«Automation and Informatization of the fuel and energy complex»

Stability of stationary total income using the apparatus of Markov processes with revaluation

UDC: 338.2
DOI: -

Authors:

¹ National University of Oil and Gas "Gubkin University", Moscow, Russia

Keywords: Markov process with income, revaluation coefficient, stationary total income, stability problem of stationary total income

Annotation:

The article formulates and solves the problem of stability of total income with revaluation. In this case, the revaluation of total income from the operation of a complex technical system is considered, which includes elements that can be restored and replaced in case of failure. This system functions over a long period of time and generates income from fulfilling contractual obligations to supply products to consumers. The behavior of the system is adequately described by a homogeneous Markov chain with income and revaluation under conditions when the transition probabilities of the chain are not exactly known, and only their interval estimates are available. The presence of an overvaluation of the total income on the Markov chain indicates the necessity of taking into account the circumstances that change the monetary value of the income from the functioning of the system during its long-term operation. Such circumstances arise as a result of inflation, various economic sanctions, and similar phenomena. Under the above-mentioned conditions, the problem of stability of the overvalued total income with respect to changes of the transition probabilities of the Markov chain within its interval estimates is formed and algorithmically solved. An example illustrating the solutions to this problem is given.

Bibliography:

1. Nadezhnost' sistem energetiki i ikh oborudovaniya: sprav.: v 4 t. T. 3. Nadezhnost' sistem gazo- i neftesnabzheniya: v 2 kn. Kn. 2 / M.G. Sukharev, S.G. Babaev, A.M. Beylin [i dr.]; pod obshch. red. Yu.N. Rudenko. – M.: Nedra, 1994. – 287 s.
2. Menk'yu N.G. Printsipy Ekonomiks. – SPb.: Piter Kom, 1999. – 784 s.
3. Khovard R. Dinamicheskoe programmirovanie i markovskie protsessy / per. s angl. V.V. Rykova; pod red. N.P. Buslenko. – M.: Sovetskoe Radio, 1964. – 189 s.
4. Mayn Kh., Osaki S. Markovskie protsessy prinyatiya resheniy / per. s angl. V.V. Kalashnikova, V.S. Manusevicha; pod red. N.N. Buslenko. – M.: Nauka, 1977. – 175 s.
5. Karmanov A.V., Orlova K.P. Ustoychivost' statsionarnogo dokhoda na odnorodnom markovskom protsesse s pereotsenkoy i nepolnymi iskhodnymi dannymi // Avtomatizatsiya i informatizatsiya TEK. – 2024. – № 8(613). – S. 54–58.
6. Kolnogorov A.V., Fedoruk R.S. Model' adaptivnogo upravleniya konechnoy tsep'yu Markova so slabo diskontiruemymi dokhodami // Vestn. Novgorod. gos. un-ta. – 2010. – № 60. – S. 43–46.
7. Avt. svid. № 2010614952 o gos. registratsii programmy dlya EVM "Raschet optimal'nogo vremeni ispytaniy v tsepi Markova" / R.S. Fedorchuk. – Zayavl. 29.07.2010.
8. Karmanov V.G. Matematicheskoe programmirovanie: ucheb. posobie. – 5-e izd., stereotip. – M.: FIZMATLIT, 2004. – 264 s.
9. Kolmogorov A.N., Fomin S.V. Elementy teorii funktsiy i funktsional'nogo analiza. – 4-e izd., pererab. – M.: Nauka, 1976. – 542 s.
10. Volkov I.K., Zagoruyko E.A. Issledovanie operatsiy: ucheb. dlya vuzov / pod red. V.S. Zarubina, A.P. Krishchenko. – M.: MGTU im. N.E. Baumana, 2000. – 436 s.