This Article 
 Bibliographic References 
 Add to: 
On Reliability Modeling of Closed Fault-Tolerant Computer Systems
April 1990 (vol. 39 no. 4)
pp. 571-575

It is observed that a large number of closed fault-tolerant systems modeled by a continuous-time Markov model referred to as the ARIES model have repeated eigenvalues. It is proven that the rate matrix representing the system is diagonalizable for every closed fault tolerant system modeled by ARIES. Consequently, the Lagrange-Sylvester interpolation formula is applicable to all closed fault-tolerant systems which ARIES models. Since the proof guarantees that the rate matrix is diagonalizable, general methods for solving arbitrary Markov chains can be tailored to solve the ARIES model for the closed systems directly.

[1] S. J. Bavuso, J. B. Dugan, K. S. Trivedi, E. M. Rothman, and W. E. Smith, "Analysis of typical fault-tolerant architectures using HARP,"IEEE Trans. Reliability, vol. R-36, June 1987.
[2] R. M. Geist and K. S. Trivedi, "Ultra-reliability prediction for fault-tolerant computers,"IEEE Trans. Comput., vol. C-32, Dec. 1983.
[3] S. V. Makam, A. A. Avizienis, and G. Grusas, "UCLA ARIES 82 users' guide," Tech. Rep., Dep. Comput. Sci., Univ. of California, Los Angeles, Aug. 1982.
[4] R. A. Marie, A. L. Reibman, and K. S. Trivedi, "Transient analysis of acyclic Markov Chains,"Perform. Eval., vol. 7, 1987.
[5] M. Mulazzani and K. S. Trivedi, "Dependability prediction: Comparison of tools and techniques," inProc. IFAC SAFECOMP '86, Sarlat, France, 1986.
[6] Y. W. Ng, "Reliability analysis and modeling for fault-tolerant computers," Ph.D. dissertation, Dep. Comput. Sci., Univ. California, Los Angeles, Sept. 1976.
[7] Y. W. Ng and A. A. Avizienis, "A unified reliability model for fault-tolerant computers,"IEEE Trans. Comput., vol. C-29, no. 11, Nov. 1980.
[8] C. S. Raghavendra and D. A. Lee, "Reliability evaluation of fault-tolerant computers for aerospace applications," inAIAA Comput. Aerospace VII Conf. Exhibit, Monterey, CA, 1989.
[9] J. J. Stiffler, L. A. Bryant, and L. Guccione, "CARE III final report. Phase 1," Tech. Rep., NASA Contr. Rep. 159122, Nov. 1979.
[10] G. Strang,Linear Algebra and its Applications. New York: Harcourt Brace Jovanovich, 1980.
[11] K. S. Trivedi,Probability and Statistics with Reliability, Queueing and Computer Science Applications. Englewood Cliffs, NJ: Prentice-Hall, 1982.
[12] L. A. Zadeh and C. A. Desoer,Linear System Theory, A State Space Approach. New York: McGraw-Hill, 1963.

Index Terms:
reliability modeling; closed fault-tolerant computer systems; continuous-time Markov model; ARIES model; eigenvalues; Lagrange-Sylvester interpolation formula; rate matrix; fault tolerant computing; Markov processes; modelling.
M. Balakrishnan, C.S. Raghavendra, "On Reliability Modeling of Closed Fault-Tolerant Computer Systems," IEEE Transactions on Computers, vol. 39, no. 4, pp. 571-575, April 1990, doi:10.1109/12.54852
Usage of this product signifies your acceptance of the Terms of Use.