Analysis of Queues: Methods and Applications
Features
- Explains concepts through applications in a variety of domains such as production, computer communication, and service systems
- Presents numerous solved examples and exercise problems that deepen students’ understanding of topics
- Includes discussion of fluid-flow queues, which is not part of any other textbook
- Contains pre-requisite material to enhance methodological understanding
- Emphasizes methodology, rather than presenting a collection of formulae
- Provides 139 solved problems and 154 unsolved problems
- Promotes classroom discussions using case studies and paradoxes
Solutions manual and PowerPoint figure slides to enhance presentations are available upon qualifying course adoption.
Summary
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.
Table of Contents
Introduction
Analysis of Queues: Where, What, and How?
Systems Analysis: Key Results
Queueing Fundamentals and Notations
Psychology in Queueing
Reference Notes
Exercises
Exponential Interarrival and Service Times: Closed-Form Expressions
Solving Balance Equations via Arc Cuts
Solving Balance Equations Using Generating Functions
Solving Balance Equations Using Reversibility
Reference Notes
Exercises
Exponential Interarrival and Service Times: Numerical Techniques and Approximations
Multidimensional Birth and Death Chains
Multidimensional Markov Chains
Finite-State Markov Chains
Reference Notes
Exercises
General Interarrival and/or Service Times: Closed-Form Expressions and Approximations
Analyzing Queues Using Discrete Time Markov Chains
Mean Value Analysis
Bounds and Approximations for General Queues
Matrix Geometric Methods for G/G/s Queues
Other General Queues but with Exact Results
Reference Notes
Exercises
Multiclass Queues under Various Service Disciplines
Introduction
Evaluating Policies for Classification Based on Types: Priorities
Evaluating Policies for Classification Based on Location: Polling Models
Evaluating Policies for Classification Based on Knowledge of Service Times
Optimal Service-Scheduling Policies
Reference Notes
Exercises
Exact Results in Network of Queues: Product Form
Acyclic Queueing Networks with Poisson Flows
Open Jackson Networks
Closed Jackson Networks
Other Product-Form Networks
Reference Notes
Exercises
Approximations for General Queueing Networks
Single-Server and Single-Class General Queueing Networks
Multiclass and Multiserver Open Queueing Networks with FCFS
Multiclass and Single-Server Open Queueing Networks with Priorities
Reference Notes
Exercises
Fluid Models for Stability, Approximations, and Analysis of Time-Varying Queues
Deterministic Fluid Queues: An Introduction
Fluid Models for Stability Analysis of Queueing Networks
Diffusion Approximations for Performance Analysis
Fluid Models for Queues with Time-Varying Parameters
Reference Notes
Exercises
Stochastic Fluid-Flow Queues: Characteristics and Exact Analysis
Introduction
Single Buffer with Markov Modulated Fluid Source
First Passage Times
Reference Notes
Exercises
Stochastic Fluid-Flow Queues: Bounds and Tail Asymptotics
Introduction and Preliminaries
Performance Analysis of a Single Queue
Multiclass Fluid Queues
Reference Notes
Exercises
Appendix A: Random Variables
Appendix B: Stochastic Processes
References
Index
Editorial Reviews
"The breadth and scope of topics in this book surpass the books currently on the market. For most graduate engineering or business courses on this topic the selection is perfect. … presented in sufficient depth for any graduate class. I like in particular the "problems" presented at regular intervals, along with detailed solutions. … excellent coverage of both classical and modern techniques in queueing theory. Compelling applications and case studies are sprinkled throughout the text. For many of us who teach graduate courses in queueing theory, this is the text we have been waiting for!"
—John J. Hasenbein, The University of Texas at Austin
"Dr. Gautam has an obvious passion for queueing theory. His delight in presenting queueing paradoxes beams through the pages of the book. His relaxed conversational style makes reading the book a pleasure. His introductory comments about having to account for a large variety of educational backgrounds among students taking graduate courses indicate that he takes education very seriously. It shows throughout the book. He has made an excellent choice of topics and presented them in his own special style. I highly recommend this queueing text by an expert who clearly loves his field."
—Dr. Myron Hlynka, University of Windsor, Ontario, Canada
"… will be a good addition to my collection of books on queueing theory."
—Attahiru S. Alfa, University of Manitoba, Canada
