| |
| |
| List of Illustrations | |
| |
| |
| Preface | |
| |
| |
| Dedication | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Networks in practice | |
| |
| |
| |
| Mathematical models | |
| |
| |
| |
| What do you need to know to read this book? | |
| |
| |
| |
| Notes | |
| |
| |
| |
| Modeling and Control | |
| |
| |
| |
| Examples | |
| |
| |
| |
| Modeling the single server queue | |
| |
| |
| |
| Klimov model | |
| |
| |
| |
| Capacity and queueing in communication systems | |
| |
| |
| |
| Multiple-access communication | |
| |
| |
| |
| Processor sharing model | |
| |
| |
| |
| Inventory model | |
| |
| |
| |
| Power transmission network | |
| |
| |
| |
| Optimization in a simple re-entrant line | |
| |
| |
| |
| Contention for resources and instability | |
| |
| |
| |
| Routing model | |
| |
| |
| |
| Braess' paradox | |
| |
| |
| |
| Notes | |
| |
| |
| |
| The Single Server Queue | |
| |
| |
| |
| Representations | |
| |
| |
| |
| Approximations | |
| |
| |
| |
| Stability | |
| |
| |
| |
| Invariance equations | |
| |
| |
| |
| Big queues | |
| |
| |
| |
| Model selection | |
| |
| |
| |
| Notes | |
| |
| |
| Exercises | |
| |
| |
| |
| Scheduling | |
| |
| |
| |
| Controlled random-walk model | |
| |
| |
| |
| Fluid model | |
| |
| |
| |
| Control techniques for the fluid model | |
| |
| |
| |
| Comparing fluid and stochastic models | |
| |
| |
| |
| Structure of optimal policies | |
| |
| |
| |
| Safety-stocks | |
| |
| |
| |
| Discrete review | |
| |
| |
| |
| MaxWeight and MinDrift | |
| |
| |
| |
| Perturbed value function | |
| |
| |
| |
| Notes | |
| |
| |
| Exercises | |
| |
| |
| |
| Workload | |
| |
| |
| |
| Workload and Scheduling | |
| |
| |
| |
| Single server queue | |
| |
| |
| |
| Workload for the CRW scheduling model | |
| |
| |
| |
| Relaxations for the fluid model | |
| |
| |
| |
| Stochastic workload models | |
| |
| |
| |
| Pathwise optimality and workload | |
| |
| |
| |
| Hedging in networks | |
| |
| |
| |
| Notes | |
| |
| |
| Exercises | |
| |
| |
| |
| Routing and Resource Pooling | |
| |
| |
| |
| Workload in general models | |
| |
| |
| |
| Resource pooling | |
| |
| |
| |
| Routing and workload | |
| |
| |
| |
| MaxWeight for routing and scheduling | |
| |
| |
| |
| Simultaneous resource possession | |
| |
| |
| |
| Workload relaxations | |
| |
| |
| |
| Relaxations and policy synthesis for stochastic models | |
| |
| |
| |
| Notes | |
| |
| |
| Exercises | |
| |
| |
| |
| Demand | |
| |
| |
| |
| Network models | |
| |
| |
| |
| Transients | |
| |
| |
| |
| Workload relaxations | |
| |
| |
| |
| Hedging in a simple inventory model | |
| |
| |
| |
| Hedging in networks | |
| |
| |
| |
| Summary of steady-state control techniques | |
| |
| |
| |
| Notes | |
| |
| |
| Exercises | |
| |
| |
| |
| Stability and Performance | |
| |
| |
| |
| Foster-Lyapunov Techniques | |
| |
| |
| |
| Lyapunov functions | |
| |
| |
| |
| Lyapunov functions for networks | |
| |
| |
| |
| Discrete review | |
| |
| |
| |
| MaxWeight | |
| |
| |
| |
| MaxWeight and the average-cost optimality equation | |
| |
| |
| |
| Linear programs for performance bounds | |
| |
| |
| |
| Brownian workload model | |
| |
| |
| |
| Notes | |
| |
| |
| Exercises | |
| |
| |
| |
| Optimization | |
| |
| |
| |
| Reachability and decomposibility | |
| |
| |
| |
| Linear programming formulations | |
| |
| |
| |
| Multiobjective optimization | |
| |
| |
| |
| Optimality equations | |
| |
| |
| |
| Algorithms | |
| |
| |
| |
| Optimization in networks | |
| |
| |
| |
| One-dimensional inventory model | |
| |
| |
| |
| Hedging and workload | |
| |
| |
| |
| Notes | |
| |
| |
| Exercises | |
| |
| |
| |
| ODE Methods | |
| |
| |
| |
| Examples | |
| |
| |
| |
| Mathematical preliminaries | |
| |
| |
| |
| Fluid limit model | |
| |
| |
| |
| Fluid-scale stability | |
| |
| |
| |
| Safety stocks and trajectory tracking | |
| |
| |
| |
| Fluid-scale asymptotic optimality | |
| |
| |
| |
| Brownian workload model | |
| |
| |
| |
| Notes | |
| |
| |
| Exercises | |
| |
| |
| |
| Simulation and Learning | |
| |
| |
| |
| Deciding when to stop | |
| |
| |
| |
| Asymptotic theory for Markov models | |
| |
| |
| |
| The single-server queue | |
| |
| |
| |
| Control variates and shadow functions | |
| |
| |
| |
| Estimating a value function | |
| |
| |
| |
| Notes | |
| |
| |
| Exercises | |
| |
| |
| |
| Markov Models | |
| |
| |
| Bibliography | |
| |
| |
| Index | |