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Author : G. Latouche,V. Ramaswami
Publisher : SIAM
Page : 331 pages
File Size : 55,6 Mb
Release : 1999-01-01
Category : Mathematics
ISBN : 9780898714258
Presents the basic mathematical ideas and algorithms of the matrix analytic theory in a readable, up-to-date, and comprehensive manner.
Author : Guy Latouche,Vaidyanathan Ramaswami,Jay Sethuraman,Karl Sigman,Mark S. Squillante,David Yao
Publisher : Springer Science & Business Media
Page : 265 pages
File Size : 45,7 Mb
Release : 2012-12-04
Category : Mathematics
ISBN : 9781461449096
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.
Author : S. Chakravarthy,Attahiru S. Alfa
Publisher : CRC Press
Page : 398 pages
File Size : 44,8 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781482292176
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.
Author : G. Latouche,V. Ramaswami
Publisher : SIAM
Page : 348 pages
File Size : 49,5 Mb
Release : 1999-01-01
Category : Mathematics
ISBN : 0898719739
Matrix analytic methods are popular as modeling tools because they give one the ability to construct and analyze a wide class of queuing models in a unified and algorithmically tractable way. The authors present the basic mathematical ideas and algorithms of the matrix analytic theory in a readable, up-to-date, and comprehensive manner. In the current literature, a mixed bag of techniques is used-some probabilistic, some from linear algebra, and some from transform methods. Here, many new proofs that emphasize the unity of the matrix analytic approach are included.
Author : Qi-Ming He
Publisher : Springer Science & Business Media
Page : 363 pages
File Size : 40,5 Mb
Release : 2013-08-13
Category : Computers
ISBN : 9781461473305
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.
Author : L. Breuer,Dieter Baum
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 54,5 Mb
Release : 2006-02-23
Category : Mathematics
ISBN : 9781402036316
The present textbook contains the recordsof a two–semester course on que- ing theory, including an introduction to matrix–analytic methods. This course comprises four hours oflectures and two hours of exercises per week andhas been taughtattheUniversity of Trier, Germany, for about ten years in - quence. The course is directed to last year undergraduate and?rst year gr- uate students of applied probability and computer science, who have already completed an introduction to probability theory. Its purpose is to present - terial that is close enough to concrete queueing models and their applications, while providing a sound mathematical foundation for the analysis of these. Thus the goal of the present book is two–fold. On the one hand, students who are mainly interested in applications easily feel bored by elaborate mathematical questions in the theory of stochastic processes. The presentation of the mathematical foundations in our courses is chosen to cover only the necessary results, which are needed for a solid foundation of the methods of queueing analysis. Further, students oriented - wards applications expect to have a justi?cation for their mathematical efforts in terms of immediate use in queueing analysis. This is the main reason why we have decided to introduce new mathematical concepts only when they will be used in the immediate sequel. On the other hand, students of applied probability do not want any heur- tic derivations just for the sake of yielding fast results for the model at hand.
Author : Quan-Lin Li
Publisher : Springer Science & Business Media
Page : 693 pages
File Size : 54,5 Mb
Release : 2011-02-02
Category : Mathematics
ISBN : 9783642114922
"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.
Author : Howard M. Taylor,Samuel Karlin
Publisher : Academic Press
Page : 410 pages
File Size : 52,9 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483269276
An Introduction to Stochastic Modeling provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.
Author : Dariusz Buraczewski,Ewa Damek,Thomas Mikosch
Publisher : Springer
Page : 320 pages
File Size : 55,9 Mb
Release : 2016-07-04
Category : Mathematics
ISBN : 9783319296791
In this monograph the authors give a systematic approach to the probabilistic properties of the fixed point equation X=AX+B. A probabilistic study of the stochastic recurrence equation X_t=A_tX_{t-1}+B_t for real- and matrix-valued random variables A_t, where (A_t,B_t) constitute an iid sequence, is provided. The classical theory for these equations, including the existence and uniqueness of a stationary solution, the tail behavior with special emphasis on power law behavior, moments and support, is presented. The authors collect recent asymptotic results on extremes, point processes, partial sums (central limit theory with special emphasis on infinite variance stable limit theory), large deviations, in the univariate and multivariate cases, and they further touch on the related topics of smoothing transforms, regularly varying sequences and random iterative systems. The text gives an introduction to the Kesten-Goldie theory for stochastic recurrence equations of the type X_t=A_tX_{t-1}+B_t. It provides the classical results of Kesten, Goldie, Guivarc'h, and others, and gives an overview of recent results on the topic. It presents the state-of-the-art results in the field of affine stochastic recurrence equations and shows relations with non-affine recursions and multivariate regular variation.
Author : Attahiru S. Alfa,Srinivas R. Chakravarthy
Publisher : Notable Publications, Incorporated
Page : 443 pages
File Size : 47,9 Mb
Release : 1998
Category : Markov processes
ISBN : 0966584708
Author : Sidney I. Resnick
Publisher : Springer Science & Business Media
Page : 640 pages
File Size : 47,8 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9781461203872
Stochastic processes are necessary ingredients for building models of a wide variety of phenomena exhibiting time varying randomness. This text offers easy access to this fundamental topic for many students of applied sciences at many levels. It includes examples, exercises, applications, and computational procedures. It is uniquely useful for beginners and non-beginners in the field. No knowledge of measure theory is presumed.
Author : Gregory S. Chirikjian
Publisher : Springer Science & Business Media
Page : 460 pages
File Size : 51,9 Mb
Release : 2011-11-15
Category : Mathematics
ISBN : 9780817649432
This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering. Extensive exercises, motivating examples, and real-world applications make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.
Author : Andreas Diekmann,Peter Mitter
Publisher : Academic Press
Page : 352 pages
File Size : 51,8 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483266565
Stochastic Modelling of Social Processes provides information pertinent to the development in the field of stochastic modeling and its applications in the social sciences. This book demonstrates that stochastic models can fulfill the goals of explanation and prediction. Organized into nine chapters, this book begins with an overview of stochastic models that fulfill normative, predictive, and structural–analytic roles with the aid of the theory of probability. This text then examines the study of labor market structures using analysis of job and career mobility, which is one of the approaches taken by sociologists in research on the labor market. Other chapters consider the characteristic trends and patterns from data on divorces. This book discusses as well the two approaches of stochastic modeling of social processes, namely competing risk models and semi-Markov processes. The final chapter deals with the practical application of regression models of survival data. This book is a valuable resource for social scientists and statisticians.
Author : Guy Latouche,Peter Taylor
Publisher : World Scientific
Page : 440 pages
File Size : 42,6 Mb
Release : 2002
Category : Fiction
ISBN : 9812777164
Matrix-analytic methods are fundamental to the analysis of a family of Markov processes rich in structure and of wide applicability. They are extensively used in the modelling and performance analysis of computer systems, telecommunication networks, network protocols and many other stochastic systems of current commercial and engineering interest.This volume deals with: (1) various aspects of the theory of block-structured Markov chains; (2) analysis of complex queueing models; and (3) parameter estimation and specific applications to such areas as cellular mobile systems, FS-ALOHA, the Internet and production systems.
Author : Hal Caswell
Publisher : Sinauer
Page : 0 pages
File Size : 46,8 Mb
Release : 2006-05-10
Category : Science
ISBN : 087893121X
This book provides a complete treatment of matrix population models and their applications in ecology and demography. It is written for graduate students and researchers in ecology, population biology, conservation biology and human demography.
