Calculating Cumulative Operational Time Distributions of Repairable Computer Systems
IEEE Transactions on Computers - The MIT Press scientific computation series
A Measure of Guaranteed Availability and its Numerical Evaluation
IEEE Transactions on Computers
Design & analysis of fault tolerant digital systems
Design & analysis of fault tolerant digital systems
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
Modeling and analysis of stochastic systems
Modeling and analysis of stochastic systems
Solving large interval availability models using a model transformation approach
Computers and Operations Research
A New General-Purpose Method for the Computation of the Interval Availability Distribution
INFORMS Journal on Computing
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This paper is concerned with the computation of the interval availability (proportion of time in a time interval in which the system is up) distribution of a fault-tolerant system modeled by a finite (homogeneous) continuous-time Markov chain (CTMC). General-purpose methods for performing that computation tend to be very expensive when the CTMC and the time interval are large. Based on a previously available method (regenerative transformation) for computing the interval availability complementary distribution, we develop a method called bounding regenerative transformation for the computation of bounds for that measure. Similar to regenerative transformation, bounding regenerative transformation requires the selection of a regenerative state. The method is targeted at a certain class of models, including both exact and bounding failure/repair models of fault-tolerant systems with increasing structure function, with exponential failure and repair time distributions and repair in every state with failed components having failure rates much smaller than repair rates (F/R models), with a “natural” selection for the regenerative state. The method is numerically stable and computes the bounds with well-controlled error. For models in the targeted class and the natural selection for the regenerative state, computational cost should be traded off with bounds tightness through a control parameter. For large models in the class, the version of the method that should have the smallest computational cost should have small computational cost relative to the model size if the value above which the interval availability has to be guaranteed to be is close to 1. In addition, under additional conditions satisfied by F/R models, the bounds obtained with the natural selection for the regenerative state by the version that should have the smallest computational cost seem to be tight for all time intervals or not small time intervals, depending on whether the initial probability distribution of the CTMC is concentrated in the regenerative state or not. CORRECTED VERSION OF RECORD, SEE LAST PAGE OF ARTICLE