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
Computing Poisson probabilities
Communications of the ACM
A Measure of Guaranteed Availability and its Numerical Evaluation
IEEE Transactions on Computers
Numerical transient analysis of Markov models
Computers and Operations Research
Performability Analysis: Measures, an Algorithm, and a Case Study
IEEE Transactions on Computers - Fault-Tolerant Computing
Journal of the ACM (JACM)
On Evaluating the Cumulative Performance Distribution of Fault-Tolerant Computer Systems
IEEE Transactions on Computers
Interval availability analysis using operational periods
Performance Evaluation - Special issue on performability modelling of computer and communication systems
Rounding errors in certain algorithms involving Markov chains
ACM Transactions on Mathematical Software (TOMS)
IEEE Transactions on Computers - Special issue on fault-tolerant computing
Performability Analysis: A New Algorithm
IEEE Transactions on Computers
Availability Analysis of Repairable Computer Systems and Stationarity Detection
IEEE Transactions on Computers
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
A Unified Framework for the Performability Evaluation of Fault-Tolerant Computer Systems
IEEE Transactions on Computers
MRMSolve: Distribution Estimation of Large Markov Reward Models
TOOLS '02 Proceedings of the 12th International Conference on Computer Performance Evaluation, Modelling Techniques and Tools
Computers and Operations Research
A new methodology for calculating distributions of reward accumulated during a finite interval
FTCS '96 Proceedings of the The Twenty-Sixth Annual International Symposium on Fault-Tolerant Computing (FTCS '96)
Solving large interval availability models using a model transformation approach
Computers and Operations Research
IEEE Transactions on Computers
Efficient implementations of the randomization method with control of the relative error
Computers and Operations Research
Comment on "Performability Analysis: A New Algorithm”
IEEE Transactions on Computers
INFORMS Journal on Computing
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We develop a new randomization-based general-purpose method for the computation of the interval availability distribution of systems modeled by continuous-time Markov chains CTMCs. The basic idea of the new method is the use of a randomization construct with different randomization rates for up and down states. The new method is numerically stable and computes the measure with well-controlled truncation error. In addition, for large CTMC models, when the maximum output rates from up and down states are significantly different, and when the interval availability has to be guaranteed to have a level close to one, the new method is significantly or moderately less costly in terms of CPU time than a previous randomization-based state-of-the-art method, depending on whether the maximum output rate from down states is larger than the maximum output rate from up states, or vice versa. Otherwise, the new method can be more costly, but a relatively inexpensive for large models switch of reasonable quality can be easily developed to choose the fastest method. Along the way, we show the correctness of a generalized randomization construct, in which arbitrarily different randomization rates can be associated with different states, for both finite CTMCs with infinitesimal generator and uniformizable CTMCs with denumerable state space.