Advertisement

Cybernetics and Systems Analysis

, Volume 51, Issue 4, pp 632–643 | Cite as

Semi-Markov Model of a Single-Server Queue with Losses and Maintenance of an Unreliable Server

  • A. I. Peschansky
  • A. I. Kovalenko
Article

Abstract

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.

Keywords

single-server queue with an unreliable server server maintenance stationary distribution of embedded Markov chain stationary characteristic two-criteria optimization 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    B. V. Gnedenko, “On a generalization of Erlang formulae,” Dopovidi AN URSR, 4, 347–360 (1959).MathSciNetGoogle Scholar
  2. 2.
    T. P. Mar’yanovich, “A single-line queuing system with an unreliable server,” Ukr. Mat. Zh., 14, No. 4, 417–422 (1962).CrossRefGoogle Scholar
  3. 3.
    T. P. Mar’yanovich, “Generalization of Erlang formulas to the case when devices may break and be repaired,” Ukr. Mat. Zh., 12, No. 3, 279–286 (1960).CrossRefGoogle Scholar
  4. 4.
    W. Gray, M. Scott, and P. Wang, “A vacation queuing model with service breakdowns,” Applied Math. Modeling, 24, 391–400 (2000).MATHCrossRefGoogle Scholar
  5. 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. 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. 7.
    V. S. Korolyuk and A. F. Turbin, Markov Renewal Processes in System Reliability Problems [in Russian], Naukova Dumka, Kiev (1982).Google Scholar
  8. 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. 9.
    A. I. Peschansky, “Semi-Markov models of one-server loss queues with recurrent input,” LAP LAMPERT Academic Publishing (2013).Google Scholar
  10. 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. 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. 12.
    V. V. Rosen, Mathematical Models of Decision-Making in Economy [in Russian], Vyssh. Shkola, Moscow (2002).Google Scholar
  13. 13.
    F. Baykhelt and P. Franken, Reliability and Maintenance: A Mathematical Approach [Russian translation], Radio i Svyaz’, Moscow (1988).Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Sevastopol Institute of Banking of the University of Banking of the National bank of UkraineSevastopolUkraine
  2. 2.Sevastopol National Technical UniversitySevastopolUkraine

Personalised recommendations