On the Positive Recurrence of Finite Regenerative Stochastic Models

Evsey Morozov and Vladimir Rykov ()
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Evsey Morozov: Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences, 185035 Petrozavodsk, Russia
Vladimir Rykov: Department of Applied Mathematics and Computer Modelling, National University of Oil and Gas (Gubkin University), 119991 Moscow, Russia

Mathematics, 2023, vol. 11, issue 23, 1-11

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.

Keywords: regenerative stochastic system; k -out-of- n repairable system; stability; unreliable component (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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