Implicit ODE solvers with good local error control for the transient analysis of Markov models

Obtaining the transient probability distribution vector of a continuous-time Markov chain (CTMC) using an implicit ordinary differential equation (ODE) solver tends to be advantageous in terms of run-time computational cost when the product of the maximum output rate of the CTMC and the largest time of interest is large. In this paper, we show that when applied to the transient analysis of CTMCs, many implicit ODE solvers are such that the linear systems involved in their steps can be solved by using iterative methods with strict control of the 1-norm of the error. This allows the development of implementations of those ODE solvers for the transient analysis of CTMCs that can be more efficient and more accurate than more standard implementations.Peer ReviewedPostprint (published version

A comparison of numerical splitting-based methods for Markovian dependability and performability models

Iterative numerical methods are an important ingredient for the solution of continuous time Markov dependability models of fault-tolerant systems. In this paper we make a numerical comparison of several splitting-based iterative methods. We consider the computation of steady-state reward rate on rewarded models. This measure requires the solution of a singular linear system. We consider two classes of models. The first class includes failure/repair models. The second class is more general and includes the modeling of periodic preventive test of spare components to reduce the probability of latent failures in inactive components. The periodic preventive test is approximated by an Erlang distribution with enough number of stages. We show that for each class of model there is a splitting-based method which is significantly more efficient than the other methods.Postprint (published version

Ressenyes

Obra ressenyada: Søren KIERKEGAARD, Temor i tremolor. Edició i traducció de Begonya Sáez Tajafuerce. Barcelona: Marbot, 2012

Onde criar as terneiras?

Localização das instalações; Temperaturas; Lotação; Instalações mais utilizadas; Material necessário para construção de uma casinha.bitstream/item/67186/1/CT-52-2002.pd