**6. Conclusions**

As can be seen from the last three sections, in order to obtain the ergodicity bounds the values of *λ*(*t*) and *μ*(*t*) for each *t* may not be needed. Instead it may be sufficient to know only the time-average intensities *λ* = <sup>1</sup> *<sup>t</sup>* lim*t*→<sup>∞</sup> *t* <sup>0</sup> *<sup>λ</sup>*(*u*)*du* and *<sup>μ</sup>* <sup>=</sup> <sup>1</sup> *<sup>t</sup>* lim*t*→<sup>∞</sup> *t* <sup>0</sup> *μ*(*u*)*du*. For periodic intensities with the smallest common multiple of the periods *T*, the values *λ* and *μ* are exactly the average arrival and service intensity over one period.

The classes of CTMC to which the logarithmic norm method is applicable and gives meaningful results is not limited to those considered in this paper, (necessary and sufficient conditions for a CTMC "to fit" the logarithmic norm method are not known). For example, the same reasoning, which has led to the Theorem 1, can be used to obtain the upper bounds for the rate of convergence of the *Mt*/*Mt*/*S*/∞ system with any (finite) number of servers. Moreover, whenever *X*(*t*) is weakly ergodic, the analysis can be carried on beyond what is stated in the *Theorem 1*. For example, one can obtain the perturbation bounds (see e.g., [40]) and study different state space truncation options: one-sided or two sided (see e.g., [29,41,42]).

**Author Contributions:** Investigation, A.Z., R.R., Y.S., I.K. and V.K. All authors contributed equally to this work. All authors have read and agreed to the published version of the manuscript.

**Funding:** The research was supported by the Ministry of Science and Higher Education of the Russian Federation, project No. 075-15-2020-799.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data sharing is not applicable to this article.

**Conflicts of Interest:** The author declares no conflict of interest.
