On the effects of using the Grassmann-Taksar-Heyman method in iterative aggregation-disaggregation

Iterative aggregation-disaggregation (IAD) is an effective method for solving finite nearly completely decomposable (NCD) Markov chains. Small perturbations in the transition probabilities of these chains may lead to considerable changes in the stationary probabilities; NCD Markov chains are known to be ill-conditioned. During an IAD step, this undesirable condition is inherited by the coupling matrix and one confronts the problem of finding the stationary probabilities of a stochastic matrix whose diagonal elements are close to 1. In this paper, the effects of using the Grassmann-Taksar-Heyman (GTH) method to solve the coupling matrix formed in the aggregation step are investigated. Then the idea is extended in such a way that the same direct method can be incorporated into the disaggregation step. Finally, the effects of using the GTH method in the IAD algorithm on various examples are demonstrated, and the conditions under which it should be employed are explained

Iterative disaggregation for a class of lumpable discrete-time stochastic automata networks

Cataloged from PDF version of article.Stochastic automata networks (SANs) have been developed and used in the last 15 years as a modeling formalism for large systems that can be decomposed into loosely connected components. In this work, we concentrate on the not so much emphasized discrete-time SANs. First, we remodel and extend an SAN that arises in wireless communications. Second, for an SAN with functional transitions, we derive conditions for a special case of ordinary lumpability in which aggregation is done automaton by automaton. Finally, for this class of lumpable discrete-time SANs we devise an efficient aggregation–iterative disaggregation algorithm and demonstrate its performance on the SAN model of interest. © 2002 Elsevier Science B.V. All rights reserved

On the Effects of Using the Grassmann-Taksar-Heyman Method in Iterative Aggregation-Disaggregation

Iterative aggregation-disaggregation (IAD) is an effective method for solving finite nearly completely decomposable (NCD) Markov chains. Small perturbations in the transition probabilities of these chains may lead to considerable changes in the stationary probabilities; NCD Markov chains are known to be ill-conditioned. During an IAD step, this undesirable condition is inherited by the coupling matrix and one confronts the problem of finding the stationary probabilities of a stochastic matrix whose diagonal elements are close to 1. In this paper, the effects of using the Grassmann-Taksar-Heyman (GTH) method to solve the coupling matrix formed in the aggregation step are investigated. Then, the idea is extended in such a way that the same direct method can be incorporated into the disaggregation step. Finally, the effects of using the GTH method in the IAD algorithm on various examples are demonstrated, and the conditions under which it should be employed are explained

Experiments with two-stage iterative solvers and preconditioned Krylov subspace methods on nearly completely decomposable Markov chains

Ankara : Department of Computer Engineering and Information Science and the Institute of Engineering and Science of Bilkent University, 1997.Thesis (Master's) -- Bilkent University, 1997.Includes bibliographical references leaves 121-124Gueaieb, WailM.S