Control Techniques for Complex Networks

Книга Control Techniques for Complex Networks Control Techniques for Complex NetworksКниги English литература Автор: Sean Meyn Год издания: 2007 Формат: pdf Издат.:Cambridge University Press Страниц: 582 Размер: 17,8 Mb ISBN: 0521884411 Язык: Английский0 (голосов: 0) Оценка:Power grids, flexible manufacturing, cellular communications: interconnectedness has consequences. This remarkable book gives the tools and philosophy you need to build network models detailed enough to capture essential dynamics but simple enough to expose the structure of effective control solutions and to clarify analysis. Core chapters assume only exposure to stochastic processes and linear algebra at the undergraduate level; later chapters are for advanced graduate students and researchers/practitioners. This gradual development bridges classical theory with the state-of-the-art. The workload model that is the basis of traditional analysis of the single queue becomes a foundation for workload relaxations used in the treatment of complex networks. Lyapunov functions and dynamic programming equations lead to the celebrated MaxWeight policy along with many generalizations. Other topics include methods for synthesizing hedging and safety stocks, stability theory for networks, and techniques for accelerated simulation. Examples and figures throughout make ideas concrete. Solutions to end-of-chapter exercises available on a companion website. Preface......Page 2 Introduction......Page 10 Networks in practice......Page 11 Mathematical models......Page 16 What do you need to know to read this book?......Page 20 Notes......Page 32 I Modeling & Control......Page 34 Modeling the single server queue......Page 35 Klimov model......Page 41 Multiple-access communication......Page 44 Processor sharing model......Page 46 Power transmission network......Page 47 Simple re-entrant line......Page 49 Contention for resources and instability......Page 53 Routing model......Page 56 Braess' paradox......Page 59 Notes......Page 61 The Single Server Queue......Page 62 Representations......Page 65 Approximations......Page 68 Stability......Page 72 Invariance equations......Page 77 Big queues......Page 87 Model selection......Page 92 Notes......Page 94 Exercises......Page 95 Scheduling......Page 99 Controlled random-walk model......Page 101 Fluid model......Page 109 Control techniques for the fluid model......Page 116 Comparing fluid and stochastic models......Page 128 Structure of optimal policies......Page 133 Safety-stocks......Page 136 Discrete review......Page 142 MaxWeight and MinDrift......Page 145 Perturbed value function......Page 148 Notes......Page 152 Exercises......Page 154 II Workload......Page 158 Workload & Scheduling......Page 159 Single server queue......Page 160 Workload for the CRW scheduling model......Page 163 Relaxations for the fluid model......Page 167 Stochastic workload models......Page 189 Pathwise optimality and workload......Page 194 Hedging in networks......Page 199 Notes......Page 209 Exercises......Page 211 Routing & Resource Pooling......Page 213 Workload in general models......Page 216 Resource pooling......Page 223 Routing and workload......Page 227 MaxWeight for routing and scheduling......Page 233 Simultaneous resource possession......Page 236 Workload relaxations......Page 239 Relaxations and policy synthesis for stochastic models......Page 253 Notes......Page 261 Exercises......Page 263 Demand......Page 266 Network models......Page 269 Transients......Page 274 Workload relaxations......Page 287 Hedging in a simple inventory model......Page 295 Hedging in networks......Page 301 Summary of steady-state control techniques......Page 312 Notes......Page 314 Exercises......Page 316 III Stability & Performance......Page 318 Foster-Lyapunov Techniques......Page 319 Lyapunov functions......Page 324 Lyapunov functions for networks......Page 328 Discrete-review......Page 338 MaxWeight......Page 342 MaxWeight and the average-cost optimality equation......Page 348 Linear programs for performance bounds......Page 352 Brownian workload model......Page 360 Notes......Page 367 Exercises......Page 369 Optimization......Page 374 Reachability and decomposibility......Page 379 Linear programming formulations......Page 381 Multi-objective optimization......Page 389 Optimality equations......Page 392 Algorithms......Page 401 Optimization in networks......Page 408 One dimensional inventory model......Page 413 Hedging and workload......Page 418 Notes......Page 430 Exercises......Page 433 ODE methods......Page 436 Examples......Page 441 Mathematical preliminaries......Page 445 Fluid limit model......Page 449 Fluid-scale stability......Page 453 Safety stocks and trajectory tracking......Page 462 Fluid-scale asymptotic optimality......Page 467 Brownian workload model......Page 474 Notes......Page 480 Exercises......Page 483 Simulation & Learning......Page 485 Deciding when to stop......Page 491 Asymptotic theory for Markov models......Page 495 The single server queue......Page 499 Control variates and shadow functions......Page 503 Estimating a value function......Page 516 Notes......Page 532 Exercises......Page 534 Every process is (almost) Markov......Page 538 Generators and value functions......Page 540 Equilibrium equations......Page 543 Criteria for stability......Page 552 Ergodic theorems and coupling......Page 560 Converse theorems......Page 568 List of Figures......Page 572 References......Page 576 Index......Page 611

Power grids, flexible manufacturing, cellular communications: interconnectedness has consequences. This remarkable book gives the tools and philosophy you need to build network models detailed enough to capture essential dynamics but simple enough to expose the structure of effective control solutions and to clarify analysis. Core chapters assume only exposure to stochastic processes and linear algebra at the undergraduate level; later chapters are for advanced graduate students and researchers/practitioners. This gradual development bridges classical theory with the state-of-the-art. The workload model that is the basis of traditional analysis of the single queue becomes a foundation for workload relaxations used in the treatment of complex networks. Lyapunov functions and dynamic programming equations lead to the celebrated MaxWeight policy along with many generalizations. Other topics include methods for synthesizing hedging and safety stocks, stability theory for networks, and techniques for accelerated simulation. Examples and figures throughout make ideas concrete. Solutions to end-of-chapter exercises available on a companion website.

Power grids, flexible manufacturing, cellular communications: interconnectedness has consequences. This remarkable book gives the tools and philosophy you need to build network models detailed enough to capture essential dynamics but simple enough to expose the structure of effective control solutions. Core chapters assume only exposure to stochastic processes and linear algebra at undergraduate level; later chapters are for advanced graduate students and researchers/practitioners. This gradual development bridges classical theory with the state-of-the-art. The workload model at the heart of traditional analysis of the single queue becomes a foundation for workload relaxations used in the treatment of complex networks. Lyapunov functions and dynamic programming equations lead to the celebrated MaxWeight policy along with many generalizations. Other topics include methods for synthesizing hedging and safety stocks, stability theory for networks, and techniques for accelerated simulation. Examples and figures throughout make ideas concrete. Solutions to end-of-chapter exercises are available on a companion website. "Power grids, flexible manufacturing, cellular communications: interconnectedness has consequences. This book gives the tools and philosophy you need to build network models detailed enough to capture essential dynamics but simple enough to expose the structure of effective control solutions and to clarify analysis." "Core chapters assume only prior exposure to stochastic processes and linear algebra at the undergraduate level; later chapters are for advanced graduate students and researchers/practitioners. This gradual development bridges classical theory with the state of the art. The workload model that is the basis of traditional analysis of the single queue becomes a foundation for workload relaxations used in the treatment of complex networks. Lyapunov functions and dynamic programming equations lead to the celebrated MaxWeight policy along with many generalizations, other topics include methods for synthesizing hedging and safety stocks, stability theory for networks, and techniques for accelerated simulation."--Jacket