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Numerical Solution Of Markov Chains
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Book Synopsis Numerical Solution of Markov Chains by : William J. Stewart
Download or read book Numerical Solution of Markov Chains written by William J. Stewart and published by CRC Press. This book was released on 1991-05-23 with total page 738 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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/disagg
Book Synopsis Introduction to the Numerical Solution of Markov Chains by : William J. Stewart
Download or read book Introduction to the Numerical Solution of Markov Chains written by William J. Stewart and published by Princeton University Press. This book was released on 2021-01-12 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: A cornerstone of applied probability, Markov chains can be used to help model how plants grow, chemicals react, and atoms diffuse--and applications are increasingly being found in such areas as engineering, computer science, economics, and education. To apply the techniques to real problems, however, it is necessary to understand how Markov chains can be solved numerically. In this book, the first to offer a systematic and detailed treatment of the numerical solution of Markov chains, William Stewart provides scientists on many levels with the power to put this theory to use in the actual world, where it has applications in areas as diverse as engineering, economics, and education. His efforts make for essential reading in a rapidly growing field. Here Stewart explores all aspects of numerically computing solutions of Markov chains, especially when the state is huge. He provides extensive background to both discrete-time and continuous-time Markov chains and examines many different numerical computing methods--direct, single-and multi-vector iterative, and projection methods. More specifically, he considers recursive methods often used when the structure of the Markov chain is upper Hessenberg, iterative aggregation/disaggregation methods that are particularly appropriate when it is NCD (nearly completely decomposable), and reduced schemes for cases in which the chain is periodic. There are chapters on methods for computing transient solutions, on stochastic automata networks, and, finally, on currently available software. Throughout Stewart draws on numerous examples and comparisons among the methods he so thoroughly explains.
Book Synopsis Numerical Methods for Structured Markov Chains by : Dario A. Bini
Download or read book Numerical Methods for Structured Markov Chains written by Dario A. Bini and published by Oxford University Press on Demand. This book was released on 2005-02-03 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 toengineers 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 andanalysis 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 bookends 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.
Book Synopsis Computations with Markov Chains by : William J. Stewart
Download or read book Computations with Markov Chains written by William J. Stewart and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Methods in Markov Chains and Bulk Queues by : T. P. Bagchi
Download or read book Numerical Methods in Markov Chains and Bulk Queues written by T. P. Bagchi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimization and Games for Controllable Markov Chains by : Julio B. Clempner
Download or read book Optimization and Games for Controllable Markov Chains written by Julio B. Clempner and published by Springer Nature. This book was released on 2023-12-13 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers a class of ergodic finite controllable Markov's chains. The main idea behind the method, described in this book, is to develop the original discrete optimization problems (or game models) in the space of randomized formulations, where the variables stand in for the distributions (mixed strategies or preferences) of the original discrete (pure) strategies in the use. The following suppositions are made: a finite state space, a limited action space, continuity of the probabilities and rewards associated with the actions, and a necessity for accessibility. These hypotheses lead to the existence of an optimal policy. The best course of action is always stationary. It is either simple (i.e., nonrandomized stationary) or composed of two nonrandomized policies, which is equivalent to randomly selecting one of two simple policies throughout each epoch by tossing a biased coin. As a bonus, the optimization procedure just has to repeatedly solve the time-average dynamic programming equation, making it theoretically feasible to choose the optimum course of action under the global restriction. In the ergodic cases the state distributions, generated by the corresponding transition equations, exponentially quickly converge to their stationary (final) values. This makes it possible to employ all widely used optimization methods (such as Gradient-like procedures, Extra-proximal method, Lagrange's multipliers, Tikhonov's regularization), including the related numerical techniques. In the book we tackle different problems and theoretical Markov models like controllable and ergodic Markov chains, multi-objective Pareto front solutions, partially observable Markov chains, continuous-time Markov chains, Nash equilibrium and Stackelberg equilibrium, Lyapunov-like function in Markov chains, Best-reply strategy, Bayesian incentive-compatible mechanisms, Bayesian Partially Observable Markov Games, bargaining solutions for Nash and Kalai-Smorodinsky formulations, multi-traffic signal-control synchronization problem, Rubinstein's non-cooperative bargaining solutions, the transfer pricing problem as bargaining.
Book Synopsis Continuous-Time Markov Chains and Applications by : G. George Yin
Download or read book Continuous-Time Markov Chains and Applications written by G. George Yin and published by Springer Science & Business Media. This book was released on 2012-11-14 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Methods for Stochastic Control Problems in Continuous Time by : Harold Kushner
Download or read book Numerical Methods for Stochastic Control Problems in Continuous Time written by Harold Kushner and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic control is a very active area of research. This monograph, written by two leading authorities in the field, has been updated to reflect the latest developments. It covers effective numerical methods for stochastic control problems in continuous time on two levels, that of practice and that of mathematical development. It is broadly accessible for graduate students and researchers.
Book Synopsis Computations with Markov Chains by : William J Stewart
Download or read book Computations with Markov Chains written by William J Stewart and published by . This book was released on 1995-02-28 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Methods for Stochastic Control Problems in Continuous Time by : Harold Kushner
Download or read book Numerical Methods for Stochastic Control Problems in Continuous Time written by Harold Kushner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Applications of Markov Chains in Chemical Engineering by : A. Tamir
Download or read book Applications of Markov Chains in Chemical Engineering written by A. Tamir and published by Elsevier. This book was released on 1998-08-26 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: Markov chains make it possible to predict the future state of a system from its present state ignoring its past history. Surprisingly, despite the widespread use of Markov chains in many areas of science and technology, their applications in chemical engineering have been relatively meager. A possible reason for this phenomenon might be that books containing material on this subject have been written in such a way that the simplicity of Markov chains has been shadowed by the tedious mathematical derivations. Thus, the major objective of writing this book has been to try to change this situation. There are many advantages, detailed in Chapter 1, of using the discrete Markov-chain model in chemical engineering. Probably, the most important advantage is that physical models can be presented in a unified description via state vector and a one-step transition probability matrix. Consequently, a process is demonstrated solely by the probability of a system to occupy or not occupy a state. The book has been written in an easy and understandable form, where complex mathematical derivations are abandoned. The fundamentals of Markov chains are presented in Chapter 2 with examples from the bible, art and real life problems. An extremely wide collection is given of examples viz., reactions, reactors, reactions and reactors as well as combined processes, including their solution and a graphical presentation of it, all of which demonstrates the usefulness of applying Markov chains in chemical engineering.
Book Synopsis Numerical Methods for Stochastic Control Problems in Continuous Time by : Harold J. Kushner
Download or read book Numerical Methods for Stochastic Control Problems in Continuous Time written by Harold J. Kushner and published by Springer Science & Business Media. This book was released on 2001 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: The required background is surveyed, and there is an extensive development of methods of approximation and computational algorithms. The book is written on two levels: algorithms and applications, and mathematical proofs. Thus, the ideas should be very accessible to a broad audience."--BOOK JACKET.
Book Synopsis Numerical Methods for Controlled Stochastic Delay Systems by : Harold Kushner
Download or read book Numerical Methods for Controlled Stochastic Delay Systems written by Harold Kushner and published by Springer Science & Business Media. This book was released on 2008-12-19 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Markov chain approximation methods are widely used for the numerical solution of nonlinear stochastic control problems in continuous time. This book extends the methods to stochastic systems with delays. The book is the first on the subject and will be of great interest to all those who work with stochastic delay equations and whose main interest is either in the use of the algorithms or in the mathematics. An excellent resource for graduate students, researchers, and practitioners, the work may be used as a graduate-level textbook for a special topics course or seminar on numerical methods in stochastic control.
Download or read book Markov Chains written by Wai-Ki Ching and published by Springer Science & Business Media. This book was released on 2013-03-27 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition of Markov Chains: Models, Algorithms and Applications has been completely reformatted as a text, complete with end-of-chapter exercises, a new focus on management science, new applications of the models, and new examples with applications in financial risk management and modeling of financial data. This book consists of eight chapters. Chapter 1 gives a brief introduction to the classical theory on both discrete and continuous time Markov chains. The relationship between Markov chains of finite states and matrix theory will also be highlighted. Some classical iterative methods for solving linear systems will be introduced for finding the stationary distribution of a Markov chain. The chapter then covers the basic theories and algorithms for hidden Markov models (HMMs) and Markov decision processes (MDPs). Chapter 2 discusses the applications of continuous time Markov chains to model queueing systems and discrete time Markov chain for computing the PageRank, the ranking of websites on the Internet. Chapter 3 studies Markovian models for manufacturing and re-manufacturing systems and presents closed form solutions and fast numerical algorithms for solving the captured systems. In Chapter 4, the authors present a simple hidden Markov model (HMM) with fast numerical algorithms for estimating the model parameters. An application of the HMM for customer classification is also presented. Chapter 5 discusses Markov decision processes for customer lifetime values. Customer Lifetime Values (CLV) is an important concept and quantity in marketing management. The authors present an approach based on Markov decision processes for the calculation of CLV using real data. Chapter 6 considers higher-order Markov chain models, particularly a class of parsimonious higher-order Markov chain models. Efficient estimation methods for model parameters based on linear programming are presented. Contemporary research results on applications to demand predictions, inventory control and financial risk measurement are also presented. In Chapter 7, a class of parsimonious multivariate Markov models is introduced. Again, efficient estimation methods based on linear programming are presented. Applications to demand predictions, inventory control policy and modeling credit ratings data are discussed. Finally, Chapter 8 re-visits hidden Markov models, and the authors present a new class of hidden Markov models with efficient algorithms for estimating the model parameters. Applications to modeling interest rates, credit ratings and default data are discussed. This book is aimed at senior undergraduate students, postgraduate students, professionals, practitioners, and researchers in applied mathematics, computational science, operational research, management science and finance, who are interested in the formulation and computation of queueing networks, Markov chain models and related topics. Readers are expected to have some basic knowledge of probability theory, Markov processes and matrix theory.
Book Synopsis Probability, Markov Chains, Queues, and Simulation by : William J. Stewart
Download or read book Probability, Markov Chains, Queues, and Simulation written by William J. Stewart and published by Princeton University Press. This book was released on 2009-07-06 with total page 777 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability, Markov Chains, Queues, and Simulation provides a modern and authoritative treatment of the mathematical processes that underlie performance modeling. The detailed explanations of mathematical derivations and numerous illustrative examples make this textbook readily accessible to graduate and advanced undergraduate students taking courses in which stochastic processes play a fundamental role. The textbook is relevant to a wide variety of fields, including computer science, engineering, operations research, statistics, and mathematics. The textbook looks at the fundamentals of probability theory, from the basic concepts of set-based probability, through probability distributions, to bounds, limit theorems, and the laws of large numbers. Discrete and continuous-time Markov chains are analyzed from a theoretical and computational point of view. Topics include the Chapman-Kolmogorov equations; irreducibility; the potential, fundamental, and reachability matrices; random walk problems; reversibility; renewal processes; and the numerical computation of stationary and transient distributions. The M/M/1 queue and its extensions to more general birth-death processes are analyzed in detail, as are queues with phase-type arrival and service processes. The M/G/1 and G/M/1 queues are solved using embedded Markov chains; the busy period, residual service time, and priority scheduling are treated. Open and closed queueing networks are analyzed. The final part of the book addresses the mathematical basis of simulation. Each chapter of the textbook concludes with an extensive set of exercises. An instructor's solution manual, in which all exercises are completely worked out, is also available (to professors only). Numerous examples illuminate the mathematical theories Carefully detailed explanations of mathematical derivations guarantee a valuable pedagogical approach Each chapter concludes with an extensive set of exercises
Book Synopsis Analyzing Markov Chains using Kronecker Products by : Tugrul Dayar
Download or read book Analyzing Markov Chains using Kronecker Products written by Tugrul Dayar and published by Springer Science & Business Media. This book was released on 2012-07-25 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author :National Aeronautics and Space Administration (NASA) Publisher :Createspace Independent Publishing Platform ISBN 13 :9781722424923 Total Pages :44 pages Book Rating :4.4/5 (249 download)
Book Synopsis Numerical Methods in Markov Chain Modeling by : National Aeronautics and Space Administration (NASA)
Download or read book Numerical Methods in Markov Chain Modeling written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-07-11 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared. Philippe, Bernard and Saad, Youcef and Stewart, William J. Unspecified Center NSF INT-86-13332; NCC2-387...
