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.
Similar content being viewed by others
References
Yechiali, U., Queues with System Disasters and Impatient Customers when System is Down, Queueing Syst., 2007, no. 56, pp. 195–202.
Rudenko, I.V., Queueing Systems with Unreliable and Restorable Servers, Cand. Sci. (Phys.-Math.) Dissertation, Moscow: Moscow State Univ., 2012.
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.
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.
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.
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.
Peschansky, A.I., Semi-Markov Models of One-Server Loss Queues with Recurrent Input, Saarbrücken: LAP LAMPERT Academic Publishing, 2013.
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.
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.
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.
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.
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.
Beichelt, F. and Franken, P., Zuverlässigkeit und Instanphaltung, mathematische Methoden, Berlin: VEB Verlag Technik, 1983.
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.
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.
Rozen, V.V., Matematicheskie modeli prinyatiya reshenii v ekonomike (Mathematical Decision Making Models in Economics), Moscow: Vysshaya Shkola, 2002.
Author information
Authors and Affiliations
Corresponding author
Additional information
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
Rights and permissions
About this article
Cite this article
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
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117916120080