Geodesic
On the exponential convergence rate of the distribution for some nonregenerative reliability system
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 1, pp. 145-160.

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Exponential upper bounds for the convergence rate of the distribution of restorable element with partially energized standby redundancy are found, in the case where all working and repair times are bounded by an exponential random variable (upper and lower), and working and repair times can be dependent. The convergence rate of the availability factor is estimated. 
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G. A. Zverkina. On the exponential convergence rate of the distribution for some nonregenerative reliability system. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 1, pp. 145-160. http://geodesic.mathdoc.fr/item/FPM_2020_23_1_a7/

[1] Gnedenko B. V., Belyaev Yu. K., Solovev A. D., Matematicheskie metody v teorii nadezhnosti, Nauka, M., 1965

[2] Gnedenko B. V., Kovalenko I. N., Vvedenie v teoriyu massovogo obsluzhivaniya, Nauka, M., 1966 | MR

[3] Dub Dzh. L., Veroyatnostnye protsessy, Izd. inostr. lit., M., 1956

[4] Zverkina G. A., “Ob odnoi obobschennoi sisteme Erlanga–Sevastyanova i ee skorosti skhodimosti”, Fundament. i prikl. matem., 22:3 (2018), 57–82 | MR

[5] Shtoiyan D., Kachestvennye svoistva i otsenki stokhasticheskikh modelei, Mir, M., 1979

[6] Afanasyeva L. G., Tkachenko A. V., “On the convergence rate for queueing and reliability models described by regenerative processes”, J. Math. Sci., 218:2 (2016), 119–136 | DOI | MR | Zbl

[7] Asmussen S., Applied Probability i Queues, Springer, New York, 2003 | MR | Zbl

[8] Doeblin W., “Exposé de la théorie des chaînes simples constantes de Markov à un nombre fini d'états”, Rev. Math. Union Interbalkan., 2 (1938), 77–105

[9] Griffeath D., “A maximal coupling for Markov chains”, Z. Wahrsch. Verw. Gebiete, 31:2 (1975), 95–106 | DOI | MR | Zbl

[10] Kalimulina E., “Rate of convergence to stationary distribution for unreliable Jackson-type queueing network with dynamic routing”, Distributed Computer and Communication Networks, 19th International Conference, DCCN 2016, Commun. Comput. Inform. Sci., 678, eds. Vishnevskiy V. M., Samouylov K. E., Kozyrev D. K., Springer, Cham, 2016, 253–265 | DOI | Zbl

[11] Kalimulina E., “Analysis of unreliable open queueing network with dynamic routing”, Distributed Computer and Communication Networks, DCCN 2017, Commun. Comput. Inform. Sci., 700, eds. Vishnevskiy V. M., Samouylov K. E., Kozyrev D. K., Springer, Cham, 2017, 355–367 | DOI | Zbl

[12] Kato K., “Coupling lemma and its application to the security analysis of quantum key distribution”, Tamagawa Univ. Quantum ICT Research Inst. Bull., 4:1 (2014), 23–30

[13] Thorisson H., Coupling, Stationarity, and Regeneration, Springer, Berlin, 2000 | MR | Zbl

[14] Veretennikov A., Butkovsky O. A., “On asymptotics for Vaserstein coupling of Markov chains”, Stoch. Process. Appl., 123:9 (2013), 3518–3541 | DOI | MR | Zbl

[15] Veretennikov A. Yu., Zverkina G. A., “Simple proof of Dynkin's formula for single-server systems and polynomial convergence rates”, Markov Process. Relat. Fields, 20 (2014), 479–504 | MR | Zbl

[16] Zverkina G., “On strong bounds of rate of convergence for regenerative processes”, Distributed Computer and Communication Networks, 19th International Conference, DCCN 2016, Commun. Comput. Inform. Sci., 678, eds. Vishnevskiy V. M., Samouylov K. E., Kozyrev D. K., Springer, Cham, 2016, 381–393 | DOI | Zbl