  In queuing theory and related problems, it is very important to know the
numerical characteristics of an investigated system - both in stationary and
non-stationary modes. In some cases, such characteristics can be calculated,
but this is possible for a limited number of real models. However, in most
cases, it is possible to calculate or estimate the stationary values of the
characteristics of the studied models. We can use linear Markov processes to
model how the overwhelming majority of queuing systems (QS), reliability
systems, and queuing networks (QNS) operate; the processes are regenerative in
many cases. In the case when the regeneration period of the Markov process has
a finite average value, this process is ergodic. An adjunction method can be
used to obtain strict upper bounds for the convergence rate of the Markov
process (MP) distribution to a stationary distribution (naturally, in cases
where the MP under consideration is ergodic). This method can be applied to
analyze queuing systems, queuing networks, and reliability systems. The purpose
of this paper is to show how to use the adjunction method to obtain strict
upper bounds for the MP distribution convergence rate as the regenerating
Markov process converges to a stationary distribution if the Markov process is
ergodic. This method can be applied to QS, QNS, and reliability systems. The
article is a summary of the plenary report of the authors at the VIII
International Youth Scientific Conference "Mathematical and software support of
information, technical, and economic systems"; (Tomsk, May 26-30, 2021). In
Russian.
