Fundamentals of Queueing Theory

Praise for the Third Edition"This is one of the best books available. Its excellentorganizational structure allows quick reference to specific modelsand its clear presentation . . . solidifies the understanding ofthe concepts being presented."IIE Transactions on Operations EngineeringThoroughly revised and expanded to reflect the latestdevelopments in the field, Fundamentals of Queueing Theory,Fourth Edition continues to present the basic statisticalprinciples that are necessary to analyze the probabilistic natureof queues. Rather than presenting a narrow focus on the subject,this update illustrates the wide-reaching, fundamental concepts inqueueing theory and its applications to diverse areas such ascomputer science, engineering, business, and operationsresearch.This update takes a numerical approach to understanding andmaking probable estimations relating to queues, with acomprehensive 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 qualityand cost of serviceEach chapter provides a self-contained presentation of keyconcepts and formulae, allowing readers to work with each sectionindependently, while a summary table at the end of the bookoutlines the types of queues that have been discussed and theirresults. In addition, two new appendices have been added,discussing transforms and generating functions as well as thefundamentals of differential and difference equations. New examplesare now included along with problems that incorporate QtsPlussoftware, which is freely available via the book's related Website.With its accessible style and wealth of real-world examples,Fundamentals of Queueing Theory, Fourth Edition is an idealbook for courses on queueing theory at the upper-undergraduate andgraduate levels. It is also a valuable resource for researchers andpractitioners who analyze congestion in the fields oftelecommunications, transportation, aviation, and managementscience.

Dedication.Preface.1. Introduction.1.1 Description of the Queueing Problem.1.2 Characteristics of Queueing Processes.1.3 Notation.1.4 Measuring System Performance.1.5 Some General Results.1.6 Simple Data Bookkeeping for Queues.1.7 Poisson Process and the Exponential Distribution.1.8 Markovian Property of the Exponential Distribution.1.9 Stochastic Processes and Markov Chains.Problems.2. Simple Markovian Queueing Models.2.1 Birth Death Processes.2.2 Single-Server Queues (M/M/1).2.3 Multi-Server Queues (M/M/c).2.4 Choosing the Number of Servers.2.5 Queues with Truncation (M/M/c/K).2.6 Erlang?s Loss Formula (M/M/c/c).2.7 Queues with Unlimited Service (M/M/1).2.8 Finite Source Queues.2.9 State-Dependent Service.2.10 Queues with Impatience.2.11 Transient Behavior.2.12 Busy-Period Analysis.Problems.3. Advanced Markovian Queueing Models.3.1 Bulk Input (M[X]/M/1).3.2 Bulk Service (M/M[Y ]/1).3.3 Erlangian Models.3.4 Priority Queue Disciplines.3.5 Retrial Queues.4. Networks, Series, and Cyclic Queues.4.1 Series Queues.4.2 Open Jackson Networks.4.3 Closed Jackson Networks.4.4 Cyclic Queues.4.5 Extensions of Jackson Networks.4.6 Non-Jackson Networks.5. General Arrival or Service Patterns.5.1 General Service, Single Server (M/G/1).5.2 General Service, Multi-Server (M/G/c/ú, M/G/1).5.3 General Input (G/M/1, G/M/c).6. More General Models and Theoretical Topics.6.1 G/Ek/1, G[k]/M/1, and G/PHk/1.6.2 General Input, General Service (G/G/1) .6.3 Multichannel Queues with Poisson Input and Constant Service(M/D/c).6.4 Semi-Markov and Markov Renewal Processes in Queueing.6.5 Other Queue Disciplines.6.6 Design and Control of Queues.6.7 Statistical Inference in Queueing.7. Bounds and Approximations.7.1 Bounds.7.2 Approximations.7.3 Network Approximations.Problems.8. Numerical Techniques and Simulation.8.1 Numerical Techniques.8.2 Numerical Inversion of Transforms.8.3 Discrete-Event Stochastic Simulation.Problems.Bibliography.Appendix 1. Symbols and Abbreviations.Appendix 2. Tables.Appendix 3. Transforms and Generating Functions.A3.1 Laplace Transforms.A3.2 Generating Functions.Appendix 4. Differential and Difference Equations.A4.1 Ordinary Differential Equations.A4.2 Difference Equations.Appendix 5. QTSPlus Software.A5.1 Instructions for Downloading.