Publisher: John Wiley (2008)Details: 500 pages, Hardcover
Edition: 4 Series: Wiley Series in Probability and Statistics
Price: $110.00
ISBN: 9780471791270
Category: Textbook
Topics: Queueing Theory
Donald Gross, John F. Shortle, James M. Thompson, and Carl M. Harris
Publisher: John Wiley (2008)
Details: 500 pages, Hardcover
Edition: 4 Series: Wiley Series in Probability and Statistics
Price: $110.00
ISBN: 9780471791270
Category: Textbook
Topics: Queueing Theory
[Reviewed by William J. Satzer, on 03/19/2009]
This classic mathematical introduction to queueing theory is now in its fourth edition. It has been honed and polished over the years and differs from the third edition only in modest additions and some reorganization. The text is aimed at advanced undergraduates or graduate students in applied probability or operations research. A comparable introduction for engineers or computer scientists is Kleinrock’s Queueing Systems, which focuses more on results than development and is a bit dated now.
Queueing theory is known for its rather distinctive notation. A queueing process is described by a series of symbols and slashes such as A/B/C/D/E where A indicates an inter-arrival time probability distribution, B identifies the distribution for service (or waiting) time, C the number of parallel service channels, D the restrictions on service capacity, and E the queue discipline. So the notation M/D/2/∞/FCFS refers to a queueing process with exponential (the M is for Markov) arrival times, deterministic service time, two parallel service channels, no restrictions on capacity, and first-come, first-served queue discipline. It sounds complicated, but is actually logical and useful. Of course, the most commonly used queueing model is just M/M/1 with exponentially distributed inter-arrival and waiting times. Just imagine waiting to pay for your groceries in a store with only one cashier.
The basics of queueing theory are introduced in the first two chapters. Chapter 1 establishes the background and terminology, provides some tools, and discusses basic (and quite powerful) results like Little’s formula. Simple Markovian queueing models of increasing complexity are taken up in Chapter 2. There is an amusing discussion here of modeling “queues with impatience”. These arise, for example, when a customer is reluctant to join a queue on arrival, doesn’t want to stay in line after joining and waiting, or chooses to jockey between lines when each of a number of parallel lines has its own queue. We have all probably practiced many forms of queue impatience.
The chapter on queues in series is quite an important one. The questions that come up are often difficult but important. The internet is a gigantic combination of queues in tandem, and understanding its performance — even estimating the end-to-end delay for a single packet traveling from your keyboard to its distant destination — is very challenging. The authors describe the major approaches in this field, but they can really only scratch the surface.
This is an accessible and attractive textbook with good writing al the way through. It has the advantage of years of classroom testing. The exercises are extensive and creative.
Bill Satzer (wjsatzer@mmm.com) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.
BLL*** — The Basic Library List Committee considers this book essential for undergraduate mathematics libraries.