Mathematical Methods in the Theory of Queuing

Author: A. Y. Khinchin

Publisher: Courier Corporation

ISBN: 0486316319

Category: Mathematics

Page: 128

View: 9011

Written by a prominent Russian mathematician, this concise monograph examines aspects of queuing theory as an application of probability. Prerequisites include a familiarity with the theory of probability and mathematical analysis. 1960 edition.

Mathematical Methods in Queuing Theory

Author: Vladimir V. Kalashnikov

Publisher: Springer Science & Business Media

ISBN: 9401721971

Category: Mathematics

Page: 382

View: 4924

The material of this book is based on several courses which have been delivered for a long time at the Moscow Institute for Physics and Technology. Some parts have formed the subject of lectures given at various universities throughout the world: Freie Universitat of Berlin, Chalmers University of Technology and the University of Goteborg, University of California at Santa Barbara and others. The subject of the book is the theory of queues. This theory, as a mathematical discipline, begins with the work of A. Erlang, who examined a model of a telephone station and obtained the famous formula for the distribution of the number of busy lines which is named after him. Queueing theory has been applied to the study of numerous models: emergency aid, road traffic, computer systems, etc. Besides, it has lead to several related disciplines such as reliability and inventory theories which deal with similar models. Nevertheless, many parts of the theory of queues were developed as a "pure science" with no practical applications. The aim of this book is to give the reader an insight into the mathematical methods which can be used in queueing theory and to present examples of solving problems with the help of these methods. Of course, the choice of the methods is quite subjective. Thus, many prominent results have not even been mentioned.

Probability, Stochastic Processes, and Queueing Theory

The Mathematics of Computer Performance Modeling

Author: Randolph Nelson

Publisher: Springer Science & Business Media

ISBN: 9780387944524

Category: Computers

Page: 583

View: 5915

We will occasionally footnote a portion of text with a "**,, to indicate Notes on the that this portion can be initially bypassed. The reasons for bypassing a Text portion of the text include: the subject is a special topic that will not be referenced later, the material can be skipped on first reading, or the level of mathematics is higher than the rest of the text. In cases where a topic is self-contained, we opt to collect the material into an appendix that can be read by students at their leisure. The material in the text cannot be fully assimilated until one makes it Notes on "their own" by applying the material to specific problems. Self-discovery Problems is the best teacher and although they are no substitute for an inquiring mind, problems that explore the subject from different viewpoints can often help the student to think about the material in a uniquely per sonal way. With this in mind, we have made problems an integral part of this work and have attempted to make them interesting as well as informative.

Advances in Queueing Theory, Methods, and Open Problems

Author: Jewgeni H. Dshalalow

Publisher: CRC Press

ISBN: 9780849380747

Category: Business & Economics

Page: 528

View: 730

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.

Computer Networks and Systems

Queueing Theory and Performance Evaluation

Author: Thomas G. Robertazzi

Publisher: Springer Science & Business Media

ISBN: 1468404733

Category: Computers

Page: 368

View: 5877

Statistical performance evaluation has assumed an increasing amount of im portance as we seek to design more and more sophisticated communication and information processing systems. The ability to predict a proposed system's performance without actually having to construct it is an extremely cost effec tive design tool. This book is meant to be a first-year graduate level introduction to the field of statIstical performance evaluation. As such, it covers continuous time queueing theory (chapters 1-4), stochastic Petri networks (chapter 5), and discrete time queueing theory (chapter 6). There is a short appendix at the end of the book that reviews basic probability theory. At Stony Brook, this mate rial would be covered in the second half of a two course sequence (the first half is an applied computer networks course). Students seem to be encouraged to pursue the analytical material of this book if they first have some idea of the potential applications.

Analysis of Queues

Methods and Applications

Author: Natarajan Gautam

Publisher: CRC Press

ISBN: 1439806586

Category: Business & Economics

Page: 802

View: 8909

Written with students and professors in mind, Analysis of Queues: Methods and Applications combines coverage of classical queueing theory with recent advances in studying stochastic networks. Exploring a broad range of applications, the book contains plenty of solved problems, exercises, case studies, paradoxes, and numerical examples. In addition to the standard single-station and single class discrete queues, the book discusses models for multi-class queues and queueing networks as well as methods based on fluid scaling, stochastic fluid flows, continuous parameter Markov processes, and quasi-birth-and-death processes, to name a few. It describes a variety of applications including computer-communication networks, information systems, production operations, transportation, and service systems such as healthcare, call centers and restaurants.

Performance Modeling and Design of Computer Systems

Queueing Theory in Action

Author: Mor Harchol-Balter

Publisher: Cambridge University Press

ISBN: 1107027500

Category: Computers

Page: 548

View: 8555

Written with computer scientists and engineers in mind, this book brings queueing theory decisively back to computer science.

Mathematical Techniques of Operational Research

Author: L. S. Goddard

Publisher: Elsevier

ISBN: 1483180603

Category: Mathematics

Page: 240

View: 4758

Mathematical Techniques of Operational Research is a seven-chapter text that covers the principles and applications of various mathematical tools and models to for operational research. Chapter I provides the basic mathematical ideas used in later chapters. Chapters II and III deal with linear programming, including the special cases of transportation and assignment, as well as their applications such as the Trim Problem. Chapters IV and V discuss the theory of queues and describe the general stationary properties of the single-channel queue, and of simple queues in series and in parallel. These chapters also examine some transient properties of queues. Chapter VI focuses on machine interference, which is an aspect of queueing theory, while Chapter VII deals with the important and mathematically subject of Stock Control or Inventory Theory. This book is intended primarily to graduate mathematicians, business manages, and industrial leaders.

An Introduction to Queueing Theory

and Matrix-Analytic Methods

Author: L. Breuer,Dieter Baum

Publisher: Springer Science & Business Media

ISBN: 1402036310

Category: Mathematics

Page: 272

View: 4315

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.

Fundamentals of Queueing Theory

Author: Donald Gross,John F. Shortle,James M. Thompson,Carl M. Harris

Publisher: John Wiley & Sons

ISBN: 1118211642

Category: Mathematics

Page: 528

View: 7385

Praise for the Third Edition "This is one of the best books available. Its excellent organizational structure allows quick reference to specific models and its clear presentation . . . solidifies the understanding of the concepts being presented." —IIE Transactions on Operations Engineering Thoroughly revised and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fourth Edition continues to present the basic statistical principles that are necessary to analyze the probabilistic nature of queues. Rather than presenting a narrow focus on the subject, this update illustrates the wide-reaching, fundamental concepts in queueing theory and its applications to diverse areas such as computer science, engineering, business, and operations research. This update takes a numerical approach to understanding and making probable estimations relating to queues, with a comprehensive outline of simple and more advanced queueing models. Newly featured topics of the Fourth Edition include: Retrial queues Approximations for queueing networks Numerical inversion of transforms Determining the appropriate number of servers to balance quality and cost of service Each chapter provides a self-contained presentation of key concepts and formulae, allowing readers to work with each section independently, while a summary table at the end of the book outlines the types of queues that have been discussed and their results. In addition, two new appendices have been added, discussing transforms and generating functions as well as the fundamentals of differential and difference equations. New examples are now included along with problems that incorporate QtsPlus software, which is freely available via the book's related Web site. With its accessible style and wealth of real-world examples, Fundamentals of Queueing Theory, Fourth Edition is an ideal book for courses on queueing theory at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners who analyze congestion in the fields of telecommunications, transportation, aviation, and management science.

Queuing Theory and Telecommunications

Networks and Applications

Author: Giovanni Giambene

Publisher: Springer Science & Business Media

ISBN: 146144084X

Category: Technology & Engineering

Page: 516

View: 7339

This book is aimed to provide a basic description of current networking technologies and protocols as well as to provide important tools for network performance analysis based on queuing theory. The second edition adds selected contents in the first part of the book for what concerns: (i) the token bucket regulator and traffic shaping issues; (ii) the TCP protocol congestion control that has a significant part in current networking; (iii) basic satellite networking issues; (iv) adding details on QoS support in IP networks. The book is organized so that we have first networking technologies and protocols (Part I) and then theory and exercises with applications to the different technologies and protocols (Part II). This book is intended as a textbook for master level courses in networking and telecommunications sectors.

The Single Server Queue

Author: J.W. Cohen

Publisher: Elsevier

ISBN: 0444596240

Category: Mathematics

Page: 709

View: 5649

This classic work, now available in paperback, concentrates on the basic models of queueing theory. It has a dual aim: to describe relevant mathematical techniques and to analyse the single server queue and its most important variants.

Stochastic Models in Queueing Theory

Author: Jyotiprasad Medhi

Publisher: Elsevier

ISBN: 008054181X

Category: Mathematics

Page: 450

View: 7623

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

Stochastic Dynamic Programming and the Control of Queueing Systems

Author: Linn I. Sennott

Publisher: John Wiley & Sons

ISBN: 0470317876

Category: Mathematics

Page: 354

View: 5499

A path-breaking account of Markov decision processes-theory and computation This book's clear presentation of theory, numerous chapter-end problems, and development of a unified method for the computation of optimal policies in both discrete and continuous time make it an excellent course text for graduate students and advanced undergraduates. Its comprehensive coverage of important recent advances in stochastic dynamic programming makes it a valuable working resource for operations research professionals, management scientists, engineers, and others. Stochastic Dynamic Programming and the Control of Queueing Systems presents the theory of optimization under the finite horizon, infinite horizon discounted, and average cost criteria. It then shows how optimal rules of operation (policies) for each criterion may be numerically determined. A great wealth of examples from the application area of the control of queueing systems is presented. Nine numerical programs for the computation of optimal policies are fully explicated. The Pascal source code for the programs is available for viewing and downloading on the Wiley Web site at The site contains a link to the author's own Web site and is also a place where readers may discuss developments on the programs or other aspects of the material. The source files are also available via ftp at Stochastic Dynamic Programming and the Control of Queueing Systems features: * Path-breaking advances in Markov decision process techniques, brought together for the first time in book form * A theorem/proof format (proofs may be omitted without loss of continuity) * Development of a unified method for the computation of optimal rules of system operation * Numerous examples drawn mainly from the control of queueing systems * Detailed discussions of nine numerical programs * Helpful chapter-end problems * Appendices with complete treatment of background material

Mathematical Methods in Defense Analyses

Author: J. S. Przemieniecki

Publisher: AIAA

ISBN: 9781600860850

Category: Military art and science

Page: 398

View: 2347

Annotation This text presents the various mathematical methods used in military operations research in one easy-to-use reference volume. The reader will find the calculations necessary to analyze all aspects of defense operations, from weapon performance to combat modeling. The text is so clearly written and organized that even newcomers to the field will find it useful. Included with the text is an updated version of Defense Analyses Software, a compendium of software subroutines that allow the reader to compute numerical values for functions or tables derived in the text. Each subroutine is provided with a detailed reference to the equation from which it was derived to ensure that its intended application is consistent with the assumptions used in the derivation. The third edition has a new chapter on theater missile defense based on the concept of layered defense with different strategies of allocating defense interceptors against short- or mid-range ballistic missiles

Difference and Differential Equations with Applications in Queueing Theory

Author: Aliakbar Montazer Haghighi,Dimitar P. Mishev

Publisher: John Wiley & Sons

ISBN: 1118393244

Category: Business & Economics

Page: 404

View: 3021

"This book features a collection of topics that are used in stochastic processes and, particularly, in queueing theory. Differential equations, difference equations, and Markovian queues (as they relate to systems of linear differential difference equations) are presented, and the relationship between the methods and applications are thoroughly addressed"--