Semi-Markov Model of a Single-Server Queue with Losses and Maintenance of an Unreliable Server
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A semi-Markov model of the single-server GI /G/ 1/ 0 queue is constructed with allowance for the maintenance of an unreliable server. Stationary reliability and economic characteristics of the queue are found, and two-criteria optimization of maintenance periodicity is carried out.
Keywordssingle-server queue with an unreliable server server maintenance stationary distribution of embedded Markov chain stationary characteristic two-criteria optimization
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- 5.G. V. Emelyanov, “A queuing system with apparatus which can go out of service and be restored,” Problems of Information Transmission, 3, No. 3, 59–63 (1967).Google Scholar
- 6.A. I. Kovalenko, B. D. Maryanin, and V. P. Smolich, “Investigation of reliability of a single-server system with losses,” Taurida Journal of Computer Science Theory and Mathematics, No. 2, 89–101 (2003).Google Scholar
- 7.V. S. Korolyuk and A. F. Turbin, Markov Renewal Processes in System Reliability Problems [in Russian], Naukova Dumka, Kiev (1982).Google Scholar
- 8.A. N. Korlat, V. N. Kuznetsov, M. I. Novikov, and A. F. Turbin, Semi-Markov Models of Restorable Systems and Queuing Systems [in Russian], Stiinta, Chisinau (1991).Google Scholar
- 9.A. I. Peschansky, “Semi-Markov models of one-server loss queues with recurrent input,” LAP LAMPERT Academic Publishing (2013).Google Scholar
- 10.A. I. Peschansky and A. I. Kovalenko, “Stationary characteristics of a single-server queue system with losses and an unreliable server,” Taurida Journal of Computer Science Theory and Mathematics, No. 1 (22), 69–79 (2013).Google Scholar
- 11.V. A. Kashtanov and A. I. Medvedev, The Reliability Theory of Complex Systems (Theory and Practice) [in Russian], European Center for Quality, Moscow (2002).Google Scholar
- 12.V. V. Rosen, Mathematical Models of Decision-Making in Economy [in Russian], Vyssh. Shkola, Moscow (2002).Google Scholar
- 13.F. Baykhelt and P. Franken, Reliability and Maintenance: A Mathematical Approach [Russian translation], Radio i Svyaz’, Moscow (1988).Google Scholar