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Format: 1 online resource (xvi, 562 pages) : , digital, PDF file(s).

ISBN: 1-107-18623-4 , 0-511-36900-X , 1-281-15596-9 , 9786611155964 , 0-511-37001-6 , 0-511-37055-5 , 0-511-36949-2 , 0-511-80441-5 , 0-511-37102-0

Content: 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.

Note: Title from publisher's bibliographic system (viewed on 05 Oct 2015). , Cover; Half-title; Title; Copyright; Contents; List of Illustrations; Preface; Acknowledgments; Dedication; 1 Introduction; 1.1 Networks in practice; 1.1.1 Flexible manufacturing; 1.1.2 The Internet; 1.1.3 Wireless networks; 1.1.4 Power distribution; 1.2 Mathematical models; 1.2.1 A range of probabilistic models; 1.2.2 What is a good model?; 1.3 What do you need to know to read this book?; 1.3.1 Linear programs; 1.3.2 Some probability theory; 1.3.3 Random walks; 1.3.4 Renewal processes; 1.3.5 Martingales; 1.3.6 Markov models; 1.4 Notes; Part I: Modeling and Control; 2 Examples , 2.1 Modeling the single server queue2.1.1 Sampling; 2.1.2 Approximation; 2.1.3 Heavy traffic and Brownian models; 2.1.4 Transient behavior and fluid models; 2.2 Klimov model; 2.3 Capacity and queueing in communication systems; 2.4 Multiple-access communication; 2.5 Processor sharing model; 2.6 Inventory model; 2.7 Power transmission network; 2.8 Optimization in a simple re-entrant line; 2.9 Contention for resources and instability; 2.10 Routing model; 2.11 Braess' paradox; 2.12 Notes; 3 The Single Server Queue; 3.1 Representations; 3.1.1 Lindley recursion; 3.1.2 Skorokhod map , 3.1.3 Loynes construction3.2 Approximations; 3.2.1 Fluid models; 3.2.2 Heavy traffic and Brownian models; 3.3 Stability; 3.3.1 Fluid and stochastic Lyapunov functions; 3.3.2 Consequences of Foster's criterion; 3.3.3 Stability of the RBM model; 3.4 Invariance equations; 3.4.1 The M/M/1 queue; 3.4.2 Existence of; 3.4.3 Refined comparison theorems; 3.4.5 Computation of the discounted cost; 3.4.6 Invariance equations for the RBM model; 3.5 Big queues; 3.5.1 Time reversal and reversibility; 3.5.2 Most likely behavior in the general model; 3.6 Model selection; 3.7 Notes; Exercises; 4 Scheduling , 4.1 Controlled random-walk model4.1.1 Basic model; 4.1.2 Policies; 4.1.3 Optimization; 4.2 Fluid model; 4.3 Control techniques for the fluid model; 4.3.1 Time-optimality; 4.3.2 Myopic policies; 4.3.3 Balancing long- and short-term costs; 4.4 Comparing fluid and stochastic models; 4.4.1 Buffer priority policies; 4.4.2 Myopic policies; 4.5 Structure of optimal policies; 4.6 Safety-stocks; 4.6.1 Static safety-stocks; 4.6.2 Dynamic safety stocks; 4.7 Discrete review; 4.8 MaxWeight and MinDrift; 4.9 Perturbed value function; 4.10 Notes; Part II: Workload; 5 Workload and Scheduling , 5.1 Single server queue5.1.1 Workload in units of time; 5.1.2 Workload, delay, and Little's law; 5.2 Workload for the CRWscheduling model; 5.2.1 Workload in units of inventory Definition 5.2.1; 5.2.2 Workload in units of time; 5.3 Relaxations for the fluid model; 5.3.1 Minimal process; 5.3.2 Effective cost; 5.3.3 Value functions; 5.3.4 Optimization; 5.4 Stochastic workload models; 5.4.1 Relaxations for the CRWmodel; 5.4.2 Controlled Brownian model; 5.5 Pathwise optimality and workload; 5.5.1 Klimov model; 5.5.2 Single station re-entrant; 5.5.3 Workload models; 5.6 Hedging in networks , 5.6.1 Height process , English

Additional Edition: ISBN 0-521-88441-1

Language: English

URL: https://doi.org/10.1017/CBO9780511804410