Analyzing Markov Chains Using Kronecker Products
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Analyzing Markov Chains Using Kronecker Products
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Author : Tugrul Dayar
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-07-25
Analyzing Markov Chains Using Kronecker Products written by Tugrul Dayar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-25 with Mathematics categories.
Kronecker products are used to define the underlying Markov chain (MC) in various modeling formalisms, including compositional Markovian models, hierarchical Markovian models, and stochastic process algebras. The motivation behind using a Kronecker structured representation rather than a flat one is to alleviate the storage requirements associated with the MC. With this approach, systems that are an order of magnitude larger can be analyzed on the same platform. The developments in the solution of such MCs are reviewed from an algebraic point of view and possible areas for further research are indicated with an emphasis on preprocessing using reordering, grouping, and lumping and numerical analysis using block iterative, preconditioned projection, multilevel, decompositional, and matrix analytic methods. Case studies from closed queueing networks and stochastic chemical kinetics are provided to motivate decompositional and matrix analytic methods, respectively.
Kronecker Modeling And Analysis Of Multidimensional Markovian Systems
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Author : Tuğrul Dayar
language : en
Publisher: Springer
Release Date : 2018-09-21
Kronecker Modeling And Analysis Of Multidimensional Markovian Systems written by Tuğrul Dayar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-21 with Mathematics categories.
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.
Introduction To Matrix Analytic Methods In Queues 1
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Author : Srinivas R. Chakravarthy
language : en
Publisher: John Wiley & Sons
Release Date : 2022-09-21
Introduction To Matrix Analytic Methods In Queues 1 written by Srinivas R. Chakravarthy and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-21 with Mathematics categories.
Matrix-analytic methods (MAM) were introduced by Professor Marcel Neuts and have been applied to a variety of stochastic models since. In order to provide a clear and deep understanding of MAM while showing their power, this book presents MAM concepts and explains the results using a number of worked-out examples. This book’s approach will inform and kindle the interest of researchers attracted to this fertile field. To allow readers to practice and gain experience in the algorithmic and computational procedures of MAM, Introduction to Matrix Analytic Methods in Queues 1 provides a number of computational exercises. It also incorporates simulation as another tool for studying complex stochastic models, especially when the state space of the underlying stochastic models under analytic study grows exponentially. The book’s detailed approach will make it more accessible for readers interested in learning about MAM in stochastic models.
Input Modeling With Phase Type Distributions And Markov Models
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Author : Peter Buchholz
language : en
Publisher: Springer
Release Date : 2014-05-20
Input Modeling With Phase Type Distributions And Markov Models written by Peter Buchholz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-20 with Mathematics categories.
Containing a summary of several recent results on Markov-based input modeling in a coherent notation, this book introduces and compares algorithms for parameter fitting and gives an overview of available software tools in the area. Due to progress made in recent years with respect to new algorithms to generate PH distributions and Markovian arrival processes from measured data, the models outlined are useful alternatives to other distributions or stochastic processes used for input modeling. Graduate students and researchers in applied probability, operations research and computer science along with practitioners using simulation or analytical models for performance analysis and capacity planning will find the unified notation and up-to-date results presented useful. Input modeling is the key step in model based system analysis to adequately describe the load of a system using stochastic models. The goal of input modeling is to find a stochastic model to describe a sequence of measurements from a real system to model for example the inter-arrival times of packets in a computer network or failure times of components in a manufacturing plant. Typical application areas are performance and dependability analysis of computer systems, communication networks, logistics or manufacturing systems but also the analysis of biological or chemical reaction networks and similar problems. Often the measured values have a high variability and are correlated. It’s been known for a long time that Markov based models like phase type distributions or Markovian arrival processes are very general and allow one to capture even complex behaviors. However, the parameterization of these models results often in a complex and non-linear optimization problem. Only recently, several new results about the modeling capabilities of Markov based models and algorithms to fit the parameters of those models have been published.
Quantitative Evaluation Of Systems
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Author : Gul Agha
language : en
Publisher: Springer
Release Date : 2016-08-02
Quantitative Evaluation Of Systems written by Gul Agha and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-02 with Computers categories.
This book constitutes the proceedings of the 13th International Conference on Quantitative Evaluation Systems, QEST 2016, held in Quebec City, Canada, in August 2016. The 21 full papers and 3 tool demonstration papers presented were carefully reviewed and selected from 46 submissions. They are organized in topical sections entitled: Markov processes; tools; sampling, inference, and optimization methods; Markov decision processes and Markovian analysis; networks.
Measurement Modelling And Evaluation Of Computing Systems
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Author : Reinhard German
language : en
Publisher: Springer
Release Date : 2018-02-16
Measurement Modelling And Evaluation Of Computing Systems written by Reinhard German and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-16 with Computers categories.
This book constitutes the proceedings of the 19th International GI/ITG Conference on Measurement, Modelling and Evaluation of Computing Systems, MMB 2018, held in Erlangen, Germany, in February 2018. The 16 full papers, 4 PhD track papers, and 9 tool papers presented in this volume were carefully reviewed and selected from 42 submissions. They are dealing with performance and dependability evaluation techniques for computer and communication systems and its related fields.
Computer Performance Engineering
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Author : Dieter Fiems
language : en
Publisher: Springer
Release Date : 2016-09-15
Computer Performance Engineering written by Dieter Fiems and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-15 with Computers categories.
This book constitutes the refereed proceedings of the 13th European Workshop on Computer Performance Engineering, EPEW 2016, held in Chios, Greece, in October 2016. The 14 papers presented together with 2 invited talks in this volume were carefully reviewed and selected from 25 submissions. The papers presented at the workshop reflect the diversity of modern performance engineering, with topics ranging from the analysis of queueing networks and stochastic processes, to performance analysis of computer systems and networks, and even modeling of human behavior.
Tools And Algorithms For The Construction And Analysis Of Systems
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Author : Hubert Garavel
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-03-14
Tools And Algorithms For The Construction And Analysis Of Systems written by Hubert Garavel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-14 with Computers categories.
This book constitutes the refereed proceedings of the 9th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2003, held in Warsaw, Poland, in April 2003. The 43 revised full papers presented were carefully reviewed and selected from 160 submissions. The papers are organized in topical sections on bounded model checking and SAT-based methods, mu-calculus and temporal logics, verification of parameterized systems, abstractions and counterexamples, real-time and scheduling, security and cryptography, modules and compositional verification, symbolic state spaces and decision diagrams, performance and mobility, state space reductions, constraint solving and decision procedures, and testing and verification.
Matrix Analytic Methods In Stochastic Models
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Author : Guy Latouche
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-04
Matrix Analytic Methods In Stochastic Models written by Guy Latouche and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-04 with Mathematics categories.
Matrix-analytic and related methods have become recognized as an important and fundamental approach for the mathematical analysis of general classes of complex stochastic models. Research in the area of matrix-analytic and related methods seeks to discover underlying probabilistic structures intrinsic in such stochastic models, develop numerical algorithms for computing functionals (e.g., performance measures) of the underlying stochastic processes, and apply these probabilistic structures and/or computational algorithms within a wide variety of fields. This volume presents recent research results on: the theory, algorithms and methodologies concerning matrix-analytic and related methods in stochastic models; and the application of matrix-analytic and related methods in various fields, which includes but is not limited to computer science and engineering, communication networks and telephony, electrical and industrial engineering, operations research, management science, financial and risk analysis, and bio-statistics. These research studies provide deep insights and understanding of the stochastic models of interest from a mathematics and/or applications perspective, as well as identify directions for future research.
Information Technologies And Mathematical Modelling Queueing Theory And Applications
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Author : Alexander Dudin
language : en
Publisher: Springer Nature
Release Date : 2023-05-12
Information Technologies And Mathematical Modelling Queueing Theory And Applications written by Alexander Dudin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-12 with Computers categories.
This book constitutes the refereed proceedings of the 21st International Conference on Information Technologies and Mathematical Modelling. Queueing Theory and Applications, ITMM 2022, held in Karshi, Uzbekistan, during October 25–29, 2022. The 19 full papers included in this book were carefully reviewed and selected from 89 submissions. The papers are devoted to new results in queueing theory and its applications. Its target audience includes specialists in probabilistic theory, random processes, mathematical modeling as well as engineers engaged in logical and technical design and operational management of data processing systems, communication, and computer networks./div