Fundamentals of Queueing Theory by Thompson, James M. -- Read -- Imperial Library of Trantor

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Cover WILEY SERIES IN PROBABILITY AND STATISTICS Title Page Copyright Dedication PREFACE ACKNOWLEDGMENTS CHAPTER 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 BOOK KEEPING 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 1.10 INTRODUCTION TO THE QTSPLUS SOFTWARE PROBLEMS

CHAPTER 2: SIMPLE MARKOVIAN QUEUEING MODELS

2.1 BIRTH-DEATH PROCESSES 2.2 SINGLE-SERVER QUEUES (M/M/1) 2.3 MULTISERVER 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/∞) 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

CHAPTER 3: ADVANCED MARKOVIAN QUEUEING MODELS

3.1 BULK INPUT (M[X]/M/L) 3.2 BULK SERVICE (M/M[Y]/1) 3.3 ERLANGIAN MODELS 3.4 PRIORITY QUEUE DISCIPLINES 3.5 RETRIAL QUEUES PROBLEMS

CHAPTER 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 PROBLEMS

CHAPTER 5: GENERAL ARRIVAL OR SERVICE PATTERNS

5.1 GENERAL SERVICE, SINGLE SERVER (M/G/L) 5.2 GENERAL SERVICE, MULTISERVER (M/G/C/·, M/G/∞) 5.3 GENERAL INPUT (G/M/L, G/M/C) PROBLEMS

CHAPTER 6: GENERAL MODELS AND THEORETICAL TOPICS

6.1 G/E K/1, G[K]/M/1, AND G/PH K/1 6.2 GENERAL INPUT, GENERAL SERVICE (G/G/1) 6.3 POISSON INPUT, CONSTANT SERVICE, MULTISERVER (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 PROBLEMS

CHAPTER 7: BOUNDS AND APPROXIMATIONS

7.1 BOUNDS 7.2 APPROXIMATIONS 7.3 NETWORK APPROXIMATIONS PROBLEMS

CHAPTER 8: NUMERICAL TECHNIQUES AND SIMULATION

8.1 NUMERICAL TECHNIQUES 8.2 NUMERICAL INVERSION OF TRANSFORMS 8.3 DISCRETE-EVENT STOCHASTIC SIMULATION PROBLEMS

REFERENCES APPENDIX A: SYMBOLS AND ABBREVIATIONS APPENDIX B: TABLES APPENDIX C: TRANSFORMS AND GENERATING FUNCTIONS

C.1 LAPLACE TRANSFORMS C.2 GENERATING FUNCTIONS

APPENDIX D: DIFFERENTIAL AND DIFFERENCE EQUATIONS

D.1 ORDINARY DIFFERENTIAL EQUATIONS D.2 DIFFERENCE EQUATIONS

APPENDIX E: QTSPIUS SOFTWARE

E.1 INSTRUCTIONS FOR DOWNLOADING

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