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Table of Contents
Intro; Preface; Contents; List of Figures; List of Tables; List of Symbols; 1 Introduction; 2 Modeling with Kronecker Products; 2.1 Stochastic Automata Networks; 2.2 Hierarchical Markovian Models; 2.3 Two Kronecker-Structured Models; 2.3.1 An Availability Model; 2.3.2 A Polling Model; 3 Avoiding Unreachable States; 3.1 Merge-Based Algorithm; 3.2 Refinement-Based Algorithm; 3.3 Two Other Kronecker-Structured Models; 3.3.1 A Production Line Model; 3.3.2 A Communications Protocol Model; 3.4 Specification of Kronecker-Structured CTMCs; 3.5 Comparison of Cartesian Product Partitioning Algorithms.
4 Preprocessing4.1 Reordering and Grouping; 4.2 Lumping; 4.3 Analyzing Diagonal Blocks for Common Schur Factors; 4.4 Handling Countable Infiniteness for Steady-State; 4.4.1 A Metabolite Synthesis Model; 4.4.2 A Call Center Model; 4.4.3 A Retrial Queueing Model; 5 Vector-Kronecker Product Multiplication; 5.1 Shuffle Algorithm; 5.2 Modified Shuffle Algorithm; 5.3 Working with Compact Solution Vectors; 6 Steady-State Analysis; 6.1 Block Iterative Methods; 6.2 Preconditioned Projection Methods; 6.3 Multilevel Methods; 6.4 Decompositional Methods; 6.5 Matrix Analytic Methods.
6.6 Working with Compact Solution Vectors7 Transient Analysis; 7.1 Uniformization; 7.2 Ordinary Differential Equation Solvers; 7.2.1 Runge-Kutta Methods; 7.2.2 Backward Differentiation Formulae; 7.3 Working with Countably Infinite State Spaces; 7.3.1 A Cascade Model; 7.3.2 State Space Truncation and Compact Solution Vectors; 8 Conclusion; References; Index.
4 Preprocessing4.1 Reordering and Grouping; 4.2 Lumping; 4.3 Analyzing Diagonal Blocks for Common Schur Factors; 4.4 Handling Countable Infiniteness for Steady-State; 4.4.1 A Metabolite Synthesis Model; 4.4.2 A Call Center Model; 4.4.3 A Retrial Queueing Model; 5 Vector-Kronecker Product Multiplication; 5.1 Shuffle Algorithm; 5.2 Modified Shuffle Algorithm; 5.3 Working with Compact Solution Vectors; 6 Steady-State Analysis; 6.1 Block Iterative Methods; 6.2 Preconditioned Projection Methods; 6.3 Multilevel Methods; 6.4 Decompositional Methods; 6.5 Matrix Analytic Methods.
6.6 Working with Compact Solution Vectors7 Transient Analysis; 7.1 Uniformization; 7.2 Ordinary Differential Equation Solvers; 7.2.1 Runge-Kutta Methods; 7.2.2 Backward Differentiation Formulae; 7.3 Working with Countably Infinite State Spaces; 7.3.1 A Cascade Model; 7.3.2 State Space Truncation and Compact Solution Vectors; 8 Conclusion; References; Index.