Abstract
A computing system can be formulated by modeling a continuous-time Markov chain with many states, and be evaluated by using the reliability/performance measures. The randomization technique is discussed to derive the transient solution for a Markov chain. A software package tool is implemented by using the randomization technique and introducing a new idea of identifying when the transient solution converges to the steady-state solution in advance. Numerical examples are illustrated by using our software package tool to evaluate the optimal maintenance policies for computing systems. Some interesting maintenance policies are suggested from the numerical examples.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Reference
A. Avizienis, “Fault-tolerant system”, IEEE Trans. Computers, vol. C-25, pp. 1304–1312, Dec. 1976.
D. P. Siewiorek and R. S. Swarz, The Theory and Practice of Reliable System Design, Digital Press, Bedford, Massachusetts, 1982.
S. V. Makam and A. Avizienis, “ARIES: A reliability and life-cycle evaluation tool for foult-tolerant system”, in Proc. 12th Int. Symp. on Fault-Tolerant Computing, Santa Monica, California, pp. 267–274, 1982.
A. Avizienis and J. C. Laprie, “Dependable Computing: From Concepts to Design Diversity”, Proc. IEEE, vol. 74, pp. 629–638, May 1986.
J. Arlat, K. Kanoun and J. C. Laprie, “Dependability evaluation of software fault-tolerance”, in Proc. 18th Int. Symp. on Fault-Tolerant Computing, Tokyo, pp. 142–147, June 1988.
S. M. Ross, Stochastic Processes, John Wiley and Sons, New York, 1983.
D. Gross and D. R. Miller, “The randomization technique as a modeling tool and solution procedure for transient Markov processes”, Operations Research, vol. 32, pp. 343–361, Mar.-Apr. 1984.
C. Moler and C. Van Loan, “Nineteen dubious ways to compute the exponential of matrix”, SIAM Review, vol. 20, pp. 801–836, Oct. 1978.
S. Y. H. Su, I. Koren, Y. K. Malaiya, “A continuous-parameter Markov model and detection procedures for intermittent faults”, IEEE Trans. Computers, vol. C-27, pp. 567–570, June 1987.
Z. Jelinski and P. B. Moranda, “Software reliabilty research”, in Statistical Computer Performance Evaluation, W. Freiberger (ed.), Accademic Press, New York, pp. 465–484, 1972.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fukumoto, S., Osaki, S. (1991). A Software Package Tool for Markovian Computing Models with Many States: Principles and its Applications. In: Beckmann, M.J., Gopalan, M.N., Subramanian, R. (eds) Stochastic Processes and their Applications. Lecture Notes in Economics and Mathematical Systems, vol 370. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58201-1_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-58201-1_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54635-1
Online ISBN: 978-3-642-58201-1
eBook Packages: Springer Book Archive