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
Median bounds and their application
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Availability Analysis of Repairable Computer Systems and Stationarity Detection
IEEE Transactions on Computers
IEEE Transactions on Computers
Computers and Operations Research
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
A New General-Purpose Method for the Computation of the Interval Availability Distribution
INFORMS Journal on Computing
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Randomization is a well-known numerical method for the transient analysis of continuous-time Markov chains. The main advantages of the method are numerical stability, well-controlled computation error and ability to specify the computation error in advance. Typical implementations of the method control the truncation error in absolute value, which is not completely satisfactory in some cases. Based on a theoretical result regarding the dependence on the parameter of the Poisson distribution of the relative error introduced when a weighted sum of Poisson probabilities is truncated by the right, in this paper we develop efficient and numerically stable implementations of the randomization method for the computation of two measures on rewarded continuous-time Markov chains with control of the relative error. The numerical stability of those implementations is analyzed using a small example. We also discuss the computational efficiency of the implementations with respect to simpler alternatives.