Abstract
In this paper, we consider various redundant systems attended by a single repairperson that services components in a First Come First Served (FCFS) order. Failure times are taken to be exponentially distributed random variables, while repair times are deterministic. As a result, the underlying stochastic process is not Markovian or semi-Markovian. However, the underlying stochastic process is Markov regenerative and as such we are able to write and solve equations for the process. We compute various dependability measures, such as reliability function, Mean Time To Failure (MTTF), time-dependent and steady-state availability.
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
J. Angus. On Computing MTBF for a k-out-of-n:G Repairable System. IEEE Transactions on Reliability, Vol. 37, 312–313, 1988.
R. Barlow and F. Proschan. Mathematical Theory of Reliability, John Wiley, 1965.
G. Ciardo, J. Muppala and K. Trivedi. SPNP: Stochastic Petri Net Package. Proc. Intl. Workshop on Petri Nets and Performance Models, 142–150, Kyoto, Japan, 1989.
E. Çinlar. Introduction to Stochastic Processes,Prentice Hall, 1975.
D. R. Cox. The Analysis of Non-Markov Stochastic Processes by the Inclusion of Supplementary Variables. Proc. Camb. Phil. Soc.,Vol. 51, 433–441, 1955.
T. Das and M. Wortman. Performance of N Machine Centers of K-out-ofM:G Type Maintained by a Single Repairman. Naval Research Logistics, Vol. 39, 919–936, 1992.
R. German and C. Lindemann. Analysis of Stochastic Petri Nets by the Method of Supplementary Variables. To appear in Performance Evaluation
D. Kincaid and W. Cheney. Numerical Analysis, Brooks/Cole, 1991.
V. G. Kulkarni. Modeling and Analysis of Stochastic Systems, Chapman Hall, 1995.
D. Logothetis and K. Trivedi. The Effect of Detection and Restoration in Communication Networks. Under Preparation.
D. Logothetis and K. Trivedi. Transient Analysis of the Leaky Bucket Rate Control Scheme Under Poisson and ON-OFF Sources, Proc. of INFOCOM 94, Toronto, Canada, 1994.
S. Mohanty A. Montazer-Haghighi and R. Trueblood. On the Transient Behavior of a Finite Birth-Death Process with an Application. Computers in Operations Research, Vol. 20, No 3, 239–248, 1993.
S. Ross. Applied Probability Models with Optimization Applications, Holden-Day, San Francisco, 1970.
O. Sharma, N. Ravichandran and J. Dass. Transient Analysis of Multiple Unit Reliability Systems. Naval Research Logistics, Vol. 36, 255–264, 1989.
L. Takacs. Introduction to the Theory of Queues, Oxford University Press, 1962.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media New York
About this paper
Cite this paper
Logothetis, D., Trivedi, K. (1995). Time-Dependent Behavior of Redundant Systems with Deterministic Repair. In: Stewart, W.J. (eds) Computations with Markov Chains. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2241-6_9
Download citation
DOI: https://doi.org/10.1007/978-1-4615-2241-6_9
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-5943-2
Online ISBN: 978-1-4615-2241-6
eBook Packages: Springer Book Archive