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E-raamat: Control Techniques for Complex Networks

(University of Illinois, Urbana-Champaign)
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  • Ilmumisaeg: 10-Dec-2007
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9780511367960
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  • Formaat: PDF+DRM
  • Ilmumisaeg: 10-Dec-2007
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9780511367960
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From foundations to state-of-the-art; the tools and philosophy you need to build network models.

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.

Arvustused

'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; Winner of the 2011 Nobel Prize in Economic Sciences '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 'In my opinion this book is written primarily for seasoned researchers in the field who need a nice source of existing results and ideas. In this vein the book is outstanding and it should become an indispensable aid to researchers and practitioners. All in all this is an excellent book ' Mathematical Reviews

Muu info

From foundations to state-of-the-art; the tools and philosophy you need to build network models.
List of Illustrations
ix
Preface xiii
Dedication xvii
Introduction
1(22)
Networks in practice
2(5)
Mathematical models
7(3)
What do you need to know to read this book?
10(11)
Notes
21(2)
Part I: Modeling and Control
23(120)
Examples
25(27)
Modeling the single server queue
25(6)
Klimov model
31(3)
Capacity and queueing in communication systems
34(1)
Multiple-access communication
34(2)
Processor sharing model
36(1)
Inventory model
37(1)
Power transmission network
37(2)
Optimization in a simple re-entrant line
39(4)
Contention for resources and instability
43(3)
Routing model
46(3)
Braess' paradox
49(1)
Notes
50(2)
The Single Server Queue
52(35)
Representations
55(3)
Approximations
58(4)
Stability
62(4)
Invariance equations
66(10)
Big queues
76(4)
Model selection
80(2)
Notes
82(5)
Exercises
82(5)
Scheduling
87(56)
Controlled random-walk model
89(8)
Fluid model
97(6)
Control techniques for the fluid model
103(12)
Comparing fluid and stochastic models
115(4)
Structure of optimal policies
119(3)
Safety-stocks
122(6)
Discrete review
128(3)
Max Weight and MinDrift
131(3)
Perturbed value function
134(4)
Notes
138(5)
Exercises
139(4)
Part II: Workload
143(152)
Workload and Scheduling
145(50)
Single server queue
146(3)
Workload for the CRW scheduling model
149(4)
Relaxations for the fluid model
153(19)
Stochastic workload models
172(6)
Pathwise optimality and workload
178(5)
Hedging in networks
183(9)
Notes
192(3)
Exercises
193(2)
Routing and Resource Pooling
195(51)
Workload in general models
198(6)
Resource pooling
204(5)
Routing and workload
209(6)
Max Weight for routing and scheduling
215(3)
Simultaneous resource possession
218(3)
Workload relaxations
221(12)
Relaxations and policy synthesis for stochastic models
233(7)
Notes
240(6)
Exercises
242(4)
Demand
246(49)
Network models
249(6)
Transients
255(12)
Workload relaxations
267(7)
Hedging in a simple inventory model
274(6)
Hedging in networks
280(11)
Summary of steady-state control techniques
291(1)
Notes
292(3)
Exercises
293(2)
Part III: Stability and Performance
295(210)
Foster-Lyapunov Techniques
297(51)
Lyapunov functions
302(3)
Lyapunov functions for networks
305(10)
Discrete review
315(4)
Max Weight
319(6)
Max Weight and the average-cost optimality equation
325(3)
Linear programs for performance bounds
328(8)
Brownian workload model
336(6)
Notes
342(6)
Exercises
343(5)
Optimization
348(59)
Reachability and decomposibility
352(2)
Linear programming formulations
354(8)
Multiobjective optimization
362(3)
Optimality equations
365(10)
Algorithms
375(6)
Optimization in networks
381(4)
One-dimensional inventory model
385(6)
Hedging and workload
391(11)
Notes
402(5)
Exercises
404(3)
ODE Methods
407(45)
Examples
412(4)
Mathematical preliminaries
416(3)
Fluid limit model
419(4)
Fluid-scale stability
423(8)
Safety stocks and trajectory tracking
431(6)
Fluid-scale asymptotic optimality
437(6)
Brownian workload model
443(5)
Notes
448(4)
Exercises
450(2)
Simulation and Learning
452(53)
Deciding when to stop
458(3)
Asymptotic theory for Markov models
461(4)
The single-server queue
465(5)
Control variates and shadow functions
470(13)
Estimating a value function
483(15)
Notes
498(7)
Exercises
499(6)
Appendix: Markov Models 505(32)
Bibliography 537(22)
Index 559


Sean Meyn is professor of electrical and computer engineering at the University of Illinois, and a fellow of the IEEE. He is co-author with Richard Tweedie of Markov Chains and Stochastic Stability, which received the 1994 ORSA/TIMS Best Publication in Applied Probability Award.