Matrix Exponential Distributions In Applied Probability

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Matrix Exponential Distributions In Applied Probability

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Author : Mogens Bladt
language : en
Publisher: Springer
Release Date : 2017-05-18

Matrix Exponential Distributions In Applied Probability written by Mogens Bladt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-18 with Mathematics categories.

This book contains an in-depth treatment of matrix-exponential (ME) distributions and their sub-class of phase-type (PH) distributions. Loosely speaking, an ME distribution is obtained through replacing the intensity parameter in an exponential distribution by a matrix. The ME distributions can also be identified as the class of non-negative distributions with rational Laplace transforms. If the matrix has the structure of a sub-intensity matrix for a Markov jump process we obtain a PH distribution which allows for nice probabilistic interpretations facilitating the derivation of exact solutions and closed form formulas. The full potential of ME and PH unfolds in their use in stochastic modelling. Several chapters on generic applications, like renewal theory, random walks and regenerative processes, are included together with some specific examples from queueing theory and insurance risk. We emphasize our intention towards applications by including an extensive treatment on statistical methods for PH distributions and related processes that will allow practitioners to calibrate models to real data. Aimed as a textbook for graduate students in applied probability and statistics, the book provides all the necessary background on Poisson processes, Markov chains, jump processes, martingales and re-generative methods. It is our hope that the provided background may encourage researchers and practitioners from other fields, like biology, genetics and medicine, who wish to become acquainted with the matrix-exponential method and its applications.

Constructive Computation In Stochastic Models With Applications

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Author : Quan-Lin Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-02

Constructive Computation In Stochastic Models With Applications written by Quan-Lin Li 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 2011-02-02 with Mathematics categories.

"Constructive Computation in Stochastic Models with Applications: The RG-Factorizations" provides a unified, constructive and algorithmic framework for numerical computation of many practical stochastic systems. It summarizes recent important advances in computational study of stochastic models from several crucial directions, such as stationary computation, transient solution, asymptotic analysis, reward processes, decision processes, sensitivity analysis as well as game theory. Graduate students, researchers and practicing engineers in the field of operations research, management sciences, applied probability, computer networks, manufacturing systems, transportation systems, insurance and finance, risk management and biological sciences will find this book valuable. Dr. Quan-Lin Li is an Associate Professor at the Department of Industrial Engineering of Tsinghua University, China.

Introduction To Matrix Analytic Methods In Queues 2

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Author : Srinivas R. Chakravarthy
language : en
Publisher: John Wiley & Sons
Release Date : 2022-10-18

Introduction To Matrix Analytic Methods In Queues 2 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 2022-10-18 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 2 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. This book's detailed approach will make it more accessible for readers interested in learning about MAM in stochastic models.

Introduction To Matrix Analytic Methods In Queues 1

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Author : Srinivas R. Chakravarthy
language : en
Publisher: John Wiley & Sons
Release Date : 2022-08-19

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 2022-08-19 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.

Phase Type Distributions Volume 2

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Author : András Horváth
language : en
Publisher: John Wiley & Sons
Release Date : 2024-10-29

Phase Type Distributions Volume 2 written by András Horváth 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 2024-10-29 with Mathematics categories.

Phase type distributions are widely applicable modeling and statistical tools for non-negative random quantities. They are built on Markov chains, which provide a simple, intuitive stochastic interpretation for their use. Phase Type Distribution starts from the Markov chain-based definition of phase type distributions and presents many interesting properties, which follow from the basic definition. As a general family of non-negative distributions with nice analytical properties, phase type distributions can be used for approximating experimental distributions by fitting or by moments matching; and, for discrete event simulation of real word systems with stochastic timing, such as production systems, service operations, communication networks, etc. This book summarizes the up-to-date fitting, matching and simulation methods, and presents the limits of flexibility of phase type distributions of a given order. Additionally, this book lists numerical examples that support the intuitive understanding of the analytical descriptions and software tools that handle phase type distributions.

Applied Probability And Queues

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Author : Soeren Asmussen
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-08

Applied Probability And Queues written by Soeren Asmussen 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 2008-01-08 with Mathematics categories.

"This book is a highly recommendable survey of mathematical tools and results in applied probability with special emphasis on queueing theory....The second edition at hand is a thoroughly updated and considerably expended version of the first edition.... This book and the way the various topics are balanced are a welcome addition to the literature. It is an indispensable source of information for both advanced graduate students and researchers." --MATHEMATICAL REVIEWS

Mathematical Modeling And Supercomputer Technologies

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Author : Dmitry Balandin
language : en
Publisher: Springer Nature
Release Date : 2021-06-23

Mathematical Modeling And Supercomputer Technologies written by Dmitry Balandin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-23 with Computers categories.

This book constitutes selected and revised papers from the 20th International Conference on Mathematical Modeling and Supercomputer Technologies, MMST 2020, held in Nizhny Novgorod, Russia, in November 2020. Due to the COVID-19 pandemic the conference was held online. The 25 full papers and 8 short papers presented in the volume were thoroughly reviewed and selected from the 106 submissions. They are organized in topical secions on ​computational methods for mathematical models analysis; computation in optimization and optimal control; supercomputer simulation.

Selected Contributions On Statistics And Data Science In Latin America

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Author : Isadora Antoniano-Villalobos
language : en
Publisher: Springer Nature
Release Date : 2019-11-05

Selected Contributions On Statistics And Data Science In Latin America written by Isadora Antoniano-Villalobos and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-05 with Mathematics categories.

The volume includes a collection of peer-reviewed contributions from among those presented at the main conference organized yearly by the Mexican Statistical Association (AME) and every two years by a Latin-American Confederation of Statistical Societies. For the 2018 edition, particular attention was placed on the analysis of highly complex or large data sets, which have come to be known as “big data”. Statistical research in Latin America is prolific and research networks span within and outside the region. The goal of this volume is to provide access to selected works from Latin-American collaborators and their research networks to a wider audience. New methodological advances, motivated in part by the challenges of a data-driven world and the Latin American context, will be of interest to academics and practitioners around the world.

Reliability And Statistics In Transportation And Communication

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Author : Igor Kabashkin
language : en
Publisher: Springer Nature
Release Date : 2021-02-06

Reliability And Statistics In Transportation And Communication written by Igor Kabashkin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-06 with Technology & Engineering categories.

This book reports on cutting-edge theories and methods for analyzing complex systems, such as transportation and communication networks and discusses multi-disciplinary approaches to dependability problems encountered when dealing with complex systems in practice. The book presents the most noteworthy methods and results discussed at the International Conference on Reliability and Statistics in Transportation and Communication (RelStat), which took place remotely from Riga, Latvia, on October 14 – 17, 2020. It spans a broad spectrum of topics, from mathematical models and design methodologies, to software engineering, data security and financial issues, as well as practical problems in technical systems, such as transportation and telecommunications, and in engineering education.

Queueing Theory 2

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Author : Vladimir Anisimov
language : en
Publisher: John Wiley & Sons
Release Date : 2021-04-13

Queueing Theory 2 written by Vladimir Anisimov 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 2021-04-13 with Mathematics categories.

The aim of this book is to reflect the current cutting-edge thinking and established practices in the investigation of queueing systems and networks. This second volume includes eight chapters written by experts wellknown in their areas. The book conducts a stability analysis of certain types of multiserver regenerative queueing systems; a transient evaluation of Markovian queueing systems, focusing on closed-form distributions and numerical techniques; analysis of queueing models in service sectors using analytical and simulation approaches; plus an investigation of probability distributions in queueing models and their use in economics, industry, demography and environmental studies. This book also considers techniques for the control of information in queueing systems and their impact on strategic customer behavior, social welfare and the revenue of monopolists. In addition, applications of maximum entropy methods of inference for the analysis of a stable M/G/1 queue with heavy tails, and inventory models with positive service time - including perishable items and stock supplied using various algorithmic control policies ((s; S); (r;Q), etc.).