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.