Dedication v
Preface xi
Acknowledgments xiii
Introduction 1
Description of the Queueing Problem 2
Characteristics of Queueing Processes 3
Notation 7
Measuring System Performance 8
Some General Results 9
Simple Data Bookkeeping for Queues 12
Poisson Process and the Exponential Distribution 16
Markovian Property of the Exponential Distribution 20
Stochastic Processes and Markov Chains 24
Introduction to the QtsPlus Software 40
Problems 41
Simple Markovian Queueing Models 49
Birth-Death Processes 49
Single-Server Queues (M/M/1) 53
Multiserver Queues (M/M/c) 66
Choosing the Number of Servers 73
Queues with Truncation (M/M/c/K) 76
Erlang's Loss Formula (M/M/c/c) 81
Queues with Unlimited Service (M/M/[infinity]) 84
Finite-Source Queues 85
State-Dependent Service 91
Queues with Impatience 95
Transient Behavior 97
Busy-Period Analysis 102
Problems 103
Advanced Markovian Queueing Models 117
Bulk Input (M[superscript X]/M/1) 117
Bulk Service (M/M[superscript Y]/1) 123
Erlangian Models 128
Priority Queue Disciplines 141
Retrial Queues 157
Problems 171
Networks, Series, and Cyclic Queues 179
Series Queues 181
Open Jackson Networks 187
Closed Jackson Networks 195
Cyclic Queues 209
Extensions of Jackson Networks 210
Non-Jackson Networks 212
Problems 214
General Arrival or Service Patterns 219
General Service, Single Server (M/G/1) 219
General Service, Multiserver (M/G/c/[infinity], M/G/[infinity]) 254
General Input (G/M/1, G/M/c) 259
Problems 270
General Models and Theoretical Topics 277
G/E[subscript k]/1, G[superscript k]/M/1, and G/PH[subscript k]/1 277
General Input, General Service (G/G/1) 284
Poisson Input, Constant Service, Multiserver (M/D/c) 294
Semi-Markov and Markov Renewal Processes in Queueing 296
Other Queue Disciplines 301
Design and Control of Queues 306
Statistical Inference in Queueing 317
Problems 325
Bounds and Approximations 329
Bounds 330
Approximations 343
Network Approximations 356
Problems 367
Numerical Techniques and Simulation 369
Numerical Techniques 369
Numerical Inversion of Transforms 385
Discrete-Event Stochastic Simulation 398
Problems 421
References 427
Symbols and Abbreviations 439
Tables 447
Transforms and Generating Functions 455
Laplace Transforms 455
Generating Functions 462
Differential and Difference Equations 467
Ordinary Differential Equations 467
Difference Equations 483
QtsPlus Software 489
Instructions for Downloading 493
Index 495
