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Stochastic Monotonicity Of Birth Death Processes
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Book Synopsis Stochastic Monotonicity and Queueing Applications of Birth-Death Processes by : Erik van Doorn
Download or read book Stochastic Monotonicity and Queueing Applications of Birth-Death Processes written by Erik van Doorn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: A stochastic process {X(t): 0 S t =} with discrete state space S c ~ is said to be stochastically increasing (decreasing) on an interval T if the probabilities Pr{X(t) i}, i E S, are increasing (decreasing) with t on T. Stochastic monotonicity is a basic structural property for process behaviour. It gives rise to meaningful bounds for various quantities such as the moments of the process, and provides the mathematical groundwork for approximation algorithms. Obviously, stochastic monotonicity becomes a more tractable subject for analysis if the processes under consideration are such that stochastic mono tonicity on an inter val 0
Book Synopsis Markov Processes for Stochastic Modeling by : Masaaki Kijima
Download or read book Markov Processes for Stochastic Modeling written by Masaaki Kijima and published by Springer. This book was released on 2013-12-19 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an algebraic development of the theory of countable state space Markov chains with discrete- and continuous-time parameters. A Markov chain is a stochastic process characterized by the Markov prop erty that the distribution of future depends only on the current state, not on the whole history. Despite its simple form of dependency, the Markov property has enabled us to develop a rich system of concepts and theorems and to derive many results that are useful in applications. In fact, the areas that can be modeled, with varying degrees of success, by Markov chains are vast and are still expanding. The aim of this book is a discussion of the time-dependent behavior, called the transient behavior, of Markov chains. From the practical point of view, when modeling a stochastic system by a Markov chain, there are many instances in which time-limiting results such as stationary distributions have no meaning. Or, even when the stationary distribution is of some importance, it is often dangerous to use the stationary result alone without knowing the transient behavior of the Markov chain. Not many books have paid much attention to this topic, despite its obvious importance.
Book Synopsis Stochastic Processes and Orthogonal Polynomials by : Wim Schoutens
Download or read book Stochastic Processes and Orthogonal Polynomials written by Wim Schoutens and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book offers an accessible reference for researchers in the probability, statistics and special functions communities. It gives a variety of interdisciplinary relations between the two main ingredients of stochastic processes and orthogonal polynomials. It covers topics like time dependent and asymptotic analysis for birth-death processes and diffusions, martingale relations for Lévy processes, stochastic integrals and Stein's approximation method. Almost all well-known orthogonal polynomials, which are brought together in the so-called Askey Scheme, come into play. This volume clearly illustrates the powerful mathematical role of orthogonal polynomials in the analysis of stochastic processes and is made accessible for all mathematicians with a basic background in probability theory and mathematical analysis. Wim Schoutens is a Postdoctoral Researcher of the Fund for Scientific Research-Flanders (Belgium). He received his PhD in Science from the Catholic University of Leuven, Belgium.
Book Synopsis Stochastic Models in Queueing Theory by : Jyotiprasad Medhi
Download or read book Stochastic Models in Queueing Theory written by Jyotiprasad Medhi and published by Elsevier. This book was released on 2002-11-06 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a graduate level textbook that covers the fundamental topics in queuing theory. The book has a broad coverage of methods to calculate important probabilities, and gives attention to proving the general theorems. It includes many recent topics, such as server-vacation models, diffusion approximations and optimal operating policies, and more about bulk-arrival and bull-service models than other general texts. - Current, clear and comprehensive coverage - A wealth of interesting and relevant examples and exercises to reinforce concepts - Reference lists provided after each chapter for further investigation
Book Synopsis Computer Performance Engineering by : Jeremy T. Bradley
Download or read book Computer Performance Engineering written by Jeremy T. Bradley and published by Springer. This book was released on 2009-07-06 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume constitutes the refereed proceedings of the 6th European Performance Engineering Workshop, EPEW 2009, held in London, UK during July 9-10, 2009. The 13 full papers and 4 short papers presented in this volume, together with the abstract of one invited paper, were carefully reviewed and selected from 33 submissions. The papers deal with modeling of auctions and markets, hardware modeling of RAID systems, performance aspects of cellular and fixed-line networks, mean value analysis, stochastic ordering to queuing networks, extension of passage-time analysis, stochastic process algebra (PEPA), tagged customers in generalised stochastic Petri nets, and representation and analysis of generally-distributed stochastic systems.
Book Synopsis Stochastic Processes by : Sheldon M. Ross
Download or read book Stochastic Processes written by Sheldon M. Ross and published by John Wiley & Sons. This book was released on 1995-02-28 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: A nonmeasure theoretic introduction to stochastic processes. Considers its diverse range of applications and provides readers with probabilistic intuition and insight in thinking about problems. This revised edition contains additional material on compound Poisson random variables including an identity which can be used to efficiently compute moments; a new chapter on Poisson approximations; and coverage of the mean time spent in transient states as well as examples relating to the Gibb's sampler, the Metropolis algorithm and mean cover time in star graphs. Numerous exercises and problems have been added throughout the text.
Book Synopsis Optimal Sequentially Planned Decision Procedures by : Norbert Schmitz
Download or read book Optimal Sequentially Planned Decision Procedures written by Norbert Schmitz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learning from experience, making decisions on the basis of the available information, and proceeding step by step to a desired goal are fundamental behavioural qualities of human beings. Nevertheless, it was not until the early 1940's that such a statistical theory - namely Sequential Analysis - was created, which allows us to investigate this kind of behaviour in a precise manner. A. Wald's famous sequential probability ratio test (SPRT; see example (1.8» turned out to have an enormous influence on the development of this theory. On the one hand, Wald's fundamental monograph "Sequential Analysis" ([Wa]*) is essentially centered around this test. On the other hand, important properties of the SPRT - e.g. Bayes optimality, minimax-properties, "uniform" optimality with respect to expected sample sizes - gave rise to the development of a general statistical decision theory. As a conse quence, the SPRT's played a dominating role in the further development of sequential analysis and, more generally, in theoretical statistics.
Book Synopsis Queueing Networks by : Richard J. Boucherie
Download or read book Queueing Networks written by Richard J. Boucherie and published by Springer Science & Business Media. This book was released on 2010-11-25 with total page 814 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook aims to highlight fundamental, methodological and computational aspects of networks of queues to provide insights and to unify results that can be applied in a more general manner. The handbook is organized into five parts: Part 1 considers exact analytical results such as of product form type. Topics include characterization of product forms by physical balance concepts and simple traffic flow equations, classes of service and queue disciplines that allow a product form, a unified description of product forms for discrete time queueing networks, insights for insensitivity, and aggregation and decomposition results that allow sub networks to be aggregated into single nodes to reduce computational burden. Part 2 looks at monotonicity and comparison results such as for computational simplification by either of two approaches: stochastic monotonicity and ordering results based on the ordering of the process generators, and comparison results and explicit error bounds based on an underlying Markov reward structure leading to ordering of expectations of performance measures. Part 3 presents diffusion and fluid results. It specifically looks at the fluid regime and the diffusion regime. Both of these are illustrated through fluid limits for the analysis of system stability, diffusion approximations for multi-server systems, and a system fed by Gaussian traffic. Part 4 illustrates computational and approximate results through the classical MVA (mean value analysis) and QNA (queueing network analyzer) for computing mean and variance of performance measures such as queue lengths and sojourn times; numerical approximation of response time distributions; and approximate decomposition results for large open queueing networks. spanPart 5 enlightens selected applications as spanloss networks originating from circuit switched telecommunications applications, capacity sharing originating from packet switching in data networks, and a hospital application that is of growing present day interest. spanThe book shows that spanthe intertwined progress of theory and practicespan will remain to be most intriguing and will continue to be the basis of further developments in queueing networks.
Author :Demetres D. Kouvatsos Publisher :Springer Science & Business Media ISBN 13 :3642027415 Total Pages :1073 pages Book Rating :4.6/5 (42 download)
Book Synopsis Network Performance Engineering by : Demetres D. Kouvatsos
Download or read book Network Performance Engineering written by Demetres D. Kouvatsos and published by Springer Science & Business Media. This book was released on 2011-05-09 with total page 1073 pages. Available in PDF, EPUB and Kindle. Book excerpt: During recent years a great deal of progress has been made in performance modelling and evaluation of the Internet, towards the convergence of multi-service networks of diverging technologies, supported by internetworking and the evolution of diverse access and switching technologies. The 44 chapters presented in this handbook are revised invited works drawn from PhD courses held at recent HETNETs International Working Conferences on Performance Modelling and Evaluation of Heterogeneous Networks. They constitute essential introductory material preparing the reader for further research and development in the field of performance modelling, analysis and engineering of heterogeneous networks and of next and future generation Internets. The handbook aims to unify relevant material already known but dispersed in the literature, introduce the readers to unfamiliar and unexposed research areas and, generally, illustrate the diversity of research found in the high growth field of convergent heterogeneous networks and the Internet. The chapters have been broadly classified into 12 parts covering the following topics: Measurement Techniques; Traffic Modelling and Engineering; Queueing Systems and Networks; Analytic Methodologies; Simulation Techniques; Performance Evaluation Studies; Mobile, Wireless and Ad Hoc Networks, Optical Networks; QoS Metrics and Algorithms; All IP Convergence and Networking; Network Management and Services; and Overlay Networks.
Book Synopsis Markov Chain Models — Rarity and Exponentiality by : J. Keilson
Download or read book Markov Chain Models — Rarity and Exponentiality written by J. Keilson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: in failure time distributions for systems modeled by finite chains. This introductory chapter attempts to provide an over view of the material and ideas covered. The presentation is loose and fragmentary, and should be read lightly initially. Subsequent perusal from time to time may help tie the mat erial together and provide a unity less readily obtainable otherwise. The detailed presentation begins in Chapter 1, and some readers may prefer to begin there directly. §O.l. Time-Reversibility and Spectral Representation. Continuous time chains may be discussed in terms of discrete time chains by a uniformizing procedure (§2.l) that simplifies and unifies the theory and enables results for discrete and continuous time to be discussed simultaneously. Thus if N(t) is any finite Markov chain in continuous time governed by transition rates vmn one may write for pet) = [Pmn(t)] • P[N(t) = n I N(O) = m] pet) = exp [-vt(I - a )] (0.1.1) v where v > Max r v ' and mn m n law ~ 1 - v-I * Hence N(t) where is governed r vmn Nk = NK(t) n K(t) is a Poisson process of rate v indep- by a ' and v dent of N • k Time-reversibility (§1.3, §2.4, §2.S) is important for many reasons. A) The only broad class of tractable chains suitable for stochastic models is the time-reversible class.
Book Synopsis Series Approximation Methods in Statistics by : John E. Kolassa
Download or read book Series Approximation Methods in Statistics written by John E. Kolassa and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book was originally compiled for a course I taught at the University of Rochester in the fall of 1991, and is intended to give advanced graduate students in statistics an introduction to Edgeworth and saddlepoint approximations, and related techniques. Many other authors have also written monographs on this subject, and so this work is narrowly focused on two areas not recently discussed in theoretical text books. These areas are, first, a rigorous consideration of Edgeworth and saddlepoint expansion limit theorems, and second, a survey of the more recent developments in the field. In presenting expansion limit theorems I have drawn heavily 011 notation of McCullagh (1987) and on the theorems presented by Feller (1971) on Edgeworth expansions. For saddlepoint notation and results I relied most heavily on the many papers of Daniels, and a review paper by Reid (1988). Throughout this book I have tried to maintain consistent notation and to present theorems in such a way as to make a few theoretical results useful in as many contexts as possible. This was not only in order to present as many results with as few proofs as possible, but more importantly to show the interconnections between the various facets of asymptotic theory. Special attention is paid to regularity conditions. The reasons they are needed and the parts they play in the proofs are both highlighted.
Book Synopsis Statistical Analysis of Counting Processes by : M. Jacobsen
Download or read book Statistical Analysis of Counting Processes written by M. Jacobsen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: A first version of these lecture notes was prepared for a course given in 1980 at the University of Copenhagen to a class of graduate students in mathematical statistics. A thorough revision has led to the result presented here. The main topic of the notes is the theory of multiplicative intens ity models for counting processes, first introduced by Odd Aalen in his Ph.D. thesis from Berkeley 1975, and in a subsequent fundamental paper in the Annals of Statistics 1978. In Copenhagen the interest in statistics on counting processes was sparked by a visit by Odd Aalen in 1976. At present the activities here are centered around Niels Keiding and his group at the Statistical Re search Unit. The Aalen theory is a fine example of how advanced probability theory may be used to develop a povlerful, and for applications very re levant, statistical technique. Aalen's work relies quite heavily on the 'theorie generale des processus' developed primarily by the French school of probability the ory. But the general theory aims at much more general and profound re sults, than what is required to deal with objects of such a relatively simple structure as counting processes on the line. Since also this process theory is virtually inaccessible to non-probabilists, it would appear useful to have an account of what Aalen has done, that includes exactly the amount of probability required to deal satisfactorily and rigorously with statistical models for counting processes.
Book Synopsis Lectures on Random Voronoi Tessellations by : Jesper Moller
Download or read book Lectures on Random Voronoi Tessellations written by Jesper Moller and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tessellations are subdivisions of d-dimensional space into non-overlapping "cells". Voronoi tessellations are produced by first considering a set of points (known as nuclei) in d-space, and then defining cells as the set of points which are closest to each nuclei. A random Voronoi tessellation is produced by supposing that the location of each nuclei is determined by some random process. They provide models for many natural phenomena as diverse as the growth of crystals, the territories of animals, the development of regional market areas, and in subjects such as computational geometry and astrophysics. This volume provides an introduction to random Voronoi tessellations by presenting a survey of the main known results and the directions in which research is proceeding. Throughout the volume, mathematical and rigorous proofs are given making this essentially a self-contained account in which no background knowledge of the subject is assumed.
Book Synopsis Differential-Geometrical Methods in Statistics by : Shun-ichi Amari
Download or read book Differential-Geometrical Methods in Statistics written by Shun-ichi Amari and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "In this Lecture Note volume the author describes his differential-geometric approach to parametrical statistical problems summarizing the results he had published in a series of papers in the last five years. The author provides a geometric framework for a special class of test and estimation procedures for curved exponential families. ... ... The material and ideas presented in this volume are important and it is recommended to everybody interested in the connection between statistics and geometry ..." #Metrika#1 "More than hundred references are given showing the growing interest in differential geometry with respect to statistics. The book can only strongly be recommended to a geodesist since it offers many new insights into statistics on a familiar ground." #Manuscripta Geodaetica#2
Book Synopsis Advances in Queueing Theory, Methods, and Open Problems by : Jewgeni H. Dshalalow
Download or read book Advances in Queueing Theory, Methods, and Open Problems written by Jewgeni H. Dshalalow and published by CRC Press. This book was released on 2023-07-21 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Functional Relations, Random Coefficients, and Nonlinear Regression with Application to Kinetic Data by : S. Johansen
Download or read book Functional Relations, Random Coefficients, and Nonlinear Regression with Application to Kinetic Data written by S. Johansen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes on regression give an introduction to some of the techniques that I have found useful when working with various data sets in collaboration with Dr. S. Keiding (Copenhagen) and Dr. J.W.L. Robinson (Lausanne). The notes are based on some lectures given at the Institute of Mathematical Statistics, University of Copenhigen, 1978-81, for graduate students, and assumes a familiarity with statistical theory corresponding to the book by C.R. Rao: "Linear Statistical Inference and its Applications". Wiley, New York (1973) . The mathematical tools needed for the algebraic treatment of the models are some knowledge of finite dimensional vector spaces with an inner product and the notion of orthogonal projection. For the analytic treatment I need characteristic functions and weak convergence as the main tools. The most important statistical concepts are the general linear model for Gaussian variables and the general methods of maximum likelihood estimation as well as the likelihood ratio test. All these topics are presented in the above mentioned book by Rao and the reader is referred to that for details. For convenience a short appendix is added where the fundamental concepts from linear algebra are discussed.
Book Synopsis Pivotal Measures in Statistical Experiments and Sufficiency by : Sakutaro Yamada
Download or read book Pivotal Measures in Statistical Experiments and Sufficiency written by Sakutaro Yamada and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the present work I want to show a mathematical study of the statistical notion of sufficiency mainly for undominated statistical experiments. The famous Burkholder's (1961) and Pitcher's(1957) examples motivated some researchers to develop new theory of sufficiency. Le Cam (1964) is probably the most excellent paper in this field of study. This note also belongs to the same area. Though it is more restrictive than Le Cam's paper(1964), a study which is connected more directly with the classical papers of Halmos and Savage(1949) , and Bahadur(1954) is shown. Namely I want to develop a study based on the notion of pivotal measure which was introduced by Halmos and Savage(1949) . It is great pleasure to have this opportunity to thank Professor H. Heyer and Professor H. Morimoto for their careful reading the manuscript and valuable comments on it. I am also thankful to Professor H. Luschgy and Professor D. Mussmann for thei r proposal of wr i ting "the note". I would like to dedicate this note to the memory of my father Eizo.
