Automatic Control and Computer Sciences

, Volume 47, Issue 2, pp 94–98 | Cite as

Reliability model for standby system with replacement delays of failed elements

  • R. V. KakubavaEmail author
International Seminar “Probabilistic Models and Statistical Inference”


The model for a wide class of any territorially distributed standby systems consisting of unreliable repairable elements is described. It represents special type of closed queuing system in which two maintenance operations — replacements and repairs of failed elements are carried out. The possible applications of the model are discussed.


standby renewal replacement queuing system 


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  1. 1.
    Ushakov, I., Reliability: past, present, future, Reliability: Theory and Applications (Electronic J.) 2006, No. 1, pp. 10–27. Google Scholar
  2. 2.
    Ushakov, I., Reliability theory: history and current state in bibliographies, Reliability: Theory and Applications (Electronic J.) 2012, No. 1, pp. 8–35. Google Scholar
  3. 3.
    Kakubava, R. and Khurodze, R., Technical systems with structural and time redundancy: a probabilistic analysis of their performance, Autom. Remote Contr., 2004, vol. 65, pp. 825–833.zbMATHCrossRefGoogle Scholar
  4. 4.
    Korolyuk, V.S. and Korolyuk, V.V., Stochastic Models of Systems Dordrecht: Kluwer, 1999.zbMATHCrossRefGoogle Scholar
  5. 5.
    Limnios, N. and Oprisan, G., Semi-Markov Processes and Reliability Boston: Birkhauser, 2001.zbMATHCrossRefGoogle Scholar
  6. 6.
    Korolyuk, V.S., Limnios, N., Stochastic Systems and Merging Phase, Singapore: Imperial College Press, 2005.CrossRefGoogle Scholar
  7. 7.
    Kakubava, R., New Markovian and semi-Markovian closed queuing systems with two types of service as mathematical models of reliability and maintenance, Proc. 6th Int. Conf. MMR 2009 — Mathematical Methods in Reliability, Moscow: RSUOG, 2009.Google Scholar
  8. 8.
    Kakubava, R., Multiline Markov closed queuing system for two maintenance operations, RTA J., 2010, no. 1, pp. 15–22.Google Scholar
  9. 9.
    Kakubava, R. and Sztrik, J., Queuing models with two types of service: applications for dependability planning of complex systems, Proc. 7th Int. Conf. MMR 2011 — Mathematical Methods in Reliability. Theory. Methods. Applications, Beijing, 2011.Google Scholar

Copyright information

© Allerton Press, Inc. 2013

Authors and Affiliations

  1. 1.Georgian Technical UniversityTbilisiGeorgia

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