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A semi-Markov model for an unreliable single-line loss queueing system with different restoration types

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Abstract

We construct a semi-Markov model for a queueing system GI/G/1/0 with an unreliable server, where after the server’s failure it is subject to minimal emergency restoration, and after reaching certain total time of operation it is subject to complete maintenance with full restoration of its reliability characteristics. We define stationary reliability and economical system parameters and perform bicriterial optimization of the maintenance period.

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References

  1. Yechiali, U., Queues with System Disasters and Impatient Customers when System is Down, Queueing Syst., 2007, no. 56, pp. 195–202.

    Article  MathSciNet  MATH  Google Scholar 

  2. Rudenko, I.V., Queueing Systems with Unreliable and Restorable Servers, Cand. Sci. (Phys.-Math.) Dissertation, Moscow: Moscow State Univ., 2012.

    Google Scholar 

  3. Kovalenko, A.I., Maryanin, B.D., and Smolich, V.P., On Reliability of a Single-Server Queueing System with Lost Customers, Tavricheskii Vestn. Informat. Mat., 2003, no. 2, pp. 89–101.

    MATH  Google Scholar 

  4. Kovalenko, A.I., Maryanin, B.D., and Smolich, V.P., Queueing System with an Unreliable Line and Impatient Customers, Tavricheskii Vestn. Informat. Mat., 2013, no. 1, pp. 53–60.

    Google Scholar 

  5. Pechinkin, A.V. and Chaplygin, V.V., Stationary Characteristics of the SM/MSP/n/r Queuing System, Autom. Remote Control, 2004, vol. 65, no. 9, pp. 1429–1443.

    Article  MathSciNet  MATH  Google Scholar 

  6. Krishna Kumar B., Arivudainambi, D., and Vijayakumar, A., An M/G/1/1 Queue with Unreliable Server and No Waiting Capacity, Inf. Manage. Sci., 2002, vol. 13, pp. 35–50.

    MathSciNet  MATH  Google Scholar 

  7. Peschansky, A.I., Semi-Markov Models of One-Server Loss Queues with Recurrent Input, Saarbrücken: LAP LAMPERT Academic Publishing, 2013.

    Google Scholar 

  8. Peschansky, A.I. and Kovalenko, A.I., Stationary Characteristics of a Single-Server Loss Queueing System with an Unreliable Server, Taurida Vestn. Inf. Mat., 2013, no. 1, pp. 69–79.

    Google Scholar 

  9. Grishunina, Yu.B., A Study of a Semi-Markov Model of Maintenance for Optimal Choice of the Repair Type, Nadezhnost’, 2010, no. 2 (33), pp. 44–53.

    Google Scholar 

  10. Peschansky, A.I. and Kovalenko, A.I., Semi-Markov Model of a Single-Server Queue with Losses and Maintenance of an Unreliable Server, Cybern. Syst. Anal., 2015, vol. 51, no. 4, pp. 632–643.

    Article  MathSciNet  MATH  Google Scholar 

  11. Peschansky, A.I. and Kovalenko, A.I., Semi-Markov Model of a Single-Server Loss Queue with Regard to Maintenance of Unreliable Channel, SevNTU Journal: Optim. Ind. Process., Sevastopol, 2014, no. 15, pp. 63–70.

    Google Scholar 

  12. Peschansky, A.I. and Kovalenko, A.I., Semi-Markov Model of Unreliable One-Server Loss Queue System with Latent Failures, SevNTU Journal: Automation of Processes and Control, Sevastopol, 2014, no. 147, pp. 64–72.

    Google Scholar 

  13. Beichelt, F. and Franken, P., Zuverlässigkeit und Instanphaltung, mathematische Methoden, Berlin: VEB Verlag Technik, 1983.

    Google Scholar 

  14. Korolyuk, V.S. and Turbin, A.F., Protsessy markovskogo vosstanovleniya v zadachakh nadezhnosti sistem (Markov Renewal Processes in the Problems of System Reliability), Kiev: Naukova Dumka, 1982.

    MATH  Google Scholar 

  15. Korlat, A.N., Kuznetsov, V.N., Novikov, M.I., et al., Polumarkovskie modeli vosstanavlivaemykh sistem i sistem massovogo obsluzhivaniya (Semi-Markov Models of Restorable Systems and Queueing Systems), Kishinev: Shtiintsa, 1991.

    Google Scholar 

  16. Rozen, V.V., Matematicheskie modeli prinyatiya reshenii v ekonomike (Mathematical Decision Making Models in Economics), Moscow: Vysshaya Shkola, 2002.

    Google Scholar 

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Correspondence to A. I. Peschansky.

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Original Russian Text © A.I. Peschansky, A.I. Kovalenko, 2016, published in Avtomatika i Telemekhanika, 2016, No. 12, pp. 112–126.

This paper was recommended for publication by A.I. Lyakhov, a member of the Editorial Board

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Peschansky, A.I., Kovalenko, A.I. A semi-Markov model for an unreliable single-line loss queueing system with different restoration types. Autom Remote Control 77, 2193–2204 (2016). https://doi.org/10.1134/S0005117916120080

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  • DOI: https://doi.org/10.1134/S0005117916120080

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