Hostname: page-component-76fb5796d-r6qrq Total loading time: 0 Render date: 2024-04-25T10:37:25.446Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Wei Li ,
Dinghua Shi  and
Xiuli Chao
Wei Li*
Affiliation:
Chinese Academy of Sciences
Dinghua Shi*
Affiliation:
Shanghai University of Science and Technology
Xiuli Chao*
Affiliation:
New Jersey Institute of Technology
*
∗Postal address: Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100080, P.R. China.
∗∗Postal address: Department of Mathematics, Shanghai University of Science and Technology, Shanghai 201800, P.R. China.
∗∗∗Postal address: Department of Industrial and Manufacturing Engineering, New Jersey Institute of Technology, Newark, NJ 07102, USA.
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

SERVER BREAKDOWNS AND REPAIRSQUEUES WITH VACATIONSRELIABILITY

MSC classification

Primary: 60K25: Queueing theory
Type
Research Article
Information
Journal of Applied Probability , Volume 34 , Issue 2 , June 1997 , pp. 546 - 555
Copyright
Copyright © Applied Probability Trust 1997 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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
Hsu, G. H. (1988) Stochastic Service Systems. 2nd edn. Science Press, Beijing.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