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**Fundamentals of queueing theory.
3rd ed.**
*(English)*
Zbl 0949.60002

Chichester: Wiley. 439 p. (1998).

For the review of the first and second edition of this monograph see Zbl 0312.60046 and Zbl 0658.60122, respectively. The most important modification of the third edition relates to the incorporation of spreadsheet-based software, which can be downloaded from Wiley’s ftp site. Some introduction and illustrations are given in the Appendix 3: QTS Software. The specific major changes made in this new edition are:

1. The old Section 1.7 on deterministic models has been combined with material on general results previously scattered throughout the book and with the data bookkeeping presentation previously found in the discussion of simulation in the old Chapter 8. Further, more discussions of queue sample paths and the development of Little’s formula as a result have been introduced. The presentation of basic results on birth-death processes has been moved from the old Section 2.1 into Section 1.10, following the discussion of Markov processes in Section 1.9.

2. Less the material on birth-death processes, the order of the material of Chapter 2 has not been changed, but the narrative has been changed somewhat. Virtually, all the models discussed there have been included in the software as distinct modules.

3. In Chapter 3 some additional results on the classical Markovian bulk and Erlang models, including more details on the \(\text{E}_j/\text{E}_k/1\) queue, have been added. The inclusion of these sorts of models in the software is especially important given their inherent numerical complexity.

4. The narrative of Chapter 4, which deals with queueing networks, has been smoothed out and new material on reversibility as well as a section on mean-value analysis (MVA) has been added.

5. The first nine subsections of Section 5.1 on M/G/1 queues and variations are largely unchanged, but Section 5.1.10 has been expanded to combine departure-point state dependence with the concepts of decomposition and server vacations. Section 5.2 contains a new proof of Erlang’s loss formula built around the reversibility of Markov processes. The material on \(\text{G/M/}c\) presented in this chapter has also been expanded by a more complete discussion on the rootfinding involved and the extension from the single-server problem to multiple servers. This chapter is also well covered in the software.

6. Chapter 6 contains new material on the \(\text{G/E}_k/1\) queue, including the extension of simple rootfinding into the complex domain. This material is combined with expanded discussions on matrix geometric solutions and quasi-birth-death processes. The discussion on the G/G/1 problem has been moved to Section 6.2. The solution of the \(\text{M/D/}c\) queue is connected back to the same sort of complex rootfinding problem as for the \(\text{G/E}_k/1\). The sections in this chapter on Markov renewal processes, alternative disciplines, design and control, and statistical inference have all been updated and expanded.

7. Chapter 7 combines the important topics of bounds, approximations, numerics, and simulation. The discussions on bounds and approximations have been updated and slightly expanded. The earlier coverage of simulation has been reduced from a full chapter (8) to just a section and moved into Chapter 7, in view of the explosive growth (since the second edition) of this topic and of the limited space available. Thus only the most general elements of simulation modelling are summarized.

The book contains a lot of examples. Many exercises and problems can be (best) solved by the software accompanying the book, which is indicated accordingly.

1. The old Section 1.7 on deterministic models has been combined with material on general results previously scattered throughout the book and with the data bookkeeping presentation previously found in the discussion of simulation in the old Chapter 8. Further, more discussions of queue sample paths and the development of Little’s formula as a result have been introduced. The presentation of basic results on birth-death processes has been moved from the old Section 2.1 into Section 1.10, following the discussion of Markov processes in Section 1.9.

2. Less the material on birth-death processes, the order of the material of Chapter 2 has not been changed, but the narrative has been changed somewhat. Virtually, all the models discussed there have been included in the software as distinct modules.

3. In Chapter 3 some additional results on the classical Markovian bulk and Erlang models, including more details on the \(\text{E}_j/\text{E}_k/1\) queue, have been added. The inclusion of these sorts of models in the software is especially important given their inherent numerical complexity.

4. The narrative of Chapter 4, which deals with queueing networks, has been smoothed out and new material on reversibility as well as a section on mean-value analysis (MVA) has been added.

5. The first nine subsections of Section 5.1 on M/G/1 queues and variations are largely unchanged, but Section 5.1.10 has been expanded to combine departure-point state dependence with the concepts of decomposition and server vacations. Section 5.2 contains a new proof of Erlang’s loss formula built around the reversibility of Markov processes. The material on \(\text{G/M/}c\) presented in this chapter has also been expanded by a more complete discussion on the rootfinding involved and the extension from the single-server problem to multiple servers. This chapter is also well covered in the software.

6. Chapter 6 contains new material on the \(\text{G/E}_k/1\) queue, including the extension of simple rootfinding into the complex domain. This material is combined with expanded discussions on matrix geometric solutions and quasi-birth-death processes. The discussion on the G/G/1 problem has been moved to Section 6.2. The solution of the \(\text{M/D/}c\) queue is connected back to the same sort of complex rootfinding problem as for the \(\text{G/E}_k/1\). The sections in this chapter on Markov renewal processes, alternative disciplines, design and control, and statistical inference have all been updated and expanded.

7. Chapter 7 combines the important topics of bounds, approximations, numerics, and simulation. The discussions on bounds and approximations have been updated and slightly expanded. The earlier coverage of simulation has been reduced from a full chapter (8) to just a section and moved into Chapter 7, in view of the explosive growth (since the second edition) of this topic and of the limited space available. Thus only the most general elements of simulation modelling are summarized.

The book contains a lot of examples. Many exercises and problems can be (best) solved by the software accompanying the book, which is indicated accordingly.

Reviewer: A.Brandt (Berlin)

### MSC:

60-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory |

90-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming |

60K25 | Queueing theory (aspects of probability theory) |

90B22 | Queues and service in operations research |