| Description |
1 online resource |
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text file |
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PDF |
| Series |
Springer series in operations research and financial engineering
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Springer series in operations research.
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| Bibliography |
Includes bibliographical references and index. |
| 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. |
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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. |
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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. |
| Summary |
This work considers Kronecker-based models with finite as well as countably infinite state spaces for multidimensional Markovian systems by paying particular attention to those whose reachable state spaces are smaller than their product state spaces. Numerical methods for steady-state and transient analysis of Kronecker-based multidimensional Markovian models are discussed in detail together with implementation issues. Case studies are provided to explain concepts and motivate use of methods. Having grown out of research from the past twenty years, this book expands upon the author's previously published book Analyzing Markov Chains using Kronecker Products (Springer, 2012). The subject matter is interdisciplinary and at the intersection of applied mathematics and computer science. The book will be of use to researchers and graduate students with an understanding of basic linear algebra, probability, and discrete mathematics.-- Provided by publisher. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Kronecker products.
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Markov processes.
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Numerical analysis. |
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Systems analysis & design. |
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Probability & statistics. |
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MATHEMATICS -- Applied. |
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MATHEMATICS -- Probability & Statistics -- General. |
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Análisis numérico |
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Markov, Procesos de |
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Kronecker products |
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Markov processes |
| Other Form: |
Print version: Dayar, Tuğrul. Kronecker modeling and analysis of multidimensional Markovian systems. Cham, Switzerland : Springer, [2018] 331997128X 9783319971285 (OCoLC)1042078723 |
| ISBN |
9783319971292 (electronic bk.) |
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3319971298 (electronic bk.) |
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9783319971308 (print) |
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3319971301 |
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9783319971285 |
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331997128X |
| Standard No. |
10.1007/978-3-319-97129-2 |
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