On the Positive Recurrence of Finite Regenerative Stochastic Models-Reference-Cited by-同舟云学术

On the Positive Recurrence of Finite Regenerative Stochastic Models

Published:2023-11-24 Issue:23 Volume:11 Page:4754
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Morozov Evsey¹²³^ORCID,Rykov Vladimir⁴⁵^ORCID

Affiliation:

1. Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences, 185035 Petrozavodsk, Russia

2. Department of Applied Mathematics and Informatics, Yaroslav-the-Wise Novgorod State University, 173020 Veliky Novgorod, Russia

3. Department of Applied Mathematics and Cybernetics, Petrozavodsk State University, 185910 Petrozavodsk, Russia

4. Department of Applied Mathematics and Computer Modelling, National University of Oil and Gas (Gubkin University), 119991 Moscow, Russia

5. Department of Applied Probability and Informatics, Peoples’ Friendship University of Russia (RUDN University), 117198 Moscow, Russia

Abstract

We consider a general approach to establish the positive recurrence (stability) of regenerative stochastic systems. The approach is based on the renewal theory and a characterization of the remaining renewal time of the embedded renewal process generated by regeneration. We discuss how this analysis is simplified for some classes of the stochastic systems. The general approach is then illustrated by the stability analysis of a k-out-of-n repairable system containing n unreliable components with exponential lifetimes. Then we extend the stability analysis to the system with non-exponential lifetimes.

Funder

Ministry of Education and Science of the Russian Federation

RUDN University Strategic Academic Leadership Program

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/23/4754/pdf

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