Page 8 - A First Course In Stochastic Models

viii CONTENTS

9.2 The M/G/1 Queue 345
9.2.1 The State Probabilities 346
9.2.2 The Waiting-Time Probabilities 349
9.2.3 Busy Period Analysis 353
9.2.4 Work in System 358
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9.3 The M /G/1 Queue 360
9.3.1 The State Probabilities 361
9.3.2 The Waiting-Time Probabilities 363
9.4 M/G/1 Queues with Bounded Waiting Times 366
9.4.1 The Finite-Buffer M/G/1 Queue 366
9.4.2 An M/G/1 Queue with Impatient Customers 369
9.5 The GI /G/1 Queue 371
9.5.1 Generalized Erlangian Services 371
9.5.2 Coxian-2 Services 372
9.5.3 The GI /Ph/1 Queue 373
9.5.4 The Ph/G/1 Queue 374
9.5.5 Two-moment Approximations 375
9.6 Multi-Server Queues with Poisson Input 377
9.6.1 The M/D/c Queue 378
9.6.2 The M/G/c Queue 384
9.6.3 The M X /G/c Queue 392
9.7 The GI /G/c Queue 398
9.7.1 The GI /M/c Queue 400
9.7.2 The GI /D/c Queue 406
9.8 Finite-Capacity Queues 408
9.8.1 The M/G/c/c + N Queue 408
9.8.2 A Basic Relation for the Rejection Probability 410
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9.8.3 The M /G/c/c + N Queue with Batch Arrivals 413
9.8.4 Discrete-Time Queueing Systems 417
Exercises 420
Bibliographic Notes 428
References 428
Appendices 431

Appendix A. Useful Tools in Applied Probability 431
Appendix B. Useful Probability Distributions 440
Appendix C. Generating Functions 449
Appendix D. The Discrete Fast Fourier Transform 455
Appendix E. Laplace Transform Theory 458
Appendix F. Numerical Laplace Inversion 462
Appendix G. The Root-Finding Problem 470
References 474

Index 475