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The Resource Kronecker modeling and analysis of multidimensional Markovian systems, Tuğrul Dayar

Kronecker modeling and analysis of multidimensional Markovian systems, Tuğrul Dayar

Creator
Author
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.--
Language
eng
Work
Publication
Extent
1 online resource.
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
Isbn
9783319971292
Instance
Label
Kronecker modeling and analysis of multidimensional Markovian systems
Title
Kronecker modeling and analysis of multidimensional Markovian systems
Statement of responsibility
Tuğrul Dayar
Creator
Author
Subject
Language
eng
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.--
Member of
Assigning source
Provided by publisher
Cataloging source
N$T
http://library.link/vocab/creatorName
Dayar, Tuğrul
Dewey number
519.233
Index
index present
LC call number
QA188
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Springer series in operations research and financial engineering
http://library.link/vocab/subjectName
  • Kronecker products
  • Markov processes
Label
Kronecker modeling and analysis of multidimensional Markovian systems, Tuğrul Dayar
Instantiates
Publication
Copyright
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9783319971292
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-97129-2
http://library.link/vocab/ext/overdrive/overdriveId
com.springer.onix.9783319971292
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • on1054129007
  • (OCoLC)1054129007
Label
Kronecker modeling and analysis of multidimensional Markovian systems, Tuğrul Dayar
Publication
Copyright
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9783319971292
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-97129-2
http://library.link/vocab/ext/overdrive/overdriveId
com.springer.onix.9783319971292
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • on1054129007
  • (OCoLC)1054129007

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