Download or read book Stochastic Network Calculus written by Yuming Jiang and published by Springer Science & Business Media. This book was released on 2009-03-01 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Stochastic Network Calculus written by Jiang and published by . This book was released on 2009-10-01 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fundamentals of Stochastic Networks written by Oliver C. Ibe and published by John Wiley & Sons. This book was released on 2011-08-24 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Stochastic Networks and Queues written by Philippe Robert and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Network Calculus written by Jean-Yves Le Boudec and published by Springer. This book was released on 2003-08-06 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Network Calculus is a set of recent developments that provide deep insights into flow problems encountered in the Internet and in intranets. The first part of the book is a self-contained, introductory course on network calculus. It presents the core of network calculus, and shows how it can be applied to the Internet to obtain results that have physical interpretations of practical importance to network engineers. The second part serves as a mathematical reference used across the book. It presents the results from Min-plus algebra needed for network calculus. The third part contains more advanced material. It is appropriate reading for a graduate course and a source of reference for professionals in networking by surveying the state of the art of research and pointing to open problems in network calculus and its application in different fields, such as mulitmedia smoothing, aggegate scheduling, adaptive guarantees in Internet differential services, renegotiated reserved services, etc.
Download or read book Stochastic Networks written by Frank Kelly and published by Cambridge University Press. This book was released on 2014-02-27 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Communication networks underpin our modern world, and provide fascinating and challenging examples of large-scale stochastic systems. Randomness arises in communication systems at many levels: for example, the initiation and termination times of calls in a telephone network, or the statistical structure of the arrival streams of packets at routers in the Internet. How can routing, flow control and connection acceptance algorithms be designed to work well in uncertain and random environments? This compact introduction illustrates how stochastic models can be used to shed light on important issues in the design and control of communication networks. It will appeal to readers with a mathematical background wishing to understand this important area of application, and to those with an engineering background who want to grasp the underlying mathematical theory. Each chapter ends with exercises and suggestions for further reading.
Download or read book Brownian Motion and Stochastic Calculus written by Ioannis Karatzas and published by Springer. This book was released on 2014-03-27 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and exercises.
Download or read book Introduction to Stochastic Networks written by Richard Serfozo and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Stochastic Calculus for Quantitative Finance written by Alexander A Gushchin and published by Elsevier. This book was released on 2015-08-26 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1994 and 1998 F. Delbaen and W. Schachermayer published two breakthrough papers where they proved continuous-time versions of the Fundamental Theorem of Asset Pricing. This is one of the most remarkable achievements in modern Mathematical Finance which led to intensive investigations in many applications of the arbitrage theory on a mathematically rigorous basis of stochastic calculus. Mathematical Basis for Finance: Stochastic Calculus for Finance provides detailed knowledge of all necessary attributes in stochastic calculus that are required for applications of the theory of stochastic integration in Mathematical Finance, in particular, the arbitrage theory. The exposition follows the traditions of the Strasbourg school. This book covers the general theory of stochastic processes, local martingales and processes of bounded variation, the theory of stochastic integration, definition and properties of the stochastic exponential; a part of the theory of Lévy processes. Finally, the reader gets acquainted with some facts concerning stochastic differential equations. Contains the most popular applications of the theory of stochastic integration Details necessary facts from probability and analysis which are not included in many standard university courses such as theorems on monotone classes and uniform integrability Written by experts in the field of modern mathematical finance
Download or read book Stochastic Project Networks written by Klaus Neumann and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Project planning, scheduling, and control are regularly used in business and the service sector of an economy to accomplish outcomes with limited resources under critical time constraints. To aid in solving these problems, network-based planning methods have been developed that now exist in a wide variety of forms, cf. Elmaghraby (1977) and Moder et al. (1983). The so-called "classical" project networks, which are used in the network techniques CPM and PERT and which represent acyclic weighted directed graphs, are able to describe only projects whose evolution in time is uniquely specified in advance. Here every event of the project is realized exactly once during a single project execution and it is not possible to return to activities previously carried out (that is, no feedback is permitted). Many practical projects, however, do not meet those conditions. Consider, for example, a production process where some parts produced by a machine may be poorly manufactured. If an inspection shows that a part does not conform to certain specifications, it must be repaired or replaced by a new item. This means that we have to return to a preceding stage of the production process. In other words, there is feedback. Note that the result of the inspection is that a certain percentage of the parts tested do not conform. That is, there is a positive probability (strictly less than 1) that any part is defective.
Download or read book Reversibility and Stochastic Networks written by Frank P. Kelly and published by John Wiley & Sons. This book was released on 1979 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Network Optimization with Application to Communication and Queueing Systems written by Michael Neely and published by Springer Nature. This book was released on 2022-05-31 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Elementary Stochastic Calculus with Finance in View written by Thomas Mikosch and published by World Scientific. This book was released on 1998 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modelling with the Ito integral or stochastic differential equations has become increasingly important in various applied fields, including physics, biology, chemistry and finance. However, stochastic calculus is based on a deep mathematical theory. This book is suitable for the reader without a deep mathematical background. It gives an elementary introduction to that area of probability theory, without burdening the reader with a great deal of measure theory. Applications are taken from stochastic finance. In particular, the Black -- Scholes option pricing formula is derived. The book can serve as a text for a course on stochastic calculus for non-mathematicians or as elementary reading material for anyone who wants to learn about Ito calculus and/or stochastic finance.
Download or read book Stochastic Networks written by Paul Glasserman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two of the most exciting topics of current research in stochastic networks are the complementary subjects of stability and rare events - roughly, the former deals with the typical behavior of networks, and the latter with significant atypical behavior. Both are classical topics, of interest since the early days of queueing theory, that have experienced renewed interest mo tivated by new applications to emerging technologies. For example, new stability issues arise in the scheduling of multiple job classes in semiconduc tor manufacturing, the so-called "re-entrant lines;" and a prominent need for studying rare events is associated with the design of telecommunication systems using the new ATM (asynchronous transfer mode) technology so as to guarantee quality of service. The objective of this volume is hence to present a sample - by no means comprehensive - of recent research problems, methodologies, and results in these two exciting and burgeoning areas. The volume is organized in two parts, with the first part focusing on stability, and the second part on rare events. But it is impossible to draw sharp boundaries in a healthy field, and inevitably some articles touch on both issues and several develop links with other areas as well. Part I is concerned with the issue of stability in queueing networks.
Download or read book Analytical and Stochastic Modelling Techniques and Applications written by Marco Gribaudo and published by Springer Nature. This book was released on 2020-11-07 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 25th International Conference on Analytical and Stochastic Modelling Techniques and Applications, ASMTA 2019, held in Moscow, Russia, in October 2019. Methods of analytical and stochastic modelling are widely used in engineering to assess and design various complex systems, like computer and communication networks, and manufacturing systems. The 13 full papers presented in this book were carefully reviewed and selected from 22 submissions. The papers detail a diverse range of analysis techniques, including Markov processes, queueing theoretical results, reliability of stochastic systems, stochastic network calculus, and wide variety of applications.
Download or read book Brownian Motion Martingales and Stochastic Calculus written by Jean-François Le Gall and published by Springer. This book was released on 2016-04-28 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested in such developments. Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.
Download or read book Stochastic Network Optimization with Application to Communication and Queueing Systems written by Michael J. Neely and published by Morgan & Claypool Publishers. This book was released on 2010 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
