Tez No	İndirme	Tez Künye	Durumu
400684		Stability and conditioning issues on the numerical solution of Markov chains / Yazar:TUĞRUL DAYAR Danışman: DR. WILLIAM J. STEWART Yer Bilgisi: North Carolina State University / Yurtdışı Enstitü Konu:Bilgisayar Mühendisliği Bilimleri-Bilgisayar ve Kontrol = Computer Engineering and Computer Science and Control Dizin:	Onaylandı Doktora İngilizce 1994 126 s.
Markovian modeling and analysis is extensively used in many disciplines in evaluating the performance of existing systems and in analyzing and designing systems to be developed. In most cases the systems under consideration are large, and therefore require the employment of numerical solution techniques. With the changing face of computing environments, there are several issues that need to be addressed in the numerical solution of Markov chains. Firstly, stability and conditioning issues in the solution of such large systems has to be of concern, and one should be in the lookout for algorithms that are more efficient and that produce more accurate results. This may be achieved by improving existing algorithms or developing new ones that take advantage of the increased computer power. In this thesis, the effects of using a modified version of Gaussian elimination in the iterative aggregation-disaggregation technique, which is especially suited to the solution of ill-conditioned nearly completely decomposable Markov chains, has been investigated. A second solution technique geared towards multivector computers has been extended to include the systems of interest. A third solution technique, which is useful in handling vast state spaces, is shown to be effective in computing performance measures for systems having highly unbalanced stationary probabilities. Experiments on real-life applications (involving mostly large systems) have been conducted in each case. Finally, the possibility of reducing the state space size by combining states in nearly completely decomposable chains is discussed.