Abstract
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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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