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Introduction To Stochastic Level Crossing Techniques

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Introduction To Stochastic Level Crossing Techniques

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Author : Percy H. Brill
language : en
Publisher: CRC Press
Release Date : 2023-10-04

Introduction To Stochastic Level Crossing Techniques written by Percy H. Brill and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-04 with Business & Economics categories.

Introduction to Stochastic Level Crossing Techniques describes stochastic models and their analysis using the System Point Level Crossing method (abbreviated SPLC or LC). This involves deriving probability density functions (pdfs) or cumulative probability distribution functions (cdfs) of key random variables, applying simple level-crossing limit theorems developed by the author. The pdfs and/or cdfs are used to specify operational characteristics about the stochastic model of interest. The chapters describe distinct stochastic models and associated key random variables in the models. For each model, a figure of a typical sample path (realization, i.e., tracing over time) of the key random variable is displayed. For each model, an analytic (Volterra) integral equation for the stationary pdf of the key random variable is created−by inspection of the sample path, using the simple LC limit theorems. This LC method bypasses a great deal of algebra, usually required by other methods of analysis. The integral equations will be solved directly, or computationally. This book is meant for students of mathematics, management science, engineering, natural sciences, and researchers who use applied probability. It will also be useful to technical workers in a range of professions. Key Features: A description of one representative stochastic model (e.g., a single-server M/G/1 queue; a multiple server M/M/c queue; an inventory system; etc.) Construction of a typical sample path of the key random variable of interest (e.g., the virtual waiting time or workload in queues; the net on-hand inventory in inventory systems; etc.) Statements of the simple LC theorems, which connect the sample-path upcrossing and downcrossing rates across state-space levels, to simple mathematical functions of the stationary pdf of the key random variable, at those state-space levels Creation of (usually Volterra) integral equations for the stationary pdf of the key random variable, by inspection of the sample path Direct analytic solution of the integral equations, where feasible; or, computational solutions of the integral equations Use of the derived stationary pdfs for obtaining operational characteristics of the model

Introduction To Stochastic Level Crossing Techniques

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Author : Percy H. Brill
language : en
Publisher: CRC Press
Release Date : 2023-09-29

Level Crossing Methods In Stochastic Models

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Author : Percy H. Brill
language : en
Publisher: Springer
Release Date : 2017-05-04

Level Crossing Methods In Stochastic Models written by Percy H. Brill and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-04 with Business & Economics categories.

This is a complete update of the first edition of Level Crossing Methods in Stochastic Models, which was published in 2008. Level crossing methods are a set of sample-path based mathematical tools used in applied probability to establish reliable probability distributions. Since the basis for solving any applied probability problem requires a reliable probability distribution, Level Crossing Methods in Stochastic Models, Second Edition is a useful tool for all researchers working on stochastic application problems, including inventory control, queueing theory, reliability theory, actuarial ruin theory, renewal theory, pharmacokinetics, and related Markov processes. The second edition includes a new section with a novel derivation of the Beneš series for M/G/1 queues. It provides new results on the service time for three M/G/I queueing models with bounded workload. It analyzes new applications of queues where zero-wait customers get exceptional service, including several examples on M/G/1 queues, and a new section on G/M/1 queues. Additionally, there are two other important new sections: on the level-crossing derivation of the finite time-t probability distributions of excess, age, and total life, in renewal theory; and on a level-crossing analysis of a risk model in Insurance. The original Chapter 10 has been split into two chapters: the new chapter 10 is on renewal theory, and the first section of the new Chapter 11 is on a risk model. More explicit use is made of the renewal reward theorem throughout, and many technical and editorial changes have been made to facilitate readability. Percy H. Brill, Ph.D., is a Professor emeritus at the University of Windsor, Canada. Dr. Brill is the creator of the level crossing method for analyzing stochastic models. He has published extensively in stochastic processes, queueing theory and related models, especially using level crossing methods.

Encyclopedia Of Operations Research And Management Science

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Author : Saul I. Gass
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Encyclopedia Of Operations Research And Management Science written by Saul I. Gass 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 2012-12-06 with Business & Economics categories.

Operations Research: 1934-1941," 35, 1, 143-152; "British The goal of the Encyclopedia of Operations Research and Operational Research in World War II," 35, 3, 453-470; Management Science is to provide to decision makers and "U. S. Operations Research in World War II," 35, 6, 910-925; problem solvers in business, industry, government and and the 1984 article by Harold Lardner that appeared in academia a comprehensive overview of the wide range of Operations Research: "The Origin of Operational Research," ideas, methodologies, and synergistic forces that combine to 32, 2, 465-475. form the preeminent decision-aiding fields of operations re search and management science (OR/MS). To this end, we The Encyclopedia contains no entries that define the fields enlisted a distinguished international group of academics of operations research and management science. OR and MS and practitioners to contribute articles on subjects for are often equated to one another. If one defines them by the which they are renowned. methodologies they employ, the equation would probably The editors, working with the Encyclopedia's Editorial stand inspection. If one defines them by their historical Advisory Board, surveyed and divided OR/MS into specific developments and the classes of problems they encompass, topics that collectively encompass the foundations, applica the equation becomes fuzzy. The formalism OR grew out of tions, and emerging elements of this ever-changing field. We the operational problems of the British and U. s. military also wanted to establish the close associations that OR/MS efforts in World War II.

Matrix Analytic Methods In Stochastic Models

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Author : S. Chakravarthy
language : en
Publisher: CRC Press
Release Date : 2016-04-19

Matrix Analytic Methods In Stochastic Models written by S. Chakravarthy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.

Based on the proceedings of the first International Conference on Matrix-Analytic Methods (MAM) in Stochastic Models, held in Flint, Michigan, this book presents a general working knowledge of MAM through tutorial articles and application papers. It furnishes information on MAM studies carried out in the former Soviet Union.

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.

The Single Server Queue

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Author : J.W. Cohen
language : en
Publisher: Elsevier
Release Date : 2012-12-02

The Single Server Queue written by J.W. Cohen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Mathematics categories.

This classic work, now available in paperback, concentrates on the basic models of queueing theory. It has a dual aim: to describe relevant mathematical techniques and to analyse the single server queue and its most important variants.

Fundamentals Of Queueing Theory

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Author : Donald Gross
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-23

Fundamentals Of Queueing Theory written by Donald Gross 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 2011-09-23 with Mathematics categories.

Praise for the Third Edition "This is one of the best books available. Its excellent organizational structure allows quick reference to specific models and its clear presentation . . . solidifies the understanding of the concepts being presented." —IIE Transactions on Operations Engineering Thoroughly revised and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fourth Edition continues to present the basic statistical principles that are necessary to analyze the probabilistic nature of queues. Rather than presenting a narrow focus on the subject, this update illustrates the wide-reaching, fundamental concepts in queueing theory and its applications to diverse areas such as computer science, engineering, business, and operations research. This update takes a numerical approach to understanding and making probable estimations relating to queues, with a comprehensive outline of simple and more advanced queueing models. Newly featured topics of the Fourth Edition include: Retrial queues Approximations for queueing networks Numerical inversion of transforms Determining the appropriate number of servers to balance quality and cost of service Each chapter provides a self-contained presentation of key concepts and formulae, allowing readers to work with each section independently, while a summary table at the end of the book outlines the types of queues that have been discussed and their results. In addition, two new appendices have been added, discussing transforms and generating functions as well as the fundamentals of differential and difference equations. New examples are now included along with problems that incorporate QtsPlus software, which is freely available via the book's related Web site. With its accessible style and wealth of real-world examples, Fundamentals of Queueing Theory, Fourth Edition is an ideal book for courses on queueing theory at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners who analyze congestion in the fields of telecommunications, transportation, aviation, and management science.

Fundamentals Of Matrix Analytic Methods

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Author : Qi-Ming He
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-13

Fundamentals Of Matrix Analytic Methods written by Qi-Ming He 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 2013-08-13 with Computers categories.

Fundamentals of Matrix-Analytic Methods targets advanced-level students in mathematics, engineering and computer science. It focuses on the fundamental parts of Matrix-Analytic Methods, Phase-Type Distributions, Markovian arrival processes and Structured Markov chains and matrix geometric solutions. New materials and techniques are presented for the first time in research and engineering design. This book emphasizes stochastic modeling by offering probabilistic interpretation and constructive proofs for Matrix-Analytic Methods. Such an approach is especially useful for engineering analysis and design. Exercises and examples are provided throughout the book.

Performance Prediction And Analytics Of Fuzzy Reliability And Queuing Models

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Author : Kusum Deep
language : en
Publisher: Springer
Release Date : 2018-08-26

Performance Prediction And Analytics Of Fuzzy Reliability And Queuing Models written by Kusum Deep and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-26 with Business & Economics categories.

This book presents the latest developments and breakthroughs in fuzzy theory and performance prediction of queuing and reliability models by using the stochastic modeling and optimization theory. The main focus is on analytics that use fuzzy logic, queuing and reliability theory for the performance prediction and optimal design of real-time engineering systems including call centers, telecommunication, manufacturing, service organizations, etc. For the day-to-day as well as industrial queuing situations and reliability prediction of machining parts embedded in computer, communication and manufacturing systems, the book assesses various measures of performance and effectiveness that can provide valuable insights and help arrive at the best decisions with regard to service and engineering systems. In twenty chapters, the book presents both theoretical developments and applications of the fuzzy logic, reliability and queuing models in a diverse range of scenarios. The topics discussed will be of interest to researchers, educators and undergraduate students in the fields of Engineering, Business Management, and the Mathematical Sciences.

Introduction To Stochastic Level Crossing Techniques

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