Hybrid reliability modeling of fault-tolerant computer systems
Computers and Electrical Engineering - Special issue: reliability and verification of computing systems
Provably Conservative Approximations to Complex Reliability Models
IEEE Transactions on Computers - The MIT Press scientific computation series
SIAM Journal on Algebraic and Discrete Methods
Journal of the ACM (JACM)
Bounding Availability of Repairable Systems
IEEE Transactions on Computers
Truncation of Markov chains with applications to queueing
Operations Research
Introduction to matrix analysis (2nd ed.)
Introduction to matrix analysis (2nd ed.)
Probability and Statistics with Reliability, Queuing and Computer Science Applications
Probability and Statistics with Reliability, Queuing and Computer Science Applications
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We consider the sensitivity of transient solutions of Markov models to perturbations in their generator matrices. The perturbations can either be of a certain structure or can be very general. We consider two different measures of sensitivity and derive upper bounds on them. The derived bounds are sharper than previously reported bounds in the literature. Since the sensitivity analysis of transient solutions is intimately related to the condition of the exponential of the CTMC matrix, we derive an expression for the condition number of the CTMC matrix exponential which leads to some interesting implications. We compare the derived sensitivity bounds both numerically and analytically with those reported in the literature.