Properties of highly reliable systems with protection in the case of Poisson renewal process
Authors:
O. O. Kushnir and V. P. Kushnir
Translated by:
N. N. Semenov
Journal:
Theor. Probability and Math. Statist. 96 (2018), 127-132
MSC (2010):
Primary 60K20; Secondary 90B25
DOI:
https://doi.org/10.1090/tpms/1038
Published electronically:
October 5, 2018
MathSciNet review:
3666876
Full-text PDF
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Additional Information
Abstract: Some upper bounds for characteristics of reliability of a highly reliable system with protection are given for the case where the renewal process in the system is Poissonian.
References
- N. V. Kartashov, Inequalities in the Rényi theorem, Teor. Veroyatnost. i Mat. Statist. 45 (1991), 27–33 (Russian); English transl., Theory Probab. Math. Statist. 45 (1992), 23–28. MR 1168444
- V. S. Korolyuk, Stokhastichnī modelī sistem, “Libīd′”, Kiev, 1993 (Ukrainian, with Ukrainian summary). MR 1817881
- O. O. Kushnīr, A study of a highly reliable system with protection by the Rényi theorem, Teor. Ĭmovīr. Mat. Stat. 55 (1996), 117–124 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 55 (1997), 121–128 (1998). MR 1641553
- O. O. Kushnīr, A quantitative lower bound for the expected value of the failure time of a highly reliable system with protection in a nonstationary regime, Teor. Ĭmovīr. Mat. Stat. 61 (1999), 91–96 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 61 (2000), 95–100 (2001). MR 1866966
- O. O. Kushnīr, A logarithmic lower bound for the expected value of the time of failure-free operation of a highly reliable system with protection in a nonstationary mode, Teor. Ĭmovīr. Mat. Stat. 65 (2001), 104–109 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 65 (2002), 115–121. MR 1936134
- D. J. Daley, Tight bounds for the renewal function of a random walk, Ann. Probab. 8 (1980), no. 3, 615–621. MR 573298
- A. Ya. Khinchine, Works on Mathematical Queueing Theory, “Fizmatgiz”, Moscow, 1963 (Russian).
References
- N. V. Kartashov, Inequalities in the Rényi theorem, Teor. Veroyatnost. Mat. Stat. 45 (1991), 27–33; English transl. in Theory Probab. Math. Statist. 45 (1992), 23–28. MR 1168444
- V. S. Korolyuk, Stochastic Models of Systems, “Lybid’ ”, Kyiv, 1993. (Ukrainian) MR 1817881
- O. O. Kushnir, A study of a highly reliable system with protection by the Rényi theorem, Teor. Imovir. Mat. Stat. 55 (1996), 117–124; English transl. in Theory Probab. Math. Statist. 55 (1997), 121–128. MR 1641553
- O. O. Kushnir, A quantitative lower bound for the expected value of the failure time of a highly reliable system with protection in a nonstationary regime, Teor. Imovir. Mat. Stat. 61 (1999), 91–96; English transl. in Theory Probab. Math. Statist. 61 (2000), 95–100. MR 1866966
- O. O. Kushnir, A logarithmic lower bound for the expected value of the time of failure-free operation of a highly reliable system with protection in a nonstationary mode, Teor. Imovir. Mat. Stat. 65 (2001), 104–109; English transl. in Theory Probab. Math. Statist. 65 (2002), 115–121. MR 1936134
- D. J. Daley, Tight bounds for the renewal function of a random walk, Ann. Probab. 8 (1980), no. 3, 615–621. MR 573298
- A. Ya. Khinchine, Works on Mathematical Queueing Theory, “Fizmatgiz”, Moscow, 1963 (Russian).
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Additional Information
O. O. Kushnir
Affiliation:
Department of Higher Mathematics, Institute of Automatics, Cybernetics and Computer Engineering, National University of Water and Enviromental Engineering, Soborna Street, 11, Rivne, Ukraine 33028
Email:
kuchniroo@gmail.com
V. P. Kushnir
Affiliation:
Department of Higher Mathematics, Institute of Automatics, Cybernetics and Computer Engineering, National University of Water and Enviromental Engineering, Soborna Street, 11, Rivne, Ukraine 33028
Email:
a{_}vp{_}kushnir@meta.ua
Keywords:
Renewal process,
alternating process,
system with protection,
Rényi’s theorem,
semi-Markov process
Received by editor(s):
April 30, 2016
Published electronically:
October 5, 2018
Article copyright:
© Copyright 2018
American Mathematical Society
