QUEUEING MODELS IN INDUSTRY AND BUSINESS SECOND EDITION

QUEUEING MODELS IN INDUSTRY AND BUSINESS SECOND EDITION

Library of Congress Cataloging-in-Publication Data

CONTENTS

IN HONOR OF PROFESSOR EMERITUS LAJOS TAKÁCS

PREFACE

PREFACE

Chapter 1 PRELIMINARIES

1.1. INTRODUCTION

1.2. STOCHASTIC PROCESSES

1.3. MARKOV CHAIN AND MARKOV PROCESS

1.4. GENERATING FUNCTIONS AND THEIR APPLICATION IN SOLUTION OF DIFFERENCE EQUATIONS

1.5. GENERAL DISCUSSION OF QUEUEING PROCESSES AND ITS HISTORICAL DEVELOPMENT

1.6. EXAMPLES OF QUEUES

1.7.MECHANISM OF A QUEUE

1.8. CHARACTERISTICS OF A QUEUE

Chapter 2 BIRTH AND DEATH PROCESSES

2.1. INTRODUCTION

2.2. POISSON PROCESS

2.3. SYSTEM OF DIFFERENTIAL DIFFERENCE EQUATIONS (DDE)

2.4. COUNTING PROCESSES

2.5. STANDARD EXAMPLES

2.6. SOJOURN TIMES

2.7. LIMITING BALANCE EQUATIONS FOR CONTINUOUS PROCESSES

Chapter 3 SINGLE-SERVER QUEUES

3.1. INTRODUCTION

3.2. THE M/M/1 QUEUEING PROCESS

3.3. THE M/M/1/K QUEUE

3.4. THE C/M/1/K SYSTEM [K-MACHINE FAILURE-REPAIR, FR(K,1)]

3.5. TAKÁCS PARADOX

3.6.M/M/1 WITH FEEDBACK

3.7. TRANSIENT BEHAVIOR OF A SINGLE-SERVER QUEUE WITH POISSON ARRIVALS AND GENERAL DISTRIBUTION OF SERVICE TIME

3.8. TAKÁCS PROCESS

3.9. EXACT TRANSIENT SOLUTION OF A STATE-DEPENDENT QUEUE IN DISCRETE-TIME

3.10. THE CONTINUOUS REVIEW (S,S) POLICY FOR PRODUCTION/INVENTORY SYSTEMS WITH POISSON DEMANDS AND ARBITRARY PROCESSING TIMES

Chapter 4 PARALLEL QUEUEING MODELS

4.1. INTRODUCTION

4.2. GENERAL CASE OF AN M-SERVER QUEUE

4.3.WAITING TIME DISTRIBUTION FOR THE M/M/M QUEUE

4.4. MANY-SERVERQUEUEING SYSTEMSWITH FEEDBACK

4.5. A CONVEYOR SYSTEM AS A PARALLEL PRIORITY QUEUEING SYSTEM WITH FINITE BUFFERS

4.6. AMULTISERVER MARKOVIAN QUEUE WITH BALKING AND RENEGING

4.7. TRANSIENT BEHAVIOR OF B-D AND THE M/M/C/K QUEUE

Chapter 5 TANDEM QUEUEING MODELS

5.1. INTRODUCTION

5.2. SIMPLE TWO-NODE TANDEM QUEUES

5.3. A TANDEM QUEUE WITH A COUPLE PROCESSOR

5.4. A RECURSIVE METHODOLOGY UTILIZED IN BLOCKING TANDEM QUEUES

5.5. BULK ARRIVA AND BATCH SERVICE TANDEM QUEUEINGPROCESS: A HIRING MODEL,

Chapter 6 A DELAYED-SERVICE QUEUEING MODEL AND FEEDBACK QUEUES WITH TASK SPLITTING AND BLOCKING

6.1. A PARALLEL MULTI-PROCESSOR SYSTEM WITH FEEDBACK AND TASK-SPLITTING

6.2. A TANDEM QUEUEING MODEL WITH TASK-SPLITTING, FEEDBACK, AND BLOCKING

6.3. A SINGLE-SERVER POISSON QUEUEING SYSTEM WITH DELAYED-SERVICE

EXERCISES

APPENDIX

REFERENCES

EDITORS’ CONTACT INFORMATION

INDEX