Fundamentals of Queueing Theory

Fundamentals of Queueing Theory : Solutions Manual

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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.
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Product details

  • Paperback | 88 pages
  • 159 x 230 x 7mm | 134g
  • New York, United States
  • English
  • 4th Edition
  • 0470077964
  • 9780470077962
  • 1,297,663

Table of contents

Dedication v Preface xi

Acknowledgments xiii

Introduction 1

Description of the Queueing Problem 2

Characteristics of Queueing Processes 3

Notation 7

Measuring System Performance 8

Some General Results 9

Simple Data Bookkeeping for Queues 12

Poisson Process and the Exponential Distribution 16

Markovian Property of the Exponential Distribution 20

Stochastic Processes and Markov Chains 24

Introduction to the QtsPlus Software 40

Problems 41

Simple Markovian Queueing Models 49

Birth-Death Processes 49

Single-Server Queues (M/M/1) 53

Multiserver Queues (M/M/c) 66

Choosing the Number of Servers 73

Queues with Truncation (M/M/c/K) 76

Erlang's Loss Formula (M/M/c/c) 81

Queues with Unlimited Service (M/M/[infinity]) 84

Finite-Source Queues 85

State-Dependent Service 91

Queues with Impatience 95

Transient Behavior 97

Busy-Period Analysis 102

Problems 103

Advanced Markovian Queueing Models 117

Bulk Input (M[superscript X]/M/1) 117

Bulk Service (M/M[superscript Y]/1) 123

Erlangian Models 128

Priority Queue Disciplines 141

Retrial Queues 157

Problems 171

Networks, Series, and Cyclic Queues 179

Series Queues 181

Open Jackson Networks 187

Closed Jackson Networks 195

Cyclic Queues 209

Extensions of Jackson Networks 210

Non-Jackson Networks 212

Problems 214

General Arrival or Service Patterns 219

General Service, Single Server (M/G/1) 219

General Service, Multiserver (M/G/c/[infinity], M/G/[infinity]) 254

General Input (G/M/1, G/M/c) 259

Problems 270

General Models and Theoretical Topics 277

G/E[subscript k]/1, G[superscript k]/M/1, and G/PH[subscript k]/1 277

General Input, General Service (G/G/1) 284

Poisson Input, Constant Service, Multiserver (M/D/c) 294

Semi-Markov and Markov Renewal Processes in Queueing 296

Other Queue Disciplines 301

Design and Control of Queues 306

Statistical Inference in Queueing 317

Problems 325

Bounds and Approximations 329

Bounds 330

Approximations 343

Network Approximations 356

Problems 367

Numerical Techniques and Simulation 369

Numerical Techniques 369

Numerical Inversion of Transforms 385

Discrete-Event Stochastic Simulation 398

Problems 421

References 427

Symbols and Abbreviations 439

Tables 447

Transforms and Generating Functions 455

Laplace Transforms 455

Generating Functions 462

Differential and Difference Equations 467

Ordinary Differential Equations 467

Difference Equations 483

QtsPlus Software 489

Instructions for Downloading 493

Index 495
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Review quote

"Despite its title, the book is rather advanced, so it is appropriate for practitioners, those in academia, and upper-class students. However, any reader will benefit from the concise introductions to the problems, the detailed descriptions supported with step-by-step formulas, the solutions provided by the manual, and the QtsPlus software." (Computing Reviews, 1 December 2011)
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About Donald Gross

Donald Gross is the author of Solutions Manual to accompany Fundamentals of Queueing Theory, 4e, published by Wiley. John F. Shortle is the author of Solutions Manual to accompany Fundamentals of Queueing Theory, 4e, published by Wiley.
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