SEMI-MARKOV RELIABILITY MODELS
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Abstract
Traditional technologies for reliability analysis of semi-Markov systems are limited to obtaining a stationary state probability distribution. However, when solving practical control problems in such systems, the study of transient processes is of considerable interest. This implies the subject of research - the analysis of the laws of distribution of the system states probabilities. The goal of the work is to obtain the desired distribution at any time. The complexity of the problem solving is determined by the need to obtain a result for arbitrary distribution laws of the duration of the system's stay in each state before leaving. An easy-to-implement method for the analysis of semi-Markov reliability models has been suggested. The method is based on the possibility of approximating probability-theoretic descriptions of failure and recovery flows in the system using the Erlang distribution laws of the proper order. The developed computational scheme uses the most important property of Erlang flows, which are formed as a result of sieving the simplest Poisson flow. In this case, the semi-Markov model is reduced to the Markov one, which radically simplifies the analysis of real systems.
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References
Gnedenko, B.V., Belyaev, Yu. K. and Solovyev, A. D. (1965), Mathematical methods in the reliability theory, Science, Moscow, 524 p.
Barzilovich, E. Yu., Belyaev, Yu. K., Kashtanov, V. A., Kovalenko, I. N., Solovyev, A. D. and Ushakov, I. A. (1983), Matters of mathematical reliability theory, Radio and communications, Moscow, 376 p.
Korolyuk, V. S. and Turbin, A. F. (1976), Semi-Markov processes and their application, Science concept, Kyiv, 172 p.
Feinberg, E. A. and Yang, F. (2016), “Optimal pricing for a G1/M/K/N queue with several customer types and holding costs”, Queuing systems, vol. 82, pp. 103-120.
Cao, X. R. (2015), ‘Optimization of average rewards of time non humongous smarkov chains”, Trans. On Automatic control, vol. 60, no. 7, pp. 1841-1856.
Li, Q. (2016), “Nonlinear markov processes in big networks”, Special matrices, vol. 4, no. 1, pp. 202-217.
Zhon,g Kai-Lai (1954), Homogeneous Markov chains, World, Moscow, 264 p.
Borisovich, A. V. and Dyakin, N. V. (2015), “A semi-Markov model for assessing the reliability indicators of an uninterruptible power supply of a data center”, Modern Scientific. Innov., no. 8, pp. 68-74.
Sorokin, A. S. (2005), “Application of semi-Markov processes to the determination of reliability performance of process diagrams”, Bulletin of KSU, no. 2, pp. 3-7.
Anishchenko, V. V. (2020), “Semi-Markov reliability models”, Computer science, vol. 17, no. 4, pp. 24-32.
Kazhak, V., Stenkin, V. and Zakharov, A. (2019), “Statistical semi-Markov model for assessing the reliability indicators of electromechanical systems”, System technologies, vol. 2(121), pp. 114-119.
Limnios, N. (2001), Semi-markov processes and reliability, Birkhauser, Boston, 214 p.
Kashtanov, V. A. and Medvedev, A. I. (2002), Complex systems reliability theory, European Center, Moscow, p. 196.
Raskin, L.G. (1997), “Markov chains analysis using phase enlargement of states”, Science, technology, equipment, education, health, NTU KhPI, p. 28.
Raskin, L.G. and Seraya, O.V. (2003), “Formation of a scalar preference criterion based on the results of pair-wise comparisons”, Bulletin of NTU KhPI, No. 6, pp. 63-68.