Convergence rates in total variation are established for some models of queueing theory and reliability theory. The analysis is based on renewal technique and asymptotic results for the renewal function. It is shown that convergence rate has an exponential asymptotics when the distribution function of the regeneration period satisfies Cramér’s condition. Results concerning polynomial convergence are also obtained.
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This paper is partially supported by grant of the Russian Foundation For Basic Research 13–01–00653.
Proceedings of the XXXII International Seminar on Stability Problems for Stochastic Models, Trondheim, Norway, June 16–21, 2014.
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Afanasyeva, L.G., Tkachenko, A. On the Convergence Rate for Queueing and Reliability Models Described by Regenerative Processes*. J Math Sci 218, 119–136 (2016). https://doi.org/10.1007/s10958-016-3015-7
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DOI: https://doi.org/10.1007/s10958-016-3015-7