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
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)
Rounding errors in certain algorithms involving Markov chains
ACM Transactions on Mathematical Software (TOMS)
IEEE Transactions on Computers - Special issue on fault-tolerant computing
A computationally efficient technique for transient analysis of repairable Markovian systems
Performance Evaluation
Performability Analysis: A New Algorithm
IEEE Transactions on Computers
Availability Analysis of Repairable Computer Systems and Stationarity Detection
IEEE Transactions on Computers
Performability Modeling with UltraSAN
IEEE Software
SPNP: Stochastic Petri Net Package
PNPM '89 The Proceedings of the Third International Workshop on Petri Nets and Performance Models
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
IEEE Transactions on Computers
Efficient implementations of the randomization method with control of the relative error
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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In this paper we generalize a method (called regenerative randomization) for the transient solution of continuous time Markov models. The generalized method allows to compute two transient measures (the expected transient reward rate and the expected averaged reward rate) for rewarded continuous time Markov models with a structure covering bounding models which are useful when a complete, exact model has unmanageable size. The method has the same good properties as the well-known (standard) randomization method: numerical stability, well-controlled computation error, and ability to specify the computation error in advance, and, for large enough models and long enough times, is significantly faster than the standard randomization method. The method requires the selection of a regenerative state and its performance depends on that selection. For a class of models, class C', including typical failure/repair models with exponential failure and repair time distributions and repair in every state with failed components, a natural selection for the regenerative state exists, and results are available assessing approximately 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 significantly faster than standard randomization for models in that class. The potentially superior efficiency of the regenerative randomization method compared to standard randomization for models not in class C' is illustrated using a large performability model of a fault-tolerant multiprocessor system.