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On Evaluating the Cumulative Performance Distribution of Fault-Tolerant Computer Systems
November 1991 (vol. 40 no. 11)
pp. 1301-1307

Fault-tolerant computer systems may be evaluated by calculating their cumulative performance (e.g., number of processes jobs) over a finite mission time. A method for calculating the cumulative performance distribution assuming that the system fault-repair behavior can be modeled by a homogeneous Markov process is described. The method proposed for calculating the probability distribution of the accumulated reward over a finite mission is applicable to models of repairable and nonrepairable systems. The related solution algorithm shows a low polynomial computational complexity. The mathematical model is introduced, and the results already presented in the literature are surveyed. A comprehensive analysis of the time and space complexity of the proposed solution algorithm is presented. A numerical example is given.

[1] M. D. Beaudry, "Performance-related reliability measures for computing systems,"IEEE Trans. Comput., vol. C-27, pp. 540-547, 1978.
[2] E. Cinlar,Introduction to Stochastic Processes. Englewood Cliffs, NJ: Prentice-Hall, 1975.
[3] D. R. Cox, "A use of complex probabilities in the theory of stochastic processes,"Proc. Cambridge Philos. Soc., vol. 51, pp. 313-319, 1955.
[4] E. de Souza e Silva and H. R. Gail, "Calculating cumulative operational time distributions of repairable computer systems,"IEEE Trans. Comput., vol. C-35, pp. 322-332, 1986.
[5] E. de Souza e Silva and H. R. Gail, "Calculating availability and performability measures of repairable computer systems using randomization,"J. ACM, vol. 36, no. 1, Jan. 1989.
[6] L. Donatiello and B. R. Iyer, "Analysis of composite performance reliability measure for fault-tolerant systems,"J. ACM, vol. 34, no. 1, 1987.
[7] W. Feller,An Introduction to Probability Theory and Its Applications, vol. 1 New York: Wiley, 1968.
[8] D. G. Furchtgott and J. F. Meyer, "A performability solution method for degradable nonrepairable systems,"IEEE Trans. Comput., vol. C-33, pp. 550-554, 1984.
[9] A. Goyal and A. N. Tantawi, "A measure of guaranteed availability and its numerical evaluation"IEEE Trans. Comput., vol. C-37, pp. 25-32, 1988.
[10] A. Goyal and A. N. Tantawi, "Evaluation of performability for degradable computer systems,"IEEE Trans. Comput., vol. C-36, no. 6, June 1987.
[11] V. Grassi, L. Donatiello, and G. Iazeolla, "Performability Evaluation of Multicomponent Fault-Tolerant Systems,"IEEE Trans. Reliability, Vol. 37, June 1988, pp. 216-222.
[12] W. K. Grassmann "Transient solutions in Markovian queueing systems,"Comput. Oper. Res., vol. 4, pp. 47-53, 1977.
[13] D. Gross and D. R. Miller, "The randomization technique as a modeling tool and solution procedure for transient Markov processes,"Oper. Res., vol. 31, pp. 343-361, 1984.
[14] R.A. Howard,Dynamic Probabilistic Systems. New York: Wiley, 1971.
[15] R. Huslende, "A combined evaluation of performance and reliability for degradable computer systems,"Perform. Eval. Rev., vol. 3, pp. 157-164, 1981.
[16] B. R. Iyer, L. Donatiello and P. Heidelberger, "Analysis of performability for stochastic models of fault-tolerant systems,"IEEE Trans. Comput., vol. C-35, no. 10, Oct. 1986.
[17] V. G. Kulkarni, V. F. Nicola, and K. S. Trivedi, "On modelling the performance and reliability of multi-mode computer systems," inInt. Workshop Modelling and Perform. Eval. Parallel Sys., M. Becker, Ed., North Holland, Amsterdam.
[18] V. G. Kulkarni, V. F. Nicola, R. M. Smith, and K. S. Trivedi, "Numerical evaluation of performability and job completion time in repairable fault-tolerant systems," inProc. FTCS-16, Vienna, Austria, 1986, pp. 252-257.
[19] J. F. Meyer, "Closed form solution of performability,"IEEE Trans. Comput., vol. C-31, pp. 648-657, 1982.
[20] D. P. Siewiorek and R. S. Swarz,The Theory and Practice of Reliable System Design. Bedford, MA: Digital, 1987.
[21] R. M. Smith, K. S. Trivedi, and A. V. Ramesh "Performability analysis: Measures, an algorithm, and a case study,"IEEE Trans. Comput., vol. 37, pp. 406-417, Apr. 1988.

Index Terms:
repairable systems; time complexity; cumulative performance distribution; fault-tolerant computer systems; system fault-repair behavior; homogeneous Markov process; probability distribution; nonrepairable systems; low polynomial computational complexity; mathematical model; space complexity; computational complexity; fault tolerant computing; Markov processes; performance evaluation; probability.
Citation:
L. Donatiello, V. Grassi, "On Evaluating the Cumulative Performance Distribution of Fault-Tolerant Computer Systems," IEEE Transactions on Computers, vol. 40, no. 11, pp. 1301-1307, Nov. 1991, doi:10.1109/12.102838
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