Boundary value methods for transient solutions of Markovian queueing networks.

by Ma Ka Chun.Thesis (M.Phil.)--Chinese University of Hong Kong, 2004.Includes bibliographical references (leaves 50-52).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.7Chapter 2 --- Queueing Networks --- p.9Chapter 2.1 --- One-queue Networks --- p.9Chapter 2.2 --- Two-queue Free Networks --- p.12Chapter 2.3 --- Two-queue Overflow Networks --- p.13Chapter 2.4 --- Networks with Batch Arrivals --- p.14Chapter 3 --- ODE Solvers --- p.16Chapter 3.1 --- The Initial Value Methods --- p.16Chapter 3.1.1 --- The Linear System of Ordinary Differential Equations --- p.16Chapter 3.1.2 --- Euler's Method --- p.17Chapter 3.1.3 --- Runge-Kutta Methods --- p.17Chapter 3.1.4 --- The Stability of the IVMs --- p.19Chapter 3.1.5 --- Applications in Queueing Networks --- p.20Chapter 3.2 --- The Boundary Value Methods --- p.20Chapter 3.2.1 --- The Generalized Backward Differentiation For- mulae --- p.21Chapter 3.2.2 --- An example --- p.24Chapter 4 --- The Linear Equation Solver --- p.26Chapter 4.1 --- Iterative Methods --- p.26Chapter 4.1.1 --- The Jacobi method --- p.27Chapter 4.1.2 --- The Gauss-Seidel Method --- p.28Chapter 4.1.3 --- Other Iterative Methods --- p.29Chapter 4.1.4 --- Preconditioning --- p.29Chapter 4.2 --- The Multigrid Method --- p.30Chapter 4.2.1 --- Iterative Refinement --- p.30Chapter 4.2.2 --- Restriction and Prolongation --- p.30Chapter 4.2.3 --- The Geometric Multigrid Method --- p.33Chapter 4.2.4 --- The Algebraic Multigrid Method --- p.38Chapter 4.2.5 --- Higher Dimensional Cases --- p.38Chapter 4.2.6 --- Applications in Queueing Networks --- p.38Chapter 5 --- Numerical Experiments --- p.41Chapter 6 --- Concluding Remarks --- p.49Bibliography --- p.5

Zero-automatic queues and product form

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A tool for model-checking Markov chains

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