Calculating Cumulative Operational Time Distributions of Repairable Computer Systems
IEEE Transactions on Computers - The MIT Press scientific computation series
Computation of the chi square and Poisson distribution
SIAM Journal on Scientific and Statistical Computing
A Measure of Guaranteed Availability and its Numerical Evaluation
IEEE Transactions on Computers
State space exploration in Markov models
SIGMETRICS '92/PERFORMANCE '92 Proceedings of the 1992 ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
Interval availability analysis using operational periods
Performance Evaluation - Special issue on performability modelling of computer and communication systems
IEEE Transactions on Computers - Special issue on fault-tolerant computing
The Cost of Eliminating Vanishing Markings from Generalized Stochastic Petri Nets
PNPM '89 The Proceedings of the Third International Workshop on Petri Nets and Performance Models
State probability of a series-parallel repairable system with two-types of failure states
International Journal of Systems Science
INFORMS Journal on Computing
INFORMS Journal on Computing
A New General-Purpose Method for the Computation of the Interval Availability Distribution
INFORMS Journal on Computing
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Fault-tolerant systems are often modeled using (homogeneous) continuous time Markov chains (CTMCs). Computation of the distribution of the interval availability, i.e. of the distribution of the fraction of time in a time interval in which the system is operational, of a fault-tolerant system modeled by a CTMC is an important problem which has received attention recently. However, currently available methods to perform that computation are very expensive for large models and large time intervals. In this paper, we develop a new method to compute the distribution of the interval availability which, for large enough models and large enough time intervals, is significantly faster than previous methods. In the method, a truncated transformed model, which has with some arbitrarily small error the same interval availability distribution as the original model, is obtained from the original model and the truncated transformed model is solved using a previous state-of-the-art method. The method requires the selection of a "regenerative" state and its performance depends on that selection. For a class of models, including typical failure/repair models of coherent fault-tolerant systems with exponential failure and repair time distributions and repair in every state with failed components, a natural selection for the regenerative state exists and theoretical results are available assessing the performance of the method for that natural selection in terms of "Visible" model characteristics. Those results can be used to anticipate when the method can be expected to be competitive for models in that class. Numerical results are presented showing that the new method can indeed be significantly faster than a previous state-of-the-art method and is able to deal with some large models and large time intervals in reasonable CPU times.