English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In queuing theory and related problems, it is very important to know thenumerical characteristics of an investigated system - both in stationary andnon-stationary modes. In some cases, such characteristics can be calculated,but this is possible for a limited number of real models. However, in mostcases, it is possible to calculate or estimate the stationary values of thecharacteristics of the studied models. We can use linear Markov processes tomodel how the overwhelming majority of queuing systems (QS), reliabilitysystems, and queuing networks (QNS) operate; the processes are regenerative inmany cases. In the case when the regeneration period of the Markov process hasa finite average value, this process is ergodic. An adjunction method can beused to obtain strict upper bounds for the convergence rate of the Markovprocess (MP) distribution to a stationary distribution (naturally, in caseswhere the MP under consideration is ergodic). This method can be applied toanalyze queuing systems, queuing networks, and reliability systems. The purposeof this paper is to show how to use the adjunction method to obtain strictupper bounds for the MP distribution convergence rate as the regeneratingMarkov process converges to a stationary distribution if the Markov process isergodic. This method can be applied to QS, QNS, and reliability systems. Thearticle is a summary of the plenary report of the authors at the VIIIInternational Youth Scientific Conference "Mathematical and software support ofinformation, technical, and economic systems"; (Tomsk, May 26-30, 2021). InRussian.

On an estimate of the rate of convergence for regenerative processes in queuing theory and related problems