Markov Modulated Stochastic Storage Processes

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Markov Modulated Stochastic Storage Processes

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Author : Yixin Zhu
language : en
Publisher:
Release Date : 1989

Markov Modulated Stochastic Storage Processes written by Yixin Zhu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Markov processes categories.

Stochastic Storage Processes

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Author : N.U. Prabhu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Stochastic Storage Processes written by N.U. Prabhu 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 2012-12-06 with Mathematics categories.

This is a revised and expanded version of the earlier edition. The new material is on Markov-modulated storage processes arising from queueing and data commu nication models. The analysis of these models is based on the fluctuation theory of Markov-additive processes and their discrete time analogues, Markov random walks. The workload and queue length processes, omitted from the earlier edition, are also presented. In addition, many sections have been rewritten, with new re sults and proofs, as well as further examples. The mathematical level and style of presentation, however, remain the same. Chapter I contains a comprefensive treatment of the waiting time and related quantities in a single server queue, combining Chapters 1 and 2 of the earlier edition. In Chapter 2 we treat the (continuous time) workload and queue length processes using their semiregenerative properties. Also included are bulk queues omitted from the earlier edition, but included in its Russian translation. The queue MIMIl is presented in Chapter 3. This is the so-called simple queue, but its treat ment in most of the literature is far from simple. Our analysis of the queue length process is elementary and yields explicit results for various distributions of interest. are treated in Chapter 4, combining Chapters 3 Continuous time storage models and 4 of the earlier edition. We present extensive new material, omitting much of the old Chapter 4. This has resulted in a streamlined account of this important class of models.

Markov Modulated Processes And Semiregenerative Phenomena

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Author : Loon Ching Tang
language : en
Publisher: World Scientific
Release Date : 2009

Markov Modulated Processes And Semiregenerative Phenomena written by Loon Ching Tang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

The book presents a coherent treatment of Markov random walks and Markov additive processes together with their applications. Part I provides the foundations of these stochastic processes underpinned by a solid theoretical framework based on Semiregenerative phenomena. Part II presents some applications to queueing and storage systems.

Stochastic Storage Processes

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Author : N.U. Prabhu
language : en
Publisher: Springer
Release Date : 2012-09-27

Stochastic Storage Processes written by N.U. Prabhu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-27 with Mathematics categories.

A self-contained treatment of stochastic processes arising from models for queues, insurance risk, and dams and data communication, using their sample function properties. The approach is based on the fluctuation theory of random walks, L vy processes, and Markov-additive processes, in which Wiener-Hopf factorisation plays a central role. This second edition includes results for the virtual waiting time and queue length in single server queues, while the treatment of continuous time storage processes is thoroughly revised and simplified. With its prerequisite of a graduate-level course in probability and stochastic processes, this book can be used as a text for an advanced course on applied probability models.

From Markov Jump Processes To Spatial Queues

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Author : L. Breuer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

From Markov Jump Processes To Spatial Queues written by L. Breuer 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 2012-12-06 with Mathematics categories.

From Markov Jump Processes to Spatial Queues aims to develop a unified theory of spatial queues that yields concrete results for the performance analysis of mobile communication networks. A particular objective is to develop the most natural generalization of existing concepts (e.g. the BMAP) toward the needs of mobile communication networks. To these belong the spatial distribution of batch arrivals and users in the system as well as time-inhomogeneous (e.g. periodic) arrival intensities and user movements. One of the major recent challenges for the stochastic modelling of communication systems is the emergence of wireless networks, which are used by more and more subscribers today. The main new feature of those, which is not covered by classical queuing theory, clearly is the importance of the user location within the area that is served by the base stations of the network. In the framework of queuing theory, this opens up the natural extension of classical queuing models towards queues with a structured space in which users are served. The present book is intended to introduce this extension under the name of spatial queues. The main point of view and the general approach will be that of Markov jump processes. We start with a closer look into the theory. Then we present new results for the theory of stochastic processes as well as for classical queuing theory. Finally we introduce the new concepts of spatial Markovian arrival processes and spatial queues. The main text is divided into three parts. The first part provides a new presentation of the theory of Markov jump processes. We derive a number of new results, especially for time-inhomogeneous processes, which have been neglected too much in the current textbooks on stochastic processes. For the first time, the class of Markov-additive jump processes is analysed in detail. This extends and unifies all Markovian arrival processes that have been proposed up to now (including arrivals for fluid queues) and provides a foundation for the subsequent introduction of spatial Markovian arrival processes. The second part contains new results for classical queues with BMAP input. These include the first explicit formulae for the distribution of periodic queues. The class of fluid Markovian arrival processes is introduced, and we give statistical estimates for the parameters of a BMAP. In the third part, the concepts of spatial Markovian arrival processes (abbreviated: SMAPs) and spatial queues are introduced. After that, periodic spatial Markovian queues are analysed as a model for the cells of a wireless communication network. From Markov Jump Processes to Spatial Queues is intended to reach queuing theorists, researchers in the field of communication systems, as well as engineers with some background in probability theory. Furthermore, it is suitable as a textbook for advanced queuing theory on the graduate or post-graduate level.

Advances In Queueing Theory Methods And Open Problems

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Author : Jewgeni H. Dshalalow
language : en
Publisher: CRC Press
Release Date : 2023-07-21

Advances In Queueing Theory Methods And Open Problems written by Jewgeni H. Dshalalow and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-21 with Business & Economics categories.

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.

Stochastic Processes For Insurance And Finance

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Author : Tomasz Rolski
language : en
Publisher: John Wiley & Sons
Release Date : 2009-09-25

Stochastic Processes For Insurance And Finance written by Tomasz Rolski 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 2009-09-25 with Mathematics categories.

Stochastic Processes for Insurance and Finance offers a thorough yet accessible reference for researchers and practitioners of insurance mathematics. Building on recent and rapid developments in applied probability, the authors describe in general terms models based on Markov processes, martingales and various types of point processes. Discussing frequently asked insurance questions, the authors present a coherent overview of the subject and specifically address: The principal concepts from insurance and finance Practical examples with real life data Numerical and algorithmic procedures essential for modern insurance practices Assuming competence in probability calculus, this book will provide a fairly rigorous treatment of insurance risk theory recommended for researchers and students interested in applied probability as well as practitioners of actuarial sciences. Wiley Series in Probability and Statistics

Frontiers In Queueing

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Author : Jewgeni H. Dshalalow
language : en
Publisher: CRC Press
Release Date : 1997-01-21

Frontiers In Queueing written by Jewgeni H. Dshalalow and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-21 with Business & Economics categories.

Queueing systems and networks are being applied to many areas of technology today, including telecommunications, computers, satellite systems, and traffic processes. This timely book, written by 26 of the most respected and influential researchers in the field, provides an overview of fundamental queueing systems and networks as applied to these technologies. Frontiers in Queueing: Models and Applications in Science and Engineering was written with more of an engineering slant than its predecessor, Advances in Queueing: Theory, Methods, and Open Problems. The earlier book was primarily concerned with methods, and was more theoretically oriented. This new volume, meant to be a sequel to the first book, was written by scientists and queueing theorists whose expertise is in technology and engineering, allowing readers to answer questions regarding the technicalities of related methods from the earlier book. Each chapter in the book surveys the classes of queueing models and networks, or the applied methods in queueing, and is followed by a discussion of open problems and future research directions. The discussion of these future trends is especially important to novice researchers, students, and even their advisors, as it provides the perspectives of eminent scientists in each area, thus showing where research efforts should be focused. Frontiers in Queueing: Models and Applications in Science and Engineering also includes applications to vital areas of engineering and technology, specifically, telecommunications, computers and computer networks, satellite systems, traffic processes, and more applied methods such as simulation, statistics, and numerical methods. All researchers, from students to advanced professionals, can benefit from the sound advice and perspective of the contributors represented in this book.

Ruin Probabilities

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Author : Soren Asmussen
language : en
Publisher: World Scientific
Release Date : 2000-07-24

Ruin Probabilities written by Soren Asmussen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-24 with Mathematics categories.

The book is a comprehensive treatment of classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (eg. for heavy-tailed claim size distributions), finite horizon ruin probabilities, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation or periodicity. Special features of the book are the emphasis on change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas like queueing theory.

Journal Of The American Statistical Association

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Author :
language : en
Publisher:
Release Date : 2002

Journal Of The American Statistical Association written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Electronic journals categories.