Fundamentals of queueing theory. 2nd ed.

*(English)*Zbl 0658.60122
Wiley Series in Probability and Mathematical Statistics. Applied Probability and Statistics. New York etc.: John Wiley & Sons. XIII, 587 p. (GĂ¶: 86A 5611) (1985).

For the review of the first edition see Zbl 0312.60046. The major changes in the second edition are:

1. The old Chapters 2 and 3 (birth-death models) are combined into a single chapter (new Chapter 2). Where useful for pedagogical reasons, we treat the M/M/1 separately within the new chapter. The combining of birth-death models into a single chapter, we believe, provides a more cohesive treatment.

2. A new section in Chapter 1 (Section 1.10) covers the fundamentals of Markov processes. This new section also incorporates the material on Chapman-Kolmogorov equations found in the beginning of the old Chapter 3 and the ergodicity discussion previously found at the beginning of the old Chapter 2. An expanded and unified treatment of the entire steady- state issue is incorporated into the new Section 1.10, as well as the fundamentals of both discrete- and continuous-parameter Markov chains.

3. Introductory material on phase-type distributions is included in the new Chapter 3 (Advanced Markovian Models) when the Erlang distribution is introduced (we show the Erlang to be a special phase-type distribution) in Section 3.3. This new Chapter 3 also includes a discussion of multichannel Erlang models.

4. An entire chapter (new Chapter 4) is devoted to the very important topic of queueing networks, particularly emphasizing Jackson network theory for both open and closed networks.

5. The matrix geometric concept is introduced in Chapter 5, Section 5.3.3, where we discuss the \(G/PH_ k/1\) queue.

6. Chapter 6 contains an expanded discussion on statistical inference in queueuing, particularly in the distribution selection portion. There we discuss the general problem of how to choose an appropriate probability distribution for arrivals and service processes. Also in Chapter 6, the design and control section is updated and slightly expanded.

7. The new Chapter 7 is entirely devoted to another important topic, bounds and approximations. The bounds discussion is updated and expanded. An entirely new section, Section 7.3, is included on numerical solution techniques for both steady-state and transient solutions, including such techniques as Runge-Kutta and randomization for transient solutions and Jacobi and Gauss-Seidel iteration for steady-state solutions.

8. An updating of the simulation chapter, Chapter 8, reflects changes in simulation languages and new results in statistical analysis of simulation output such as regenerative techniques.

1. The old Chapters 2 and 3 (birth-death models) are combined into a single chapter (new Chapter 2). Where useful for pedagogical reasons, we treat the M/M/1 separately within the new chapter. The combining of birth-death models into a single chapter, we believe, provides a more cohesive treatment.

2. A new section in Chapter 1 (Section 1.10) covers the fundamentals of Markov processes. This new section also incorporates the material on Chapman-Kolmogorov equations found in the beginning of the old Chapter 3 and the ergodicity discussion previously found at the beginning of the old Chapter 2. An expanded and unified treatment of the entire steady- state issue is incorporated into the new Section 1.10, as well as the fundamentals of both discrete- and continuous-parameter Markov chains.

3. Introductory material on phase-type distributions is included in the new Chapter 3 (Advanced Markovian Models) when the Erlang distribution is introduced (we show the Erlang to be a special phase-type distribution) in Section 3.3. This new Chapter 3 also includes a discussion of multichannel Erlang models.

4. An entire chapter (new Chapter 4) is devoted to the very important topic of queueing networks, particularly emphasizing Jackson network theory for both open and closed networks.

5. The matrix geometric concept is introduced in Chapter 5, Section 5.3.3, where we discuss the \(G/PH_ k/1\) queue.

6. Chapter 6 contains an expanded discussion on statistical inference in queueuing, particularly in the distribution selection portion. There we discuss the general problem of how to choose an appropriate probability distribution for arrivals and service processes. Also in Chapter 6, the design and control section is updated and slightly expanded.

7. The new Chapter 7 is entirely devoted to another important topic, bounds and approximations. The bounds discussion is updated and expanded. An entirely new section, Section 7.3, is included on numerical solution techniques for both steady-state and transient solutions, including such techniques as Runge-Kutta and randomization for transient solutions and Jacobi and Gauss-Seidel iteration for steady-state solutions.

8. An updating of the simulation chapter, Chapter 8, reflects changes in simulation languages and new results in statistical analysis of simulation output such as regenerative techniques.

##### MSC:

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

60-02 | Research exposition (monographs, survey articles) pertaining to probability theory |

60K20 | Applications of Markov renewal processes (reliability, queueing networks, etc.) |