Numerical Methods for Structured Markov Chains

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Author: Dario A. Bini,Guy Latouche,Beatrice Meini

Publisher: Oxford University Press on Demand

ISBN: 0198527683

Category: Computers

Page: 327

View: 5460

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.

Markov Chains

Theory and Applications

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Author: Bruno Sericola

Publisher: John Wiley & Sons

ISBN: 1118731530

Category: Mathematics

Page: 416

View: 3559

Markov chains are a fundamental class of stochastic processes.They are widely used to solve problems in a large number of domainssuch as operational research, computer science, communicationnetworks and manufacturing systems. The success of Markov chains ismainly due to their simplicity of use, the large number ofavailable theoretical results and the quality of algorithmsdeveloped for the numerical evaluation of many metrics ofinterest. The author presents the theory of both discrete-time andcontinuous-time homogeneous Markov chains. He carefully examinesthe explosion phenomenon, the Kolmogorov equations, the convergenceto equilibrium and the passage time distributions to a state and toa subset of states. These results are applied to birth-and-deathprocesses. He then proposes a detailed study of the uniformizationtechnique by means of Banach algebra. This technique is used forthe transient analysis of several queuing systems. Contents 1. Discrete-Time Markov Chains 2. Continuous-Time Markov Chains 3. Birth-and-Death Processes 4. Uniformization 5. Queues About the Authors Bruno Sericola is a Senior Research Scientist at Inria Rennes– Bretagne Atlantique in France. His main research activityis in performance evaluation of computer and communication systems,dependability analysis of fault-tolerant systems and stochasticmodels.

Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics

The Albrecht Böttcher Anniversary Volume

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Author: Dario A. Bini,Torsten Ehrhardt,Alexei Yu. Karlovich,Ilya Spitkovsky

Publisher: Birkhäuser

ISBN: 3319491822

Category: Mathematics

Page: 740

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This book presents a collection of expository and research papers on various topics in matrix and operator theory, contributed by several experts on the occasion of Albrecht Böttcher’s 60th birthday. Albrecht Böttcher himself has made substantial contributions to the subject in the past. The book also includes a biographical essay, a complete bibliography of Albrecht Böttcher’s work and brief informal notes on personal encounters with him. The book is of interest to graduate and advanced undergraduate students majoring in mathematics, researchers in matrix and operator theory as well as engineers and applied mathematicians.

Chaînes de Markov : Théorie, algorithmes et applications

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Author: SERICOLA Bruno

Publisher: Lavoisier

ISBN: 2746289164

Category:

Page: 389

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Les chaînes de Markov sont des modèles probabilistes utilisés dans des domaines variés comme la logistique, l'informatique, la fiabilité, les télécommunications, ou encore la biologie et la physique-chimie. On les retrouve également dans la finance, l’économie et les sciences sociales. Cet ouvrage présente une étude approfondie des chaînes de Markov à temps discret et à temps continu avec des applications détaillées aux processus de naissance et mort et aux files d'attente. Ces applications sont illustrées par des algorithmes généraux de calcul de probabilités d'état et de distribution de temps de passage. Le développement de ces algorithmes repose sur l'utilisation de la technique d'uniformisation des chaînes de Markov qui est présentée de manière théorique et intuitive. Ce livre s'adresse aux ingénieurs et chercheurs ayant besoin de modèles probabilistes pour évaluer et prédire le comportement des systèmes qu'ils étudient ou qu'ils développent. Il est aussi très bien adapté pour un cours de master.

Matrix-Analytic Methods in Stochastic Models

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Author: Guy Latouche,Vaidyanathan Ramaswami,Jay Sethuraman,Karl Sigman,Mark S. Squillante,David Yao

Publisher: Springer Science & Business Media

ISBN: 146144909X

Category: Mathematics

Page: 258

View: 3228

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.

Analytical and Stochastic Modeling Techniques and Applications

15th International Conference, ASMTA 2008 Nicosia, Cyprus, June 4-6, 2008 Proceedings

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Author: Khalid Al-Begain,Armin Heindl,Miklos Telek

Publisher: Springer Science & Business Media

ISBN: 354068980X

Category: Computers

Page: 323

View: 4189

This book constitutes the refereed proceedings of the 15th International Conference on Analytical and Stochastic Modeling Techniques and Applications, ASMTA 2008, held in Nicosia, Cyprus, in June 2008 in conjunction with ECMS 2008, the 22nd European Conference on Modeling and Simulation. The 22 revised full papers presented were carefully reviewed and selected from 55 submissions. The papers are organized in topical sections on traffic modeling, queueing systems, analytical methods and applications, distributions in stochastic modeling, queueing networks, simulation and model checking, as well as wireless networks.

Numerical Methods for Large Eigenvalue Problems

Revised Edition

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Author: Yousef Saad

Publisher: SIAM

ISBN: 9781611970739

Category: Eigenvalues

Page: 276

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This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.

Numerical Analysis and Its Applications

Second International Conference, NAA 2000 Rousse, Bulgaria, June 11-15, 2000. Revised Papers

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Author: Lubin Vulkov,Jerzy Wasniewski

Publisher: Springer Science & Business Media

ISBN: 3540418148

Category: Computers

Page: 779

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 A. R. Ansari,A. F. HegartyandG. I. Shishkin AnAlgorithmBasedonOrthogonalPolynomialVectors forToeplitzLeastSquaresProblems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 M. VanBarel, G. Heinig andP. Kravanja FromSensitivityAnalysistoRandomFloatingPointArithmetics– ApplicationtoSylvesterEquations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 A. Barraud, S. LesecqandN. Christov ConstructionofSeminumericalSchemes: ApplicationtotheArti?cialSatelliteProblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 R. Barrio StabilityAnalysisofParallelEvaluationofFiniteSeries ofOrthogonalPolynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 R. Barrio andP. Yalamov OnSolvingLarge-ScaleWeightedLeastSquaresProblems. . . . . . . . . . . . . . . . . . 59 V.

Algorithmic Probability

A Collection of Problems

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Author: Marcel F. Neuts

Publisher: CRC Press

ISBN: 9780412996917

Category: Mathematics

Page: 472

View: 2935

This unique text collects more than 400 problems in combinatorics, derived distributions, discrete and continuous Markov chains, and models requiring a computer experimental approach. The first book to deal with simplified versions of models encountered in the contemporary statistical or engineering literature, Algorithmic Probability emphasizes correct interpretation of numerical results and visualization of the dynamics of stochastic processes. A significant contribution to the field of applied probability, Algorithmic Probability is ideal both as a secondary text in probability courses and as a reference. Engineers and operations analysts seeking solutions to practical problems will find it a valuable resource, as will advanced undergraduate and graduate students in mathematics, statistics, operations research, industrial and electrical engineering, and computer science.

Numerical Analysis and Optimization

An Introduction to Mathematical Modelling and Numerical Simulation

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Author: Grégoire Allaire

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Mathematics

Page: 455

View: 4669

Based on the Author's teaching notes at the Ecole Polytechnique,iNumerical Analysis and Optimization/i familiarises students with existingmathematical models (often partial differential equations) and their methods ofnumerical solution and optimization. The role of modelling and scientificcomputing has increased dramatically over recent years, and new applications ofmathematical models have emerged in Biology, Environmental Science, Finance,Medicine, and Social Science, as well as the classical applications inChemistry, Mechanics and Physics.Including numerous exercises and examples, this is an ideal text for advancedundergraduates and graduates and researchers in Applied Mathematics,Engineering, Computer Science, and the Physical Sciences.

Probability, Markov Chains, Queues, and Simulation

The Mathematical Basis of Performance Modeling

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Author: William J. Stewart

Publisher: Princeton University Press

ISBN: 1400832810

Category: Mathematics

Page: 776

View: 7997

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

Formal Methods in Systems Biology

First International Workshop, FMSB 2008, Cambridge, UK, June 4-5, 2008, Proceedings

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Author: Jasmin Fisher

Publisher: Springer Science & Business Media

ISBN: 3540684107

Category: Computers

Page: 139

View: 353

Thisvolumecontainstheproceedingsofthe?rstinternationalmeetingonFormal Methods in Systems Biology, held at Microsoft Research, Cambridge, UK, June 4–5, 2008. While there are several venues that cover computational methods in systems biology,there is to date no single conference that brings together the application of the range of formal methods in biology. Therefore, convening such a meeting could prove extremely productive. The purpose of this meeting was to identify techniques for the speci?cation, development and veri?cation of biological m- els.Italsofocusedonthedesignoftoolstoexecuteandanalyzebiologicalmodels in ways that can signi?cantly advance our understanding of biological systems. As a forum for this discussion we invited key scientists in the area of formal methods to this unique meeting. Although this was a one-o? meeting, we are exploring the possibility of this forming the ?rst of what might become an annual conference. Presentations at the meeting were by invitation only; future meetings are expected to operate on a submission and review basis. The Steering Committee and additional referees reviewed the invited papers. Each submission was evaluated by at least two referees. The volume includes nine invited contributions. Formal Methods in Systems Biology 2008 was made possible by the cont- bution and dedication ofmany people. First of all,we wouldlike to thank allthe authors who submitted papers. Secondly, we would like to thank our additional invited speakers and participants. We would also like to thank the members of the Steering Committee for their valuable comments. Finally, we ackno- edge the help of the administrative and technical sta? at the MicrosoftResearch Cambridge lab.

Quantitative Evaluation of Computing and Communication Systems

8th International Conference on Modelling Techniques and Tools for Computer Performance Evaluation, Performance Tools '95, 8th GI/ITG Conference on Measuring, Modelling and Evaluating Computing and Communication Systems, MMB '95Heidelberg, Germany, Septem

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Author: Heinz Beilner,Falko Bause,International Conference on Modelling Techniques and Tools for Computer Performance Evaluation

Publisher: Springer Science & Business Media

ISBN: 9783540603009

Category: Computers

Page: 415

View: 5757

This book constitutes the proceedings of the 8th International Conference on Modelling Techniques and Tools for Computer Performance Evaluation (Performance Tools '95) and of the 8th GI/ITG Conference on Measuring, Modelling and Evaluating Computing and Communication Systems, MMB '95, held jointly in Heidelberg, Germany in September 1995. The volume presents 26 full refereed papers selected from a total of 86 submissions, together with two invited contributions. The scope of the papers includes measurement- and model-based approaches for quantitative systems assessment, reports on theoretical and methodological progress, and novel and improved assessment techniques and their tool implementations and applications.

Introduction to the Numerical Solution of Markov Chains

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Author: William J. Stewart

Publisher: Princeton University Press

ISBN: 0691036993

Category: Mathematics

Page: 539

View: 3194

Markov chains; Direct methods; Iterative methods; Projection methods; Block hessenberg matrices and solution by recursion; decompositional methods; P-cyclic markov chains; Trasient solutions; Stochastic automata networks; Software; Bibliography; Index.

Constructive Computation in Stochastic Models with Applications

The RG-Factorizations

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Author: Quan-Lin Li

Publisher: Springer Science & Business Media

ISBN: 9783642114922

Category: Mathematics

Page: 650

View: 7871

"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.

Numerical Analysis 1997

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Author: D.F. Griffiths,G.A. Watson,D J Higham

Publisher: CRC Press

ISBN: 9780582312616

Category: Mathematics

Page: 264

View: 5298

This book forms a valuable guide to the direction in which current numerical analysis research is heading. It will be of particular interest to graduate students and researchers concerned with the theoretical and practical issues associated with scientific computation. The main topics include ordinary and partial differential equations, fluid flow, optimization, linear algebra, and approximation theory. Two recurring themes are the need for adaptive and structure preserving numerical methods. The work presented here has a list of direct applications that include colliding black holes, molecular dynamics, blow-up problems, and card shuffling.

Computations with Markov Chains

Proceedings of the 2nd International Workshop on the Numerical Solution of Markov Chains

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Author: William J. Stewart

Publisher: Springer

ISBN: N.A

Category: Mathematics

Page: 600

View: 7597

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 Stochastic Differential Equations

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Author: Peter E. Kloeden,Eckhard Platen

Publisher: Springer Science & Business Media

ISBN: 9783540540625

Category: Mathematics

Page: 636

View: 1921

The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP

Fundamentals of Matrix-Analytic Methods

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Author: Qi-Ming He

Publisher: Springer Science & Business Media

ISBN: 1461473306

Category: Computers

Page: 349

View: 2642

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.