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Control Techniques for Complex Networks

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Hardcover | 11 February 2008

At a Glance

Hardcover
584 Pages

Dimensions(cm)
18.5 x 26.2 x 3.7

Hardcover

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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.

Industry Reviews

'Sean Meyn's text is a wonderful piece of work ... It progresses through a series of important topics, running the gamut from modern control techniques for queuing system analysis, to optimization of deterministic network models, to computer simulation methods; and all the while, it provides rigorous mathematical foundations alongside a variety of clever, practical applications. The lively writing style and apt examples keep everything interesting, and I believe that readers will greatly appreciate and benefit from this unique book.' David M. Goldsman, Georgia Institute of Technology 'Sean Meyn's earlier book with Tweedie is the bible for economists who use Markov models to do everything from formulating asset pricing models to constructing Bayesian posteriors for dynamic models. This book is a gold mine of useful new ideas. I predict that the ideas in chapter 11 alone will have a big impact on the way we think about computing rational expectations equilibria.' Thomas Sargent, New York University 'The first comprehensive account of some major strands of research in modeling, approximation, stability analysis and optimization of stochastic networks, from a leader in the field ... Notable among these are its coverage of deterministic fluid limits, controlled random walk models, approximation via workload relaxation, and implications of these to stability and optimization of networks. Several important special instances are worked out in detail. A valuable resource for both researchers and practitioners.' Vivek S. Borkar, Tata Institute of Fundamental Research

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You Can Find This Book In

Non-Fiction Science Science in General Computing & I.T.Computer Networking & Communications Engineering & Technology Electronics & Communications Engineering Electronics Engineering Automatic Control Engineering Mathematics Probability & Statistics Optimisation

List of Illustrations	p. ix
Preface	p. xiii
Dedication	p. xvii
Introduction	p. 1
Networks in practice	p. 2
Mathematical models	p. 7
What do you need to know to read this book?	p. 10
Notes	p. 21
Modeling and Control	p. 23
Examples	p. 25
Modeling the single server queue	p. 25
Klimov model	p. 31
Capacity and queueing in communication systems	p. 34
Multiple-access communication	p. 34
Processor sharing model	p. 36
Inventory model	p. 37
Power transmission network	p. 37
Optimization in a simple re-entrant line	p. 39
Contention for resources and instability	p. 43
Routing model	p. 46
Braess' paradox	p. 49
Notes	p. 50
The Single Server Queue	p. 52
Representations	p. 55
Approximations	p. 58
Stability	p. 62
Invariance equations	p. 66
Big queues	p. 76
Model selection	p. 80
Notes	p. 82
Exercises	p. 82
Scheduling	p. 87
Controlled random-walk model	p. 89
Fluid model	p. 97
Control techniques for the fluid model	p. 103
Comparing fluid and stochastic models	p. 115
Structure of optimal policies	p. 119
Safety-stocks	p. 122
Discrete review	p. 128
MaxWeight and MinDrift	p. 131
Perturbed value function	p. 134
Notes	p. 138
Exercises	p. 139
Workload	p. 143
Workload and Scheduling	p. 145
Single server queue	p. 146
Workload for the CRW scheduling model	p. 149
Relaxations for the fluid model	p. 153
Stochastic workload models	p. 172
Pathwise optimality and workload	p. 178
Hedging in networks	p. 183
Notes	p. 192
Exercises	p. 193
Routing and Resource Pooling	p. 195
Workload in general models	p. 198
Resource pooling	p. 204
Routing and workload	p. 209
MaxWeight for routing and scheduling	p. 215
Simultaneous resource possession	p. 218
Workload relaxations	p. 221
Relaxations and policy synthesis for stochastic models	p. 233
Notes	p. 240
Exercises	p. 242
Demand	p. 246
Network models	p. 249
Transients	p. 255
Workload relaxations	p. 267
Hedging in a simple inventory model	p. 274
Hedging in networks	p. 280
Summary of steady-state control techniques	p. 291
Notes	p. 292
Exercises	p. 293
Stability and Performance	p. 295
Foster-Lyapunov Techniques	p. 297
Lyapunov functions	p. 302
Lyapunov functions for networks	p. 305
Discrete review	p. 315
MaxWeight	p. 319
MaxWeight and the average-cost optimality equation	p. 325
Linear programs for performance bounds	p. 328
Brownian workload model	p. 336
Notes	p. 342
Exercises	p. 343
Optimization	p. 348
Reachability and decomposibility	p. 352
Linear programming formulations	p. 354
Multiobjective optimization	p. 362
Optimality equations	p. 365
Algorithms	p. 375
Optimization in networks	p. 381
One-dimensional inventory model	p. 385
Hedging and workload	p. 391
Notes	p. 402
Exercises	p. 404
ODE Methods	p. 407
Examples	p. 412
Mathematical preliminaries	p. 416
Fluid limit model	p. 419
Fluid-scale stability	p. 423
Safety stocks and trajectory tracking	p. 431
Fluid-scale asymptotic optimality	p. 437
Brownian workload model	p. 443
Notes	p. 448
Exercises	p. 450
Simulation and Learning	p. 452
Deciding when to stop	p. 458
Asymptotic theory for Markov models	p. 461
The single-server queue	p. 465
Control variates and shadow functions	p. 470
Estimating a value function	p. 483
Notes	p. 498
Exercises	p. 499
Markov Models	p. 505
Bibliography	p. 537
Index	p. 559
Table of Contents provided by Ingram. All Rights Reserved.

Control Techniques for Complex Networks

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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