Download or read book Uniform Limit Theorems for Synchronous Processes with Applications to Queues written by Peter W. Glynn and published by . This book was released on 1989 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the present paper we investigate conditions under which the Cesaro averaged functionals. We show that to obtain uniform convergence requires placing further conditions on the Positive Recurrence Process (PRS). This is in sharp contrast to both classical regenerative processes and discrete time Harris recurrent Markov chains (where renewal theory can be applied) where such uniform convergence holds without any further conditions. For continuous time positive Harris recurrent Markov processes (where renewal theory can not be applied) we show that these further conditions are in fact automatically satisfied. In this context, applications to queueing models are given. Synchronous process, Cesaro convergence, Limit theorems, Point processes. (eg).
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1990 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sample Path Analysis of Queueing Systems written by Muhammad El-Taha and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sample-Path Analysis of Queueing Systems uses a deterministic (sample-path) approach to analyze stochastic systems, primarily queueing systems and more general input-output systems. Among other topics of interest it deals with establishing fundamental relations between asymptotic frequencies and averages, pathwise stability, and insensitivity. These results are utilized to establish useful performance measures. The intuitive deterministic approach of this book will give researchers, teachers, practitioners, and students better insights into many results in queueing theory. The simplicity and intuitive appeal of the arguments will make these results more accessible, with no sacrifice of mathematical rigor. Recent topics such as pathwise stability are also covered in this context. The book consistently takes the point of view of focusing on one sample path of a stochastic process. Hence, it is devoted to providing pure sample-path arguments. With this approach it is possible to separate the issue of the validity of a relationship from issues of existence of limits and/or construction of stationary framework. Generally, in many cases of interest in queueing theory, relations hold, assuming limits exist, and the proofs are elementary and intuitive. In other cases, proofs of the existence of limits will require the heavy machinery of stochastic processes. The authors feel that sample-path analysis can be best used to provide general results that are independent of stochastic assumptions, complemented by use of probabilistic arguments to carry out a more detailed analysis. This book focuses on the first part of the picture. It does however, provide numerous examples that invoke stochastic assumptions, which typically are presented at the ends of the chapters.
Download or read book Analysis of Communication Networks written by David R. McDonald and published by American Mathematical Soc.. This book was released on 2000 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of the proceedings of the Workshop on Analysis and Simulation of Communication Networks held at The Fields Institute (Toronto). The workshop was divided into two main themes, entitled "Stability and Load Balancing of a Network of Call Centres" and "Traffic and Performance". The call centre industry is large and fast-growing. In order to provide top-notch customer service, it needs good mathematical models. The first part of the volume focuses on probabilistic issues involved in optimizing the performance of a call centre. While this was the motivating application, many of the papers are also applicable to more general distributed queueing networks. The second part of the volume discusses the characterization of traffic streams and how to estimate their impact on the performance of a queueing system. The performance of queues under worst-case traffic flows or flows with long bursts is treated. These studies are motivated by questions about buffer dimensioning and call admission control in ATM or IP networks. This volume will serve researchers as a comprehensive, state-of-the-art reference source on developments in this rapidly expanding field.
Download or read book Stability Analysis of Regenerative Queueing Models written by Evsey Morozov and published by Springer Nature. This book was released on 2021-09-20 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: The stability analysis of stochastic models for telecommunication systems is an intensively studied topic. The analysis is, as a rule, a difficult problem requiring a refined mathematical technique, especially when one endeavors beyond the framework of Markovian models. The primary purpose of this book is to present, in a unified way, research into the stability analysis of a wide variety of regenerative queueing systems. It describes the theoretical foundations of this method, and then shows how it works with particular models, both classic ones as well as more recent models that have received attention. The focus lies on an in-depth and insightful mathematical explanation of the regenerative stability analysis method. The unique volume can serve as a textbook for students working in these and related scientific areas. The material is also of interest to engineers working in telecommunications field, who may be faced with the problem of stability of queueing systems.
Download or read book Advancing the Frontiers of Simulation written by Christos Alexopoulos and published by Springer Science & Business Media. This book was released on 2009-09-18 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift honors George Samuel Fishman, one of the founders of the eld of computer simulation and a leader of the disciplines of operations research and the management sciences for the past ve decades, on the occasion of his seventieth birthday. The papers in this volume span the theory, methodology, and application of computer simulation. The lead article is appropriately titled “George Fishman’s Professional Career.” In this article we discuss George’s contributions to operations research and the m- agement sciences, with special emphasis on his role in the advancement of the eld of simulation since the 1960s. We also include a brief personal biography together with comments by several individuals about the extraordinary effect that George has had on all his students, colleagues, and friends. Thesecondarticle,titled“AConversationwithGeorgeFishman,”isthetranscript of an extended interview with George that we conducted in October 2007. In the article titled “Computer Intensive Statistical Model Building,” Russell Cheng studies resampling methods for building parsimonious multiple linear regr- sion models so as to represent accurately the behavior of the dependent variable in terms of the smallest possible subset of explanatory (independent) variables. The author shows how bootstrap resampling can be used not only for rapid identi cation of good models but also for ef cient comparison of competing models.
Download or read book Stochastic Petri Nets written by Peter J. Haas and published by Springer Science & Business Media. This book was released on 2006-04-10 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a leading researcher this book presents an introduction to Stochastic Petri Nets covering the modeling power of the proposed SPN model, the stability conditions and the simulation methods. Its unique and well-written approach provides a timely and important addition to the literature. Appeals to a wide range of researchers in engineering, computer science, mathematics and OR.
Download or read book Random Measures Theory and Applications written by Olav Kallenberg and published by Springer. This book was released on 2017-04-12 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offering the first comprehensive treatment of the theory of random measures, this book has a very broad scope, ranging from basic properties of Poisson and related processes to the modern theories of convergence, stationarity, Palm measures, conditioning, and compensation. The three large final chapters focus on applications within the areas of stochastic geometry, excursion theory, and branching processes. Although this theory plays a fundamental role in most areas of modern probability, much of it, including the most basic material, has previously been available only in scores of journal articles. The book is primarily directed towards researchers and advanced graduate students in stochastic processes and related areas.
Download or read book Research in Progress written by and published by . This book was released on 1990 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Government reports annual index written by and published by . This book was released on 199? with total page 1570 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advances in Applied Probability written by and published by . This book was released on 1993 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1608 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Limit Theorem for the Queueing Output Process with an Application to Tandem Queues written by Esa Nummelin and published by . This book was released on 1979 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Current Index to Statistics Applications Methods and Theory written by and published by . This book was released on 1997 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Current Index to Statistics (CIS) is a bibliographic index of publications in statistics, probability, and related fields.
Download or read book Government Reports Announcements Index written by and published by . This book was released on 1996 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Regenerative Processes in Queueing Theory written by Jacob W. Cohen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: I. The single server queue GIIG/1 1 1. 1 Definitions 1 1. 2 Regenerative processes 2 1. 3 The sequence n 1,2, . . . 4 = !::!n' 1. 4 The process t dO,co)} 11 {~t' The process t dO,co)} 1. 5 15 {~t' Applications to the GIIG/1 queue 1. 6 16 The average virtual waiting time during a busy 17 cycle ii. Little's formula 17 iii. The relation between the stationary distributions 18 of the virtual and actual waiting time iv. The relation between the distribution of the idle 20 period and the stationary distribution of the actual waiting time v. The limiting distribution of the residual service 24 time £. , -pw vi. The relation for ~ rn E{e -n} 25 n=O 1. 7 Some notes on chapter I 27 II. The M/G/K system 31 2. 1 On the stationary distribution of the actual and virtua131 waiting time for the M/G/K queueing system 2. 2 The M/G/K loss system 36 2. 3 Proof of Erlang's formula for the M/G/K loss system 43 i. Proof for the system MIMI'" 45 ii. Proof for the system M/G/co 47 VI iii. Proof fol' the MIG IK los s system III. The M/G/1 system 3. 1 Introduction 71 (K) 3. 2 Downcrossings of the ~t -process 74 3. 3 The distribution of the supremum of the virtual waiting 75 • (00) d' b 1 tlme ~t urlng a usy cyc e i. The exit probability 76 ii.
Download or read book Computer Networks and Systems written by Thomas G. Robertazzi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended for a first course in performance evaluation, this is a self-contained treatment covering all aspects of queuing theory. It starts by introducing readers to the terminology and usefulness of queueing theory and continues by considering Markovian queues in equilibrium, Littles law, reversibility, transient analysis, and computation, plus the M/G/1 queuing system. It then moves on to cover networks of queues, and concludes with techniques for numerical solutions, a discussion of the PANACEA technique, discrete time queueing systems and simulation, and stochastic Petri networks. The whole is backed by case studies of distributed queueing networks arising in industrial applications. This third edition includes a new chapter on self-similar traffic, many new problems, and solutions for many exercises.
