Ergodicity Bounds and Limiting Characteristics for a Modified Prendiville Model

Ilya Usov, Yacov Satin, Alexander Zeifman () and Victor Korolev
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Ilya Usov: Department of Applied Mathematics, Vologda State University, 15 Lenina Str., 160000 Vologda, Russia
Yacov Satin: Department of Applied Mathematics, Vologda State University, 15 Lenina Str., 160000 Vologda, Russia
Alexander Zeifman: Department of Applied Mathematics, Vologda State University, 15 Lenina Str., 160000 Vologda, Russia
Victor Korolev: Federal Research Center “Computer Sciences and Control” of the Russian Academy of Sciences, 44-2 Vavilova Str., 119333 Moscow, Russia

Mathematics, 2022, vol. 10, issue 23, 1-14

Abstract: We consider the time-inhomogeneous Prendiville model with failures and repairs. The property of weak ergodicity is considered, and estimates of the rate of convergence for the main probabilistic characteristics of the model are obtained. Several examples are considered showing how such estimates are obtained and how the limiting characteristics themselves are constructed.

Keywords: bounds on the rate of convergence; C-matrix method; limiting regime; logarithmic norm method; perturbation bounds; Prendiville Model; queuing system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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