of the Type $[SM|GI|∞]^r$

Lebedev E. O.

Abstract

By using methods of the Markov renewal theory, we find conditions for the existence of a stationary mode for multichannel networks with semi-Markov input stream. As a tool of stationary distribution analysis, we introduce multivariate binomial moments and investigate their asymptotic properties. For a multichannel queuing system with periodic input stream, we construct the generating function of the stationary distribution in explicit form in terms of the parameters of the system under consideration.

English version (Springer): Ukrainian Mathematical Journal 54 (2002), no. 10, pp 1656–1668.

Citation Example: Lebedev E. O. Stationary Mode and Binomial Moments for Networks of the Type $[SM|GI|∞]^r$ // Ukr. Mat. Zh. - 2002. - 54, № 10. - pp. 1371-1380.

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