Stability Of Queueing Networks
DOWNLOAD
Download Stability Of Queueing Networks PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Stability Of Queueing Networks book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Stability Of Queueing Networks
DOWNLOAD
Author : Maury Bramson
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-06-26
Stability Of Queueing Networks written by Maury Bramson 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 2008-06-26 with Mathematics categories.
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.
Stability Of Queueing Networks
DOWNLOAD
Author : Douglas Graham Down
language : en
Publisher: Ann Arbor, Mich. : University Microfilms International
Release Date : 1995
Stability Of Queueing Networks written by Douglas Graham Down and has been published by Ann Arbor, Mich. : University Microfilms International this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.
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.
Stability Of Queueing Networks
DOWNLOAD
Author : Maury Bramson
language : en
Publisher: Springer
Release Date : 2009-08-29
Stability Of Queueing Networks written by Maury Bramson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-29 with Mathematics categories.
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.
Stochastic Control And Stability For Queueing Networks In Random Environments
DOWNLOAD
Author : Yi Zheng
language : en
Publisher:
Release Date : 2021
Stochastic Control And Stability For Queueing Networks In Random Environments written by Yi Zheng and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
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.
Stability And Approximation Of Queueing Networks
DOWNLOAD
Author : Antonios Dimakis
language : en
Publisher:
Release Date : 2006
Stability And Approximation Of Queueing Networks written by Antonios Dimakis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
Queueing Theory 1
DOWNLOAD
Author : Vladimir Anisimov
language : en
Publisher: John Wiley & Sons
Release Date : 2021-03-05
Queueing Theory 1 written by Vladimir Anisimov 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 2021-03-05 with Mathematics categories.
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.
Fundamentals Of Queueing Networks
DOWNLOAD
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.
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.
Rate Stability And Output Rates In Queueing Networks With Shared Resources
DOWNLOAD
Author : Matthieu Jonckheere
language : en
Publisher:
Release Date : 2007
Rate Stability And Output Rates In Queueing Networks With Shared Resources written by Matthieu Jonckheere and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
Stability Analysis Of Regenerative Queueing Models
DOWNLOAD
Author : Evsey Morozov
language : en
Publisher: Springer Nature
Release Date : 2021-09-20
Stability Analysis Of Regenerative Queueing Models written by Evsey Morozov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-20 with Computers categories.
The stability analysis of stochastic models for telecommunication systems is an intensively studied topic. The analysis is, as a rule, a difficult problem requiring a refined mathematical technique, especially when one endeavors beyond the framework of Markovian models. The primary purpose of this book is to present, in a unified way, research into the stability analysis of a wide variety of regenerative queueing systems. It describes the theoretical foundations of this method, and then shows how it works with particular models, both classic ones as well as more recent models that have received attention. The focus lies on an in-depth and insightful mathematical explanation of the regenerative stability analysis method. The unique volume can serve as a textbook for students working in these and related scientific areas. The material is also of interest to engineers working in telecommunications field, who may be faced with the problem of stability of queueing systems.
Stability Criteria For Queueing Networks With A Monotonicity Property
DOWNLOAD
Author : Wojciech Szpankowski
language : en
Publisher:
Release Date : 1994
Stability Criteria For Queueing Networks With A Monotonicity Property written by Wojciech Szpankowski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.