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K.R. Pattipati, S.A. Shah, "On the Computational Aspects of Performability Models of FaultTolerant Computer Systems," IEEE Transactions on Computers, vol. 39, no. 6, pp. 832836, June, 1990.  
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@article{ 10.1109/12.53605, author = {K.R. Pattipati and S.A. Shah}, title = {On the Computational Aspects of Performability Models of FaultTolerant Computer Systems}, journal ={IEEE Transactions on Computers}, volume = {39}, number = {6}, issn = {00189340}, year = {1990}, pages = {832836}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.53605}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  On the Computational Aspects of Performability Models of FaultTolerant Computer Systems IS  6 SN  00189340 SP832 EP836 EPD  832836 A1  K.R. Pattipati, A1  S.A. Shah, PY  1990 KW  scaled conditional moments; computational aspects; performability models; faulttolerant computer systems; Markov models; continuoustime dynamic system; finite mission time; cascaded system representation; stable algorithms; doubling algorithm; diagonal Pade approximation; reliability; availability models; approximation theory; fault tolerant computing; Markov processes. VL  39 JA  IEEE Transactions on Computers ER   
It is shown that the (scaled) conditional moments of performability in Markov models are the states of a cascaded, linear, continuoustime dynamic system with identical system matrices in each stage. This interpretation leads to a simple method of computing the first moment for nonhomogeneous Markov models with finite mission time. In addition, the cascaded system representation leads to the derivation of a set of two stable algorithms for propagating the conditional moments of performability in homogeneous Markov models. In particular, a very fast doubling algorithm using diagonal Pade approximation to compute the matrix exponential and repeated squaring is derived. The algorithms are widely recognized, to be superior to those based on eigenvalue analysis in terms of both the computational efficiency and stability. The algorithms have obvious implications in solving reliability/availability models with large mission times.
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