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Graph-theoretic approach in Gaussian elimination and queueing analysis.

by Tang Chi Nang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 104-[109]). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Gaussian elimination --- p.2 / Chapter 1.1.1 --- Numerical stability --- p.2 / Chapter 1.2 --- Block Gaussian elimination --- p.3 / Chapter 1.2.1 --- Numerical stability --- p.4 / Chapter 1.3 --- Elimination graph --- p.4 / Chapter 1.4 --- Elimination ordering --- p.5 / Chapter 1.5 --- Computation and storage requirement --- p.6 / Chapter 1.6 --- Outline of the thesis --- p.7 / Chapter 2 --- Weighted graph elimination --- p.8 / Chapter 2.1 --- Weighted elimination graph --- p.8 / Chapter 2.2 --- Sparse Gaussian elimination --- p.9 / Chapter 2.3 --- Computation and storage requirement --- p.12 / Chapter 2.3.1 --- Computation requirement --- p.12 / Chapter 2.3.2 --- Storage requirement --- p.14 / Chapter 2.4 --- Elimination ordering --- p.15 / Chapter 2.5 --- Repeated structure --- p.18 / Chapter 3 --- Main theory --- p.21 / Chapter 3.1 --- Motivation --- p.21 / Chapter 3.2 --- Notations --- p.22 / Chapter 3.2.1 --- Connectivity --- p.23 / Chapter 3.2.2 --- Separator --- p.23 / Chapter 3.2.3 --- Equivalence --- p.24 / Chapter 3.3 --- Repetition separator --- p.25 / Chapter 3.4 --- Repetition elimination process --- p.30 / Chapter 3.5 --- Multiple Separators --- p.32 / Chapter 3.6 --- Feasibility --- p.33 / Chapter 3.6.1 --- Two-separator case --- p.34 / Chapter 3.6.2 --- General case --- p.39 / Chapter 3.6.3 --- Successive repetition elimination process (SREP) --- p.41 / Chapter 3.7 --- Generalized repetition elimination process --- p.42 / Chapter 3.7.1 --- Extra edges --- p.42 / Chapter 3.7.2 --- Acyclic edges --- p.43 / Chapter 3.7.3 --- Generalized repetition separator --- p.45 / Chapter 4 --- Application in queueing analysis --- p.52 / Chapter 4.1 --- Markov Chain Reduction Principle --- p.54 / Chapter 4.1.1 --- Numerical stability --- p.57 / Chapter 4.2 --- Multi-class MMPP/M/1/L queue --- p.57 / Chapter 4.2.1 --- Single-class case (QBD case) --- p.58 / Chapter 4.2.2 --- Preemptive LCFS case --- p.63 / Chapter 4.2.3 --- Non-preemptive LCFS case --- p.70 / Chapter 4.2.4 --- FCFS case --- p.72 / Chapter 4.2.5 --- Extension to phase type service time --- p.77 / Chapter 4.3 --- 2-class priority system --- p.77 / Chapter 5 --- Choosing the right algorithm --- p.85 / Chapter 5.1 --- MMPP/M/1/L system with bursty arrival --- p.86 / Chapter 5.1.1 --- Algorithm Comparison --- p.89 / Chapter 5.1.2 --- Numerical Examples --- p.90 / Chapter 5.2 2 --- -class priority system --- p.90 / Chapter 5.2.1 --- Algorithm Comparison --- p.95 / Chapter 5.2.2 --- Numerical Examples --- p.95 / Chapter 5.3 --- Conclusion --- p.95 / Chapter 6 --- Conclusion --- p.98 / Chapter 6.1 --- Further research --- p.99 / Chapter A --- List of frequently-used notations --- p.101 / Chapter A.l --- System of equations and Digraph --- p.101 / Chapter A.2 --- General-purpose functions --- p.102 / Chapter A.3 --- Single repetition separator --- p.102 / Chapter A.4 --- Sequence of repetition separators --- p.103 / Chapter A.5 --- Compatibility --- p.103 / Bibliography --- p.104

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_320656
Date January 1995
ContributorsTang, Chi Nang., Chinese University of Hong Kong Graduate School. Division of Information Engineering.
PublisherChinese University of Hong Kong
Source SetsThe Chinese University of Hong Kong
LanguageEnglish
Detected LanguageEnglish
TypeText, bibliography
Formatprint, x, 104, [5] leaves : ill. ; 30 cm.
RightsUse of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

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