Moments' analysis in homogeneous Markov reward models
type: Item
instance of: scholarly article
title: Moments' analysis in homogeneous Markov reward models
zbMATH Open document ID: 1187.60055
author: Guillaume Dujardin
author: Francois Castella
author: Bruno Sericola
published in: Methodology and Computing in Applied Probability
publication date: 2009-12-02T00:00:00Z
review text: Let \(X=(X_t:\, t\geq 0)\) be a continuous-time Markov process with finite state space \(S\), and let \(f:S\to \mathbb{R}\) be a reward function. The (normalized) accumulated reward over time interval \((0,t)\) is defined by \[ Y_t=\frac{1}{t\|f\|_{\infty}} \int_0^t f(X_s)\, ds\, . \] This paper deals with numerical computation of the moments of \(Y_t\). The proposed algorithm depends on the uniformization method which reduces the computation of moments to computation of certain coefficients \(U_i(n,r)\). By analyzing convergence of those coefficients as \(n\to \infty\) (\textit{stationarity detection}), the authors derive an improved procedure for the numerical computation of first moments. The paper concludes with an example dealing with fault-tolerant multiprocessor system.
Mathematics Subject Classification ID: 60J22
Mathematics Subject Classification ID: 60J27
zbMATH DE Number: 5641456
zbMATH Keywords: Markov models
zbMATH Keywords: accumulated reward
zbMATH Keywords: performability
zbMATH Keywords: uniformization
reviewed by: Zoran Vondraček
MaRDI profile type: Publication
full work available at URL: s11009-008-9075-5
OpenAlex ID: W2009083477
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DOI: 10.1007/S11009-008-9075-5
description: scientific article; zbMATH DE number 5641456