Hybrid reliability modeling of fault-tolerant computer systems
Computers and Electrical Engineering - Special issue: reliability and verification of computing systems
Computational geometry: an introduction
Computational geometry: an introduction
A hybrid, combinatorial-Markov method of solving performance and reliability models
A hybrid, combinatorial-Markov method of solving performance and reliability models
Transient analysis of acyclic markov chains
Performance Evaluation
Performability Analysis: Measures, an Algorithm, and a Case Study
IEEE Transactions on Computers - Fault-Tolerant Computing
The algebraic eigenvalue problem
The algebraic eigenvalue problem
On Reliability Modeling of Closed Fault-Tolerant Computer Systems
IEEE Transactions on Computers
Reliability evaluation of fault-tolerant computing systems and networks
Reliability evaluation of fault-tolerant computing systems and networks
An Algorithm for Numerical Computation of the Jordan Normal Form of a Complex Matrix
ACM Transactions on Mathematical Software (TOMS)
Probability and Statistics with Reliability, Queuing and Computer Science Applications
Probability and Statistics with Reliability, Queuing and Computer Science Applications
Semi-numerical Solution of Stochastic Process Algebra Models
ARTS '99 Proceedings of the 5th International AMAST Workshop on Formal Methods for Real-Time and Probabilistic Systems
SHARPE at the age of twenty two
ACM SIGMETRICS Performance Evaluation Review
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We present a new O(n3) algorithm for seminumerical transient analysis of continuous time Markov chains with n states. The algorithm is based on spectral decomposition of the transition rate matrix in combination with partial fraction expansion based on Laplace transforms. The algorithm acknowledges the inherent numerical difficulties associated with illconditioned problems and finite machine precision by incorporating a realistic assessment of the condition and sensitivity of the problem. It is more efficient and provides more accurate solutions in the face of round-off error when compared to similar algorithms in the literature. We demonstrate the performance of the algorithm on many ill-conditioned applications.