Introduction To Stochastic Networks
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Introduction To Stochastic Networks
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Author : Richard Serfozo
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-07-30
Introduction To Stochastic Networks written by Richard Serfozo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-07-30 with Mathematics categories.
Beginning with Jackson networks and ending with spatial queuing systems, this book describes several basic stochastic network processes, with the focus on network processes that have tractable expressions for the equilibrium probability distribution of the numbers of units at the stations. Intended for graduate students and researchers in engineering, science and mathematics interested in the basics of stochastic networks that have been developed over the last twenty years, the text assumes a graduate course in stochastic processes without measure theory, emphasising multi-dimensional Markov processes. Alongside self-contained material on point processes involving real analysis, the book also contains complete introductions to reversible Markov processes, Palm probabilities for stationary systems, Little laws for queuing systems and space-time Poisson processes.
Stochastic Networks
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Author : Frank Kelly
language : en
Publisher: Cambridge University Press
Release Date : 2014-02-27
Stochastic Networks written by Frank Kelly and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-27 with Computers categories.
A compact, highly-motivated introduction to some of the stochastic models found useful in the study of communications networks.
Stochastic Network Calculus
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Author : Yuming Jiang
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-01
Stochastic Network Calculus written by Yuming Jiang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-01 with Computers categories.
Network calculus is a theory dealing with queuing systems found in computer networks. Its focus is on performance guarantees. Central to the theory is the use of alternate algebras such as the min-plus algebra to transform complex network systems into analytically tractable systems. To simplify the ana- sis, another idea is to characterize tra?c and service processes using various bounds. Since its introduction in the early 1990s, network calculus has dev- oped along two tracks—deterministic and stochastic. This book is devoted to summarizing results for stochastic network calculus that can be employed in the design of computer networks to provide stochastic service guarantees. Overview and Goal Like conventional queuing theory, stochastic network calculus is based on properly de?ned tra?c models and service models. However, while in c- ventional queuing theory an arrival process is typically characterized by the inter-arrival times of customers and a service process by the service times of customers, the arrival process and the service process are modeled in n- work calculus respectively by some arrival curve that (maybe probabilis- cally) upper-bounds the cumulative arrival and by some service curve that (maybe probabilistically) lower-bounds the cumulative service. The idea of usingboundstocharacterizetra?candservicewasinitiallyintroducedfor- terministic network calculus. It has also been extended to stochastic network calculus by exploiting the stochastic nature of arrival and service processes.
Fundamentals Of Queueing Networks
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Author : Hong Chen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Fundamentals Of Queueing Networks written by Hong Chen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
The objective of this book is to collect in a single volume the essentials of stochastic networks, from the classical product-form theory to the more re cent developments such as diffusion and fluid limits, stochastic comparisons, stability, control (dynamic scheduling) and optimization. The selection of materials inevitably is a reflection upon our bias and preference, but it is also driven to a large extent by our desire to provide a graduate-level text that is well balanced in breadth and depth, suitable for the classroom. Given the wide-ranging applications of stochastic networks in recent years, from supply chains to telecommunications, it is also our hope that the book will serve as a useful reference for researchers and students alike in these diverse fields. The book consists of three parts. The first part, Chapters 1 through 4, covers (continuous-time) Markov-chain models, including the classical Jackson and Kelly networks, the notion of quasi-reversible queues, and stochastic comparisons. The second part, Chapters 5 through 10, focuses on Brownian models, including limit theorems for generalized Jackson net works and multiclass feedforward networks, an in-depth examination of stability in a Kumar-Seidman network, and Brownian approximations for general multiclass networks with a mixture of priority and first-in-first-out disciplines. The third part, Chapters 11 and 12, discusses scheduling in both queueing (stochastic) and fluid (deterministic) networks, along with topics such as conservation laws, polymatroid optimization, and linear pro gramming.
Stochastic Networks And Queues
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Author : Philippe Robert
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Stochastic Networks And Queues written by Philippe Robert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
Queues and stochastic networks are analyzed in this book with purely probabilistic methods. The purpose of these lectures is to show that general results from Markov processes, martingales or ergodic theory can be used directly to study the corresponding stochastic processes. Recent developments have shown that, instead of having ad-hoc methods, a better understanding of fundamental results on stochastic processes is crucial to study the complex behavior of stochastic networks. In this book, various aspects of these stochastic models are investigated in depth in an elementary way: Existence of equilibrium, characterization of stationary regimes, transient behaviors (rare events, hitting times) and critical regimes, etc. A simple presentation of stationary point processes and Palm measures is given. Scaling methods and functional limit theorems are a major theme of this book. In particular, a complete chapter is devoted to fluid limits of Markov processes.
Introduction To Stochastic Programming
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Author : John R. Birge
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-06
Introduction To Stochastic Programming written by John R. Birge and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-06 with Mathematics categories.
This rapidly developing field encompasses many disciplines including operations research, mathematics, and probability. Conversely, it is being applied in a wide variety of subjects ranging from agriculture to financial planning and from industrial engineering to computer networks. This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability. The authors present a broad overview of the main themes and methods of the subject, thus helping students develop an intuition for how to model uncertainty into mathematical problems, what uncertainty changes bring to the decision process, and what techniques help to manage uncertainty in solving the problems. The early chapters introduce some worked examples of stochastic programming, demonstrate how a stochastic model is formally built, develop the properties of stochastic programs and the basic solution techniques used to solve them. The book then goes on to cover approximation and sampling techniques and is rounded off by an in-depth case study. A well-paced and wide-ranging introduction to this subject.
Fundamentals Of Stochastic Networks
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Author : Oliver C. Ibe
language : en
Publisher: Wiley
Release Date : 2011-09-27
Fundamentals Of Stochastic Networks written by Oliver C. Ibe and has been published by Wiley this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-27 with Mathematics categories.
An interdisciplinary approach to understanding queueing and graphical networks In today's era of interdisciplinary studies and research activities, network models are becoming increasingly important in various areas where they have not regularly been used. Combining techniques from stochastic processes and graph theory to analyze the behavior of networks, Fundamentals of Stochastic Networks provides an interdisciplinary approach by including practical applications of these stochastic networks in various fields of study, from engineering and operations management to communications and the physical sciences. The author uniquely unites different types of stochastic, queueing, and graphical networks that are typically studied independently of each other. With balanced coverage, the book is organized into three succinct parts: Part I introduces basic concepts in probability and stochastic processes, with coverage on counting, Poisson, renewal, and Markov processes Part II addresses basic queueing theory, with a focus on Markovian queueing systems and also explores advanced queueing theory, queueing networks, and approximations of queueing networks Part III focuses on graphical models, presenting an introduction to graph theory along with Bayesian, Boolean, and random networks The author presents the material in a self-contained style that helps readers apply the presented methods and techniques to science and engineering applications. Numerous practical examples are also provided throughout, including all related mathematical details. Featuring basic results without heavy emphasis on proving theorems, Fundamentals of Stochastic Networks is a suitable book for courses on probability and stochastic networks, stochastic network calculus, and stochastic network optimization at the upper-undergraduate and graduate levels. The book also serves as a reference for researchers and network professionals who would like to learn more about the general principles of stochastic networks.
Stochastic Network Optimization With Application To Communication And Queueing Systems
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Author : Michael Neely
language : en
Publisher: Springer Nature
Release Date : 2022-05-31
Stochastic Network Optimization With Application To Communication And Queueing Systems written by Michael Neely and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Computers categories.
This text presents a modern theory of analysis, control, and optimization for dynamic networks. Mathematical techniques of Lyapunov drift and Lyapunov optimization are developed and shown to enable constrained optimization of time averages in general stochastic systems. The focus is on communication and queueing systems, including wireless networks with time-varying channels, mobility, and randomly arriving traffic. A simple drift-plus-penalty framework is used to optimize time averages such as throughput, throughput-utility, power, and distortion. Explicit performance-delay tradeoffs are provided to illustrate the cost of approaching optimality. This theory is also applicable to problems in operations research and economics, where energy-efficient and profit-maximizing decisions must be made without knowing the future. Topics in the text include the following: - Queue stability theory - Backpressure, max-weight, and virtual queue methods - Primal-dual methods for non-convex stochastic utility maximization - Universal scheduling theory for arbitrary sample paths - Approximate and randomized scheduling theory - Optimization of renewal systems and Markov decision systems Detailed examples and numerous problem set questions are provided to reinforce the main concepts. Table of Contents: Introduction / Introduction to Queues / Dynamic Scheduling Example / Optimizing Time Averages / Optimizing Functions of Time Averages / Approximate Scheduling / Optimization of Renewal Systems / Conclusions
Reversibility And Stochastic Networks
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Author : Frank P. Kelly
language : en
Publisher: John Wiley & Sons
Release Date : 1979
Reversibility And Stochastic Networks written by Frank P. Kelly and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.
Stochastic Geometry For Wireless Networks
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Author : Martin Haenggi
language : en
Publisher: Cambridge University Press
Release Date : 2013
Stochastic Geometry For Wireless Networks written by Martin Haenggi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Computers categories.
Analyse wireless network performance and improve design choices for future architectures and protocols with this rigorous introduction to stochastic geometry.