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Author : Antonios Dimakis
Publisher :
ISBN 13 :
Total Pages : 154 pages
Book Rating : 4.:/5 (35 download)
Download or read book Stability and Approximation of Queueing Networks written by Antonios Dimakis and published by . This book was released on 2006 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Maury Bramson
Publisher : Springer Science & Business Media
ISBN 13 : 3540688951
Total Pages : 201 pages
Book Rating : 4.5/5 (46 download)
Download or read book Stability of Queueing Networks written by Maury Bramson and published by Springer Science & Business Media. This book was released on 2008-06-26 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Queueing networks constitute a large family of stochastic models, involving jobs that enter a network, compete for service, and eventually leave the network upon completion of service. Since the early 1990s, substantial attention has been devoted to the question of when such networks are stable. This volume presents a summary of such work. Emphasis is placed on the use of fluid models in showing stability, and on examples of queueing networks that are unstable even when the arrival rate is less than the service rate. The material of this volume is based on a series of nine lectures given at the Saint-Flour Probability Summer School 2006. Lectures were also given by Alice Guionnet and Steffen Lauritzen.
Author : Hengqing Ye
Publisher :
ISBN 13 :
Total Pages : 296 pages
Book Rating : 4.:/5 (436 download)
Download or read book Stability and Diffusion Approximation of Multiclass Queueing Networks written by Hengqing Ye and published by . This book was released on 1999 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Richard J. Boucherie
Publisher : Springer Science & Business Media
ISBN 13 : 144196472X
Total Pages : 814 pages
Book Rating : 4.4/5 (419 download)
Download or read book Queueing Networks written by Richard J. Boucherie and published by Springer Science & Business Media. This book was released on 2010-11-25 with total page 814 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook aims to highlight fundamental, methodological and computational aspects of networks of queues to provide insights and to unify results that can be applied in a more general manner. The handbook is organized into five parts: Part 1 considers exact analytical results such as of product form type. Topics include characterization of product forms by physical balance concepts and simple traffic flow equations, classes of service and queue disciplines that allow a product form, a unified description of product forms for discrete time queueing networks, insights for insensitivity, and aggregation and decomposition results that allow sub networks to be aggregated into single nodes to reduce computational burden. Part 2 looks at monotonicity and comparison results such as for computational simplification by either of two approaches: stochastic monotonicity and ordering results based on the ordering of the process generators, and comparison results and explicit error bounds based on an underlying Markov reward structure leading to ordering of expectations of performance measures. Part 3 presents diffusion and fluid results. It specifically looks at the fluid regime and the diffusion regime. Both of these are illustrated through fluid limits for the analysis of system stability, diffusion approximations for multi-server systems, and a system fed by Gaussian traffic. Part 4 illustrates computational and approximate results through the classical MVA (mean value analysis) and QNA (queueing network analyzer) for computing mean and variance of performance measures such as queue lengths and sojourn times; numerical approximation of response time distributions; and approximate decomposition results for large open queueing networks. spanPart 5 enlightens selected applications as spanloss networks originating from circuit switched telecommunications applications, capacity sharing originating from packet switching in data networks, and a hospital application that is of growing present day interest. spanThe book shows that spanthe intertwined progress of theory and practicespan will remain to be most intriguing and will continue to be the basis of further developments in queueing networks.
Author : Richard J. Boucherie
Publisher : Springer
ISBN 13 : 9781441964731
Total Pages : 800 pages
Book Rating : 4.9/5 (647 download)
Download or read book Queueing Networks written by Richard J. Boucherie and published by Springer. This book was released on 2011-04-07 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook aims to highlight fundamental, methodological and computational aspects of networks of queues to provide insights and to unify results that can be applied in a more general manner. The handbook is organized into five parts: Part 1 considers exact analytical results such as of product form type. Topics include characterization of product forms by physical balance concepts and simple traffic flow equations, classes of service and queue disciplines that allow a product form, a unified description of product forms for discrete time queueing networks, insights for insensitivity, and aggregation and decomposition results that allow sub networks to be aggregated into single nodes to reduce computational burden. Part 2 looks at monotonicity and comparison results such as for computational simplification by either of two approaches: stochastic monotonicity and ordering results based on the ordering of the process generators, and comparison results and explicit error bounds based on an underlying Markov reward structure leading to ordering of expectations of performance measures. Part 3 presents diffusion and fluid results. It specifically looks at the fluid regime and the diffusion regime. Both of these are illustrated through fluid limits for the analysis of system stability, diffusion approximations for multi-server systems, and a system fed by Gaussian traffic. Part 4 illustrates computational and approximate results through the classical MVA (mean value analysis) and QNA (queueing network analyzer) for computing mean and variance of performance measures such as queue lengths and sojourn times; numerical approximation of response time distributions; and approximate decomposition results for large open queueing networks. spanPart 5 enlightens selected applications as spanloss networks originating from circuit switched telecommunications applications, capacity sharing originating from packet switching in data networks, and a hospital application that is of growing present day interest. spanThe book shows that spanthe intertwined progress of theory and practicespan will remain to be most intriguing and will continue to be the basis of further developments in queueing networks.
Author : Otis Brian Jennings
Publisher :
ISBN 13 :
Total Pages : 538 pages
Book Rating : 4.:/5 (448 download)
Download or read book Multiclass Queueing Networks with Setup Delays written by Otis Brian Jennings and published by . This book was released on 2000 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hong Chen
Publisher : Springer Science & Business Media
ISBN 13 : 1475753012
Total Pages : 407 pages
Book Rating : 4.4/5 (757 download)
Download or read book Fundamentals of Queueing Networks written by Hong Chen and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible book aims to collect in a single volume the essentials of stochastic networks. Stochastic networks have become widely used as a basic model of many physical systems in a diverse range of fields. Written by leading authors in the field, this book is meant to be used as a reference or supplementary reading by practitioners in operations research, computer systems, communications networks, production planning, and logistics.
Author :
Publisher : John Wiley & Sons
ISBN 13 : 1119755425
Total Pages : 336 pages
Book Rating : 4.1/5 (197 download)
Download or read book Queueing Theory 1 written by and published by John Wiley & Sons. This book was released on 2021-04-27 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to reflect the current cutting-edge thinking and established practices in the investigation of queueing systems and networks. This first volume includes ten chapters written by experts well-known in their areas. The book studies the analysis of queues with interdependent arrival and service times, characteristics of fluid queues, modifications of retrial queueing systems and finite-source retrial queues with random breakdowns, repairs and customers’ collisions. Some recent tendencies in the asymptotic analysis include the average and diffusion approximation of Markov queueing systems and networks, the diffusion and Gaussian limits of multi-channel queueing networks with rather general input flow, and the analysis of two-time-scale nonhomogenous Markov chains using the large deviations principle. The book also analyzes transient behavior of infinite-server queueing models with a mixed arrival process, the strong stability of queueing systems and networks, and applications of fast simulation methods for solving high-dimension combinatorial problems.
Author : Erol Gelenbe
Publisher : Wiley-Blackwell
ISBN 13 :
Total Pages : 272 pages
Book Rating : 4.3/5 (91 download)
Download or read book Introduction to Queueing Networks written by Erol Gelenbe and published by Wiley-Blackwell. This book was released on 1998-07-07 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Queueing Networks Second Edition Erol Gelenbe, Duke University, North Carolina, USA and Guy Pujolle, University of Versailles, France With new concepts emerging in recent literature, this is a timely update to a highly successful and well established first edition. Queueing networks are particularly important as digital communications continue to grow; this text provides a through and comprehensive introduction to the concept of applying mathematical queueing network theory to data communications. New additions: * G-nets, i.e. generalized (or "Gelenbe") queueing networks which allow the analysis of on-line network control functions such as traffic re-routing, * discrete time queueing networks with application to ATM networks As leading authorities in this area, the authors' focus on the practical approach where aspects of queueing theory are applied directly to communications systems and networks. Included is a series of exercises and examples at the end of each chapter as well as a fully annotated bibliography. This book is of particular interest to communications and computer engineers and is essential reading for network. managers and administrators. It will also benefit students and researchers in the area of networks, as well as Web server administrators and personal computer users. Visit Our Web Page! http://www.wiley.com/
Author : Gideon Weiss
Publisher : Cambridge University Press
ISBN 13 : 1108245773
Total Pages : 448 pages
Book Rating : 4.1/5 (82 download)
Download or read book Scheduling and Control of Queueing Networks written by Gideon Weiss and published by Cambridge University Press. This book was released on 2021-10-14 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applications of queueing network models have multiplied in the last generation, including scheduling of large manufacturing systems, control of patient flow in health systems, load balancing in cloud computing, and matching in ride sharing. These problems are too large and complex for exact solution, but their scale allows approximation. This book is the first comprehensive treatment of fluid scaling, diffusion scaling, and many-server scaling in a single text presented at a level suitable for graduate students. Fluid scaling is used to verify stability, in particular treating max weight policies, and to study optimal control of transient queueing networks. Diffusion scaling is used to control systems in balanced heavy traffic, by solving for optimal scheduling, admission control, and routing in Brownian networks. Many-server scaling is studied in the quality and efficiency driven Halfin–Whitt regime and applied to load balancing in the supermarket model and to bipartite matching in ride-sharing applications.
Author : Maury Bramson
Publisher : Springer
ISBN 13 : 9783540864608
Total Pages : 198 pages
Book Rating : 4.8/5 (646 download)
Download or read book Stability of Queueing Networks written by Maury Bramson and published by Springer. This book was released on 2009-08-29 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Queueing networks constitute a large family of stochastic models, involving jobs that enter a network, compete for service, and eventually leave the network upon completion of service. Since the early 1990s, substantial attention has been devoted to the question of when such networks are stable. This volume presents a summary of such work. Emphasis is placed on the use of fluid models in showing stability, and on examples of queueing networks that are unstable even when the arrival rate is less than the service rate. The material of this volume is based on a series of nine lectures given at the Saint-Flour Probability Summer School 2006. Lectures were also given by Alice Guionnet and Steffen Lauritzen.
Author : Natarajan Gautam
Publisher : CRC Press
ISBN 13 : 1439806586
Total Pages : 804 pages
Book Rating : 4.4/5 (398 download)
Download or read book Analysis of Queues written by Natarajan Gautam and published by CRC Press. This book was released on 2012-04-26 with total page 804 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written with students and professors in mind, Analysis of Queues: Methods and Applications combines coverage of classical queueing theory with recent advances in studying stochastic networks. Exploring a broad range of applications, the book contains plenty of solved problems, exercises, case studies, paradoxes, and numerical examples. In addition to the standard single-station and single class discrete queues, the book discusses models for multi-class queues and queueing networks as well as methods based on fluid scaling, stochastic fluid flows, continuous parameter Markov processes, and quasi-birth-and-death processes, to name a few. It describes a variety of applications including computer-communication networks, information systems, production operations, transportation, and service systems such as healthcare, call centers and restaurants.
Author : Jewgeni H. Dshalalow
Publisher : CRC Press
ISBN 13 : 9780849380747
Total Pages : 530 pages
Book Rating : 4.3/5 (87 download)
Download or read book Advances in Queueing Theory, Methods, and Open Problems written by Jewgeni H. Dshalalow and published by CRC Press. This book was released on 1995-09-18 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: The progress of science and technology has placed Queueing Theory among the most popular disciplines in applied mathematics, operations research, and engineering. Although queueing has been on the scientific market since the beginning of this century, it is still rapidly expanding by capturing new areas in technology. Advances in Queueing provides a comprehensive overview of problems in this enormous area of science and focuses on the most significant methods recently developed. Written by a team of 24 eminent scientists, the book examines stochastic, analytic, and generic methods such as approximations, estimates and bounds, and simulation. The first chapter presents an overview of classical queueing methods from the birth of queues to the seventies. It also contains the most comprehensive bibliography of books on queueing and telecommunications to date. Each of the following chapters surveys recent methods applied to classes of queueing systems and networks followed by a discussion of open problems and future research directions. Advances in Queueing is a practical reference that allows the reader quick access to the latest methods.
Author : Simonetta Balsamo
Publisher : Springer Science & Business Media
ISBN 13 : 1475733453
Total Pages : 256 pages
Book Rating : 4.4/5 (757 download)
Download or read book Analysis of Queueing Networks with Blocking written by Simonetta Balsamo and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Queueing network models have been widely applied as a powerful tool for modelling, performance evaluation, and prediction of discrete flow systems, such as computer systems, communication networks, production lines, and manufacturing systems. Queueing network models with finite capacity queues and blocking have been introduced and applied as even more realistic models of systems with finite capacity resources and with population constraints. In recent years, research in this field has grown rapidly. Analysis of Queueing Networks with Blocking introduces queueing network models with finite capacity and various types of blocking mechanisms. It gives a comprehensive definition of the analytical model underlying these blocking queueing networks. It surveys exact and approximate analytical solution methods and algorithms and their relevant properties. It also presents various application examples of queueing networks to model computer systems and communication networks. This book is organized in three parts. Part I introduces queueing networks with blocking and various application examples. Part II deals with exact and approximate analysis of queueing networks with blocking and the condition under which the various techniques can be applied. Part III presents a review of various properties of networks with blocking, describing several equivalence properties both between networks with and without blocking and between different blocking types. Approximate solution methods for the buffer allocation problem are presented.
Author : Douglas Graham Down
Publisher : Ann Arbor, Mich. : University Microfilms International
ISBN 13 :
Total Pages : 226 pages
Book Rating : 4.:/5 (346 download)
Download or read book Stability of Queueing Networks written by Douglas Graham Down and published by Ann Arbor, Mich. : University Microfilms International. This book was released on 1995 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, the stability of queueing networks is studied. The use of test functions is a unifying thread. Tools are provided to construct appropriate test functions for complex networks, and the structure of such test functions is examined for specific network models. The analysis of queueing networks is performed in a manner that progresses in increasing complexity for increasingly complex networks. Single class networks are considered first. The particular form studied is open generalized Jackson networks with general arrival streams and general service time distributions. Assuming that the arrival rate does not exceed the network capacity and that the service times possess conditionally bounded second moments, stability is deduced by bounding the expected waiting time for a customer entering the network. For Markovian networks convergence of the total work in the system is obtained, as well as convergence of the mean queue size and mean customer delay, to a unique finite steady state value. Acyclic multiclass networks are the next topic. Once again, assuming that the arrival rate does not exceed the network capacity, stability of the network is deduced using the tools of ergodic theory. The distributions of the process are shown to converge to a unique steady state value, and under appropriate moment conditions, the convergence takes place at an exponential rate. The final topic is general re-entrant lines. In this case, piecewise linear test functions are developed for the analysis of both queueing networks and their associated fluid models. It is found that if an associated LP admits a positive solution, then a Lyapunov function exists. This implies that the fluid model is stable and, hence, that the network model is positive Harris recurrent with a finite polynomial moment. Also, it is found that if a different appropriate LP admits a solution, then the network model is transient.
Author : J.K. Skwirzynski
Publisher : Springer Science & Business Media
ISBN 13 : 9400927940
Total Pages : 437 pages
Book Rating : 4.4/5 (9 download)
Download or read book Performance Limits in Communication Theory and Practice written by J.K. Skwirzynski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Study Institute on Performance Limits in Communication: Theory and Practice, Il Ciocco, Castelvecchio, Pascoli, Tuscany, Italy, July 7-19, 1986
Author : Yi Zheng
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (13 download)
Download or read book Stochastic Control and Stability for Queueing Networks in Random Environments written by Yi Zheng and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The service systems, such as data centers and healthcare systems, are usually of large scale which makes the system more sensitive to environments and more vulnerable to interruptions. It is thus important to better design the system and develop optimal scheduling policies that will help to minimize the cost in random environments and prevent interruptions. On the other hand, the control of jump diffusions has attracted much attention due to its vast applicability to stochastic networks, mathematical finance, telecommunications, etc. The primary goal of this dissertation is to study the stability and optimal scheduling of large-scale stochastic networks in random environments and address control problems of jump diffusions. I study multiclass many-server queues for which the arrival, service, and abandonment rates are all modulated by a common finite-state Markov process in the "averaged" Halfin-Whitt regime. I establish a functional central limit theorem for the diffusion-scaled queueing process and show that the limiting process is a controlled diffusion. I address the infinite-horizon discounted and long-run average (ergodic) optimal control problems and establish asymptotic optimality. The ergodic properties of a class of Markov-modulated general birth-death processes under fast regime switching are studied. I show the ergodic properties of the properly scaled joint Markov process with a parameter that is taken large. Under very weak hypotheses, it is shown that if the averaged process is exponentially ergodic for large values of the parameter, then the same applies to the original joint Markov process. The ergodic control problem for a class of controlled jump diffusions driven by a compound Poisson process is studied. I provide a full characterizations of optimality via the Hamilton--Jacobi--Bellman (HJB) equation, for which the regularity of solutions under mild hypotheses is established. In addition, I show that optimal stationary Markov controls are a.s. pathwise optimal. I show that one can fix a stable control outside a compact set and obtain near-optimal solutions by solving the HJB on a sufficiently large bounded domain. The optimal scheduling problems for multiclass many-server queues in an alternating renewal random environment in the Halfin-Whitt regime are studied. Assuming that the downtimes are asymptotically negligible and only the service processes are affected, I show that the limits of the diffusion-scaled state processes are controlled jump diffusions driven by a compound Poisson jump process. I establish the asymptotic optimality of the infinite-horizon discounted and ergodic problems for the queueing dynamics.
