Article contents
Reliability analysis of M/G/1 queueing systems with server breakdowns and vacations
Part of:
Special processes
Published online by Cambridge University Press: 14 July 2016
Abstract
This note introduces reliability issues to the analysis of queueing systems. We consider an M/G/1 queue with Bernoulli vacations and server breakdowns. The server uptimes are assumed to be exponential, and the server repair times are arbitrarily distributed. Using a supplementary variable method we obtain a transient solution for both queueing and reliability measures of interest. These results provide insight into the effect of server breakdowns and repairs on system performance.
MSC classification
Primary:
60K25: Queueing theory
- Type
- Research Article
- Information
- Copyright
- Copyright © Applied Probability Trust 1997
References
Cox, D. R. (1955) The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables.
Proc. Cambridge Phil. Soc.
51, 433–441.Google Scholar
Doshi, B. T. (1990) Single server queues with vacations. In
Stochastic Analysis of Computer and Communication Systems.
ed. Tokagi, H.
Elsevier, Amsterdam.Google Scholar
Keilson, J. and Kooharian, A. (1960) Time dependent queueing processes.
Ann. Math. Statist.
31, 104–112.CrossRefGoogle Scholar
Keilson, J. and Servi, L. (1986) Oscillating random walk models for GI/G/1 vacation systems with Bernoulli schedules.
J. Appl. Prob.
23, 790–802.CrossRefGoogle Scholar
Servi, L. (1986) Average delay approximation of M/G/1 cyclic service queue with Bernoulli schedule.
IEEE Select. Areas Commun.
4, 813–820.CrossRefGoogle Scholar
Shi, D. H. (1985) A new method for calculating the mean failure numbers of a repairable system during (0, t].
Acta Math. Appl. Sinica
8, 101–110.Google Scholar
Shi, D. H. and Li, W. (1990) Some transient properties of the repairable queueing system Em/G(M/G)/1.
Chinese J. Operat. Res.
2, 38–40.Google Scholar
Takács, L. (1962)
Introduction to the Theory of Queues.
Oxford University Press, New York.Google Scholar
- 77
- Cited by