# Book:D.R. Cox/Queues

## D.R. Cox and Walter L. Smith: *Queues*

Published $1961$, **Chapman and Hall**.

### Subject Matter

### Contents

- Preface

**I. Introduction**- 1. Some examples
- 2. The aims of an investigation of congestion
- 3. The arrival pattern
- 4. The service mechanism
- 5. The queue-discipline
- 6. The measurement of congestion
- 7. The investigation of queueing systems
- 8. The modification of queueing systems

**II. Some simple queues with random arrivals**- 1. Introduction
- 2. Statistical equilibrium
- 3. Single-server queue with random arrivals and exponential service-times
- 4. Arrival rates and service-times dependent on queue size
- 5. Further remarks on equilibrium conditions
- 6. Single-server queue with random arrivals and general distribution of service-times
- 7. The busy-period distribution

**III. More about simple queues**- 1. Non-equilibrium theory
- 2. Queue with many servers
- 3. Queues with priorities

**IV. Machine Interference**- 1. Statement of problem
- 2. The simplest probability model
- 3. Some complications

**V. More specialized topics**- 1. Introduction
- 2. The method of stages
- 3. The integral equation of a single-server queue
- 4. Simulation and Monte-Carlo methods
- 5. Series of queues
- 6. The busy-period distribution

**Appendices**- I. Bibliographical notes
- II. Exercises and further results
- III. Notes on the theory of probability and Laplace-Stieltjes transforms

**Author Index**

**Subject Index**