Abstract
This paper studies the Gnedenko system attended by a repairman with k-vacations. It is assumed that the life of the operating unit and the standby, and the vacation time of the repairman are all exponential distributions, while the repair time of the unit has a general continuous distribution. By using the supplementary variable method, we obtain the explicit expressions of the steady-state availability and the steady-state failure frequency of the system.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Gnedenko, B.V.: Some theorems on standby. In: Proc. Fifth Berkeley Symp. And Prob., vol. 3, pp. 285–291 (1967)
Cao, J.H.: Reliability analysis of Gnedenko system with a replaceable repair facility. Chinese Applied Probability and Statistic 5(3), 265–275 (1989)
Su, B.H., Shi, D.H.: Reliability analysis of n-unit series systems with multiple vacations of a repairman. Math. Stat. Appl. Probab. 10, 78–82 (1995)
Hu, L.M., Li, J.D.: Reliability analysis of a three-unit system with vacation and priority. ICIC Exp. Lett. 3(2), 171–176 (2009)
Takagi, H.: Queueing Analysis: A Foundation of Performance Evaluation, Vacation and Priority Systems, Part 1, vol. 1. North-Holland, Amsterdam (1991)
Zhang, Z.G., Tian, N.S.: Discrete-time Geo/G/1 queue with multiple adaptive vacation. Queueing Systems 38, 419–429 (2001)
Shi, D.H.: A new method to calculate the mean time of failure times in (0,t] of a repairable system. J. Appl. Math. 8(1), 101–110 (1985)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cao, J., Yue, D. (2011). Probabilistic Analysis of Gnedenko System with K-Vacations of a Repairman. In: Jin, D., Lin, S. (eds) Advances in Computer Science, Intelligent System and Environment. Advances in Intelligent and Soft Computing, vol 106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23753-9_44
Download citation
DOI: https://doi.org/10.1007/978-3-642-23753-9_44
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23752-2
Online ISBN: 978-3-642-23753-9
eBook Packages: EngineeringEngineering (R0)