Abstract
We consider a system of two conditionally independent alternating renewal processes with restructuring and with a general form of the distribution densities of interval lengths. The system models the operation of two units taking into account operation and repair intervals. The restructuring time is associated with the instant when the two-dimensional process first reaches a state where both components are operational. For a process as a whole, each such time corresponds to the system’s Markov regeneration when it begins working anew, from another initial state. Time intervals between restructurings depend on the so-called fixed guaranteed service times. We use the evolution property of the two-dimensional process between Markov regeneration times, which transforms such an evolution into a breaking second-order semi-Markov process. We derive integral equations for the expectations of system efficiency over the time interval from zero to the time of restructuring.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Malykh, N.P. and Savinov, L.V., Estimation and Control for the Level of Reserves of Gasodynamical Stability of Turbocompressors, in Reliability of Technical Systems, Preprint of Inst. of Problems of Mechanical Engineering, Russ. Acad. Sci., St. Petersburg, 1992, no. 79, pp. 61–72.
Cox, D.R. and Smith, W.L., Renewal Theory, New York: Wiley, 1962. Translated under the title Teoriya vosstanovleniya, Moscow: Sovetskoe Radio, 1966.
Shurenkov, V.M., Ergodicheskie protsessy Markova (Ergodic Markov Processes), Moscow: Nauka, 1989.
Feller, W., An Introduction to Probability Theory and Its Applications, New York: Wiley, 1966. Translated under the title Vvedenie v teoriyu veroyatnostei i ee prilozheniya, Moscow: Mir, 1967, vol.2.
Harlamov, B.P., Nepreryvnye polumarkovskie protsessy (Continuous Semi-Markov Processes), St. Petersburg: Nauka, 2001.
Kemeny, J. and Snell, J., Finite Markov Chains, Princeton: Van Nostrand, 1960. Translated under the title Konechnye tsepi Markova, Moscow: Nauka, 1970.
Gikhman, I.I. and Skorokhod, A.V., Teoriya sluchainykh protsessov (Theory of Random Processes), Moscow: Nauka, 1973, vol.2.
Korolyuk, V.S. and Turbin, A.F., Polumarkovskie protsessy i ikh prilozheniya (Semi-Markov Processes and Their Applications), Kiev: Naukova Dumka, 1975.
Dynkin, E.B., Markovskie protsessy (Markov Processes), Moscow: Fizmatgiz, 1963.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © S.S. Rasova, B.P. Harlamov, 2018, published in Avtomatika i Telemekhanika, 2018, No. 4, pp. 46–64.
Rights and permissions
About this article
Cite this article
Rasova, S.S., Harlamov, B.P. Efficiency of a Two-Channel System with Restructuring and Insurance. Autom Remote Control 79, 617–631 (2018). https://doi.org/10.1134/S0005117918040045
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117918040045