Numerical Methods In Markov Chains And Bulk Queues
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Numerical Methods In Markov Chains And Bulk Queues
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Author : T. P. Bagchi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Numerical Methods In Markov Chains And Bulk Queues written by T. P. Bagchi 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 Mathematics categories.
Numerical Methods For Structured Markov Chains
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Author : Dario A. Bini
language : en
Publisher: OUP Oxford
Release Date : 2005-02-03
Numerical Methods For Structured Markov Chains written by Dario A. Bini and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-03 with Mathematics categories.
Intersecting two large research areas - numerical analysis and applied probability/queuing theory - this book is a self-contained introduction to the numerical solution of structured Markov chains, which have a wide applicability in queuing theory and stochastic modeling and include M/G/1 and GI/M/1-type Markov chain, quasi-birth-death processes, non-skip free queues and tree-like stochastic processes. Written for applied probabilists and numerical analysts, but accessible to engineers and scientists working on telecommunications and evaluation of computer systems performances, it provides a systematic treatment of the theory and algorithms for important families of structured Markov chains and a thorough overview of the current literature. The book, consisting of nine Chapters, is presented in three parts. Part 1 covers a basic description of the fundamental concepts related to Markov chains, a systematic treatment of the structure matrix tools, including finite Toeplitz matrices, displacement operators, FFT, and the infinite block Toeplitz matrices, their relationship with matrix power series and the fundamental problems of solving matrix equations and computing canonical factorizations. Part 2 deals with the description and analysis of structure Markov chains and includes M/G/1, quasi-birth-death processes, non-skip-free queues and tree-like processes. Part 3 covers solution algorithms where new convergence and applicability results are proved. Each chapter ends with bibliographic notes for further reading, and the book ends with an appendix collecting the main general concepts and results used in the book, a list of the main annotations and algorithms used in the book, and an extensive index.
Computations With Markov Chains
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Author : William J. Stewart
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computations With Markov Chains written by William J. Stewart 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 Mathematics categories.
Computations with Markov Chains presents the edited and reviewed proceedings of the Second International Workshop on the Numerical Solution of Markov Chains, held January 16--18, 1995, in Raleigh, North Carolina. New developments of particular interest include recent work on stability and conditioning, Krylov subspace-based methods for transient solutions, quadratic convergent procedures for matrix geometric problems, further analysis of the GTH algorithm, the arrival of stochastic automata networks at the forefront of modelling stratagems, and more. An authoritative overview of the field for applied probabilists, numerical analysts and systems modelers, including computer scientists and engineers.
Numerical Solution Of Markov Chains
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Author : William J. Stewart
language : en
Publisher: CRC Press
Release Date : 2021-06-30
Numerical Solution Of Markov Chains written by William J. Stewart and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-30 with Mathematics categories.
Papers presented at a workshop held January 1990 (location unspecified) cover just about all aspects of solving Markov models numerically. There are papers on matrix generation techniques and generalized stochastic Petri nets; the computation of stationary distributions, including aggregation/disaggregation.
Numerical Methods For Stochastic Control Problems In Continuous Time
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Author : Harold Kushner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Numerical Methods For Stochastic Control Problems In Continuous Time written by Harold Kushner 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 Science categories.
This book is concerned with numerical methods for stochastic control and optimal stochastic control problems. The random process models of the controlled or uncontrolled stochastic systems are either diffusions or jump diffusions. Stochastic control is a very active area of research and new prob lem formulations and sometimes surprising applications appear regularly. We have chosen forms of the models which cover the great bulk of the for mulations of the continuous time stochastic control problems which have appeared to date. The standard formats are covered, but much emphasis is given to the newer and less well known formulations. The controlled process might be either stopped or absorbed on leaving a constraint set or upon first hitting a target set, or it might be reflected or "projected" from the boundary of a constraining set. In some of the more recent applications of the reflecting boundary problem, for example the so-called heavy traffic approximation problems, the directions of reflection are actually discontin uous. In general, the control might be representable as a bounded function or it might be of the so-called impulsive or singular control types. Both the "drift" and the "variance" might be controlled. The cost functions might be any of the standard types: Discounted, stopped on first exit from a set, finite time, optimal stopping, average cost per unit time over the infinite time interval, and so forth.
Iterative Methods For Queuing And Manufacturing Systems
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Author : Wai K. Ching
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-02-26
Iterative Methods For Queuing And Manufacturing Systems written by Wai K. Ching 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 2001-02-26 with Mathematics categories.
An introduction to the recent advances and developments in iterative methods for solving Markovian queuing and manufacturing problems. With numerous exercises and fully-worked examples, this book is essential reading for anyone interested in the formulation and computation of queuing and manufacturing systems.
Advances In Queueing Theory Methods And Open Problems
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Author : Jewgeni H. Dshalalow
language : en
Publisher: CRC Press
Release Date : 2023-07-21
Advances In Queueing Theory Methods And Open Problems written by Jewgeni H. Dshalalow and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-21 with Business & Economics categories.
The progress of science and technology has placed Queueing Theory among the most popular disciplines in applied mathematics, operations research, and engineering. Although queueing has been on the scientific market since the beginning of this century, it is still rapidly expanding by capturing new areas in technology. Advances in Queueing provides a comprehensive overview of problems in this enormous area of science and focuses on the most significant methods recently developed. Written by a team of 24 eminent scientists, the book examines stochastic, analytic, and generic methods such as approximations, estimates and bounds, and simulation. The first chapter presents an overview of classical queueing methods from the birth of queues to the seventies. It also contains the most comprehensive bibliography of books on queueing and telecommunications to date. Each of the following chapters surveys recent methods applied to classes of queueing systems and networks followed by a discussion of open problems and future research directions. Advances in Queueing is a practical reference that allows the reader quick access to the latest methods.
Continuous Time Markov Chains And Applications
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Author : G. George Yin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-14
Continuous Time Markov Chains And Applications written by G. George Yin 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 2012-11-14 with Mathematics categories.
This book gives a systematic treatment of singularly perturbed systems that naturally arise in control and optimization, queueing networks, manufacturing systems, and financial engineering. It presents results on asymptotic expansions of solutions of Komogorov forward and backward equations, properties of functional occupation measures, exponential upper bounds, and functional limit results for Markov chains with weak and strong interactions. To bridge the gap between theory and applications, a large portion of the book is devoted to applications in controlled dynamic systems, production planning, and numerical methods for controlled Markovian systems with large-scale and complex structures in the real-world problems. This second edition has been updated throughout and includes two new chapters on asymptotic expansions of solutions for backward equations and hybrid LQG problems. The chapters on analytic and probabilistic properties of two-time-scale Markov chains have been almost completely rewritten and the notation has been streamlined and simplified. This book is written for applied mathematicians, engineers, operations researchers, and applied scientists. Selected material from the book can also be used for a one semester advanced graduate-level course in applied probability and stochastic processes.
Linear Algebra Markov Chains And Queueing Models
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Author : Carl D Meyer
language : en
Publisher:
Release Date : 1993-09-10
Linear Algebra Markov Chains And Queueing Models written by Carl D Meyer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-09-10 with categories.
Computational Probability
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Author : Winfried K. Grassmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Computational Probability written by Winfried K. Grassmann 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 2013-03-14 with Business & Economics categories.
Great advances have been made in recent years in the field of computational probability. In particular, the state of the art - as it relates to queuing systems, stochastic Petri-nets and systems dealing with reliability - has benefited significantly from these advances. The objective of this book is to make these topics accessible to researchers, graduate students, and practitioners. Great care was taken to make the exposition as clear as possible. Every line in the book has been evaluated, and changes have been made whenever it was felt that the initial exposition was not clear enough for the intended readership. The work of major research scholars in this field comprises the individual chapters of Computational Probability. The first chapter describes, in nonmathematical terms, the challenges in computational probability. Chapter 2 describes the methodologies available for obtaining the transition matrices for Markov chains, with particular emphasis on stochastic Petri-nets. Chapter 3 discusses how to find transient probabilities and transient rewards for these Markov chains. The next two chapters indicate how to find steady-state probabilities for Markov chains with a finite number of states. Both direct and iterative methods are described in Chapter 4. Details of these methods are given in Chapter 5. Chapters 6 and 7 deal with infinite-state Markov chains, which occur frequently in queueing, because there are times one does not want to set a bound for all queues. Chapter 8 deals with transforms, in particular Laplace transforms. The work of Ward Whitt and his collaborators, who have recently developed a number of numerical methods for Laplace transform inversions, is emphasized in this chapter. Finally, if one wants to optimize a system, one way to do the optimization is through Markov decision making, described in Chapter 9. Markov modeling has found applications in many areas, three of which are described in detail: Chapter 10 analyzes discrete-time queues, Chapter 11 describes networks of queues, and Chapter 12 deals with reliability theory.