A new general-purpose method for the computation of the interval availability distribution

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.Preprin

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Efficient implementations of the randomization method with control of the relative error

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 Markovchains 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

Efficient implementations of the randomization method with control of the relative error

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 Markovchains 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