Book:D.R. Cox/Queues

D.R. Cox and Walter L. Smith: Queues

Published $\text {1961}$, Chapman and Hall

Subject Matter

• Probability Theory

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