Contents

pp v-x

Notation

pp xi-xii

Introduction

pp xiii-xvi

Part I - The Single Queue

pp 1-2

1 - Queues and Their Simulations, Birth and Death Queues

pp 3-15

2 - The M/G/1 Queue

pp 16-41

3 - Scheduling

pp 42-58

Part II - Approximations of the Single Queue

pp 59-60

4 - The G/G/1 Queue

pp 61-70

5 - The Basic Probability Functional Limit Theorems

pp 71-82

6 - Scaling of G/G/1 and G/G/∞

pp 83-101

7 - Diffusions and Brownian Processes

pp 102-122

Part III - Queueing Networks

pp 123-124

8 - Product-Form Queueing Networks

pp 125-142

9 - Generalized Jackson Networks

pp 143-156

Part IV - Fluid Models of Multi-Class Queueing

pp 157-158

10 - Multi-Class QueueingNetworks, Instability, and MarkovRepresentations

pp 159-174

11 - Stability of MCQN via Fluid Limits

pp 175-196

12 - Processing Networks and Maximum Pressure Policies

pp 197-218

13 - Processing Networks with Infinite Virtual Queues

pp 219-235

14 - Optimal Control of Transient Networks

pp 236-256

Part V - Diffusion Scaled Balanced Heavy Traffic

pp 257-258

15 - Join the Shortest Queue in Parallel Servers

pp 259-269

16 - Control in Balanced Heavy Traffic

pp 270-304

17 - MCQN with Discretionary Routing

pp 305-320

Part VI - Many-Server Systems

pp 321-322

18 - Infinite Servers Revisited

pp 323-329

19 - Asymptotics under Halfin.Whitt Regime

pp 330-345

20 - Many Servers with Abandonment

pp 346-359