Sample-Path Analysis of Queueing Systems

Sample-Path Analysis of Queueing Systems

Author: Muhammad El-Taha

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 303

ISBN-13: 1461557216

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Sample-Path Analysis of Queueing Systems uses a deterministic (sample-path) approach to analyze stochastic systems, primarily queueing systems and more general input-output systems. Among other topics of interest it deals with establishing fundamental relations between asymptotic frequencies and averages, pathwise stability, and insensitivity. These results are utilized to establish useful performance measures. The intuitive deterministic approach of this book will give researchers, teachers, practitioners, and students better insights into many results in queueing theory. The simplicity and intuitive appeal of the arguments will make these results more accessible, with no sacrifice of mathematical rigor. Recent topics such as pathwise stability are also covered in this context. The book consistently takes the point of view of focusing on one sample path of a stochastic process. Hence, it is devoted to providing pure sample-path arguments. With this approach it is possible to separate the issue of the validity of a relationship from issues of existence of limits and/or construction of stationary framework. Generally, in many cases of interest in queueing theory, relations hold, assuming limits exist, and the proofs are elementary and intuitive. In other cases, proofs of the existence of limits will require the heavy machinery of stochastic processes. The authors feel that sample-path analysis can be best used to provide general results that are independent of stochastic assumptions, complemented by use of probabilistic arguments to carry out a more detailed analysis. This book focuses on the first part of the picture. It does however, provide numerous examples that invoke stochastic assumptions, which typically are presented at the ends of the chapters.


Book Synopsis Sample-Path Analysis of Queueing Systems by : Muhammad El-Taha

Download or read book Sample-Path Analysis of Queueing Systems written by Muhammad El-Taha and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sample-Path Analysis of Queueing Systems uses a deterministic (sample-path) approach to analyze stochastic systems, primarily queueing systems and more general input-output systems. Among other topics of interest it deals with establishing fundamental relations between asymptotic frequencies and averages, pathwise stability, and insensitivity. These results are utilized to establish useful performance measures. The intuitive deterministic approach of this book will give researchers, teachers, practitioners, and students better insights into many results in queueing theory. The simplicity and intuitive appeal of the arguments will make these results more accessible, with no sacrifice of mathematical rigor. Recent topics such as pathwise stability are also covered in this context. The book consistently takes the point of view of focusing on one sample path of a stochastic process. Hence, it is devoted to providing pure sample-path arguments. With this approach it is possible to separate the issue of the validity of a relationship from issues of existence of limits and/or construction of stationary framework. Generally, in many cases of interest in queueing theory, relations hold, assuming limits exist, and the proofs are elementary and intuitive. In other cases, proofs of the existence of limits will require the heavy machinery of stochastic processes. The authors feel that sample-path analysis can be best used to provide general results that are independent of stochastic assumptions, complemented by use of probabilistic arguments to carry out a more detailed analysis. This book focuses on the first part of the picture. It does however, provide numerous examples that invoke stochastic assumptions, which typically are presented at the ends of the chapters.

Sample Path Analysis of Queueing Systems: New Results

Sample Path Analysis of Queueing Systems: New Results

Author: Muhammad Ahmad el Taha

Publisher:

Published: 1987

Total Pages:

ISBN-13:

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Book Synopsis Sample Path Analysis of Queueing Systems: New Results by : Muhammad Ahmad el Taha

Download or read book Sample Path Analysis of Queueing Systems: New Results written by Muhammad Ahmad el Taha and published by . This book was released on 1987 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Sample-path Analysis of Queueing Systems

Sample-path Analysis of Queueing Systems

Author: Muhammad A. El-Taha

Publisher:

Published: 1986

Total Pages: 282

ISBN-13:

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Book Synopsis Sample-path Analysis of Queueing Systems by : Muhammad A. El-Taha

Download or read book Sample-path Analysis of Queueing Systems written by Muhammad A. El-Taha and published by . This book was released on 1986 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Sample Path Analysis and Control of Finite Capacity Queueing Systems

Sample Path Analysis and Control of Finite Capacity Queueing Systems

Author: Panayotis D. Sparaggis

Publisher:

Published: 1994

Total Pages: 432

ISBN-13:

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Book Synopsis Sample Path Analysis and Control of Finite Capacity Queueing Systems by : Panayotis D. Sparaggis

Download or read book Sample Path Analysis and Control of Finite Capacity Queueing Systems written by Panayotis D. Sparaggis and published by . This book was released on 1994 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Sample Path Analysis of Stochastic Processes

Sample Path Analysis of Stochastic Processes

Author: Chaitanya N. Garikiparthi

Publisher:

Published: 2008

Total Pages: 180

ISBN-13:

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A number of processes that occur in nature as well as those that are manifestations of human activities are correlated in nature and can be describe by stochastic non-Markovian processes. Most known theoretical results for these systems are in the steady state domain, assuming that the system has been in operation for a long enough time, and that the state in which the system starts has no effect on the current behavior of the system. Nevertheless steady state assumptions do not hold in many applied situations. In this thesis we provide a framework to stochastically track these processes. Application of this theory provide valuable insights into the transient behavior of these stochastic processes and allows us to model and study the effect of auto-correlations in the driving processes on transient probabilistic (performance) metrics of interest. In order to develop accurate models to represent these systems, we allow the arrival and the service processes that characterize the system to be both general and correlated. We specifically study the busy period and other first passages of and auto-correlated MEP/MEP/1 single server queue to demonstrate the application of tracking these memory-full processes. Analysis presented here is the transient domain and does not require the underlying processes to be in a steady state. In the first part of the thesis we provide solutions to compute the probabilities for exactly 'n' customers being served in a busy period of MEP/MEP/1 queueing system. We then present matrix exponential representations to characterize the lengths of sample paths during these busy periods and derive expressions to compute moments for length of the busy period as well as for the number of customers served during the busy period. In the second part of the thesis, we study the effect of increase in threshold level and the correlations in the arrival and service processes on the mean first passage time to go below a given threshold. Finally we study the busy periods for finite queueing systems, and again study both the length of the busy period and the number of customers served during such a time.


Book Synopsis Sample Path Analysis of Stochastic Processes by : Chaitanya N. Garikiparthi

Download or read book Sample Path Analysis of Stochastic Processes written by Chaitanya N. Garikiparthi and published by . This book was released on 2008 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: A number of processes that occur in nature as well as those that are manifestations of human activities are correlated in nature and can be describe by stochastic non-Markovian processes. Most known theoretical results for these systems are in the steady state domain, assuming that the system has been in operation for a long enough time, and that the state in which the system starts has no effect on the current behavior of the system. Nevertheless steady state assumptions do not hold in many applied situations. In this thesis we provide a framework to stochastically track these processes. Application of this theory provide valuable insights into the transient behavior of these stochastic processes and allows us to model and study the effect of auto-correlations in the driving processes on transient probabilistic (performance) metrics of interest. In order to develop accurate models to represent these systems, we allow the arrival and the service processes that characterize the system to be both general and correlated. We specifically study the busy period and other first passages of and auto-correlated MEP/MEP/1 single server queue to demonstrate the application of tracking these memory-full processes. Analysis presented here is the transient domain and does not require the underlying processes to be in a steady state. In the first part of the thesis we provide solutions to compute the probabilities for exactly 'n' customers being served in a busy period of MEP/MEP/1 queueing system. We then present matrix exponential representations to characterize the lengths of sample paths during these busy periods and derive expressions to compute moments for length of the busy period as well as for the number of customers served during the busy period. In the second part of the thesis, we study the effect of increase in threshold level and the correlations in the arrival and service processes on the mean first passage time to go below a given threshold. Finally we study the busy periods for finite queueing systems, and again study both the length of the busy period and the number of customers served during such a time.

An Introduction to Queueing Theory

An Introduction to Queueing Theory

Author: U. Narayan Bhat

Publisher: Birkhäuser

Published: 2015-07-09

Total Pages: 343

ISBN-13: 0817684212

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This introductory textbook is designed for a one-semester course on queueing theory that does not require a course on stochastic processes as a prerequisite. By integrating the necessary background on stochastic processes with the analysis of models, the work provides a sound foundational introduction to the modeling and analysis of queueing systems for a broad interdisciplinary audience of students in mathematics, statistics, and applied disciplines such as computer science, operations research, and engineering. This edition includes additional topics in methodology and applications. Key features: • An introductory chapter including a historical account of the growth of queueing theory in more than 100 years. • A modeling-based approach with emphasis on identification of models • Rigorous treatment of the foundations of basic models commonly used in applications with appropriate references for advanced topics. • A chapter on matrix-analytic method as an alternative to the traditional methods of analysis of queueing systems. • A comprehensive treatment of statistical inference for queueing systems. • Modeling exercises and review exercises when appropriate. The second edition of An Introduction of Queueing Theory may be used as a textbook by first-year graduate students in fields such as computer science, operations research, industrial and systems engineering, as well as related fields such as manufacturing and communications engineering. Upper-level undergraduate students in mathematics, statistics, and engineering may also use the book in an introductory course on queueing theory. With its rigorous coverage of basic material and extensive bibliography of the queueing literature, the work may also be useful to applied scientists and practitioners as a self-study reference for applications and further research. "...This book has brought a freshness and novelty as it deals mainly with modeling and analysis in applications as well as with statistical inference for queueing problems. With his 40 years of valuable experience in teaching and high level research in this subject area, Professor Bhat has been able to achieve what he aimed: to make [the work] somewhat different in content and approach from other books." - Assam Statistical Review of the first edition


Book Synopsis An Introduction to Queueing Theory by : U. Narayan Bhat

Download or read book An Introduction to Queueing Theory written by U. Narayan Bhat and published by Birkhäuser. This book was released on 2015-07-09 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory textbook is designed for a one-semester course on queueing theory that does not require a course on stochastic processes as a prerequisite. By integrating the necessary background on stochastic processes with the analysis of models, the work provides a sound foundational introduction to the modeling and analysis of queueing systems for a broad interdisciplinary audience of students in mathematics, statistics, and applied disciplines such as computer science, operations research, and engineering. This edition includes additional topics in methodology and applications. Key features: • An introductory chapter including a historical account of the growth of queueing theory in more than 100 years. • A modeling-based approach with emphasis on identification of models • Rigorous treatment of the foundations of basic models commonly used in applications with appropriate references for advanced topics. • A chapter on matrix-analytic method as an alternative to the traditional methods of analysis of queueing systems. • A comprehensive treatment of statistical inference for queueing systems. • Modeling exercises and review exercises when appropriate. The second edition of An Introduction of Queueing Theory may be used as a textbook by first-year graduate students in fields such as computer science, operations research, industrial and systems engineering, as well as related fields such as manufacturing and communications engineering. Upper-level undergraduate students in mathematics, statistics, and engineering may also use the book in an introductory course on queueing theory. With its rigorous coverage of basic material and extensive bibliography of the queueing literature, the work may also be useful to applied scientists and practitioners as a self-study reference for applications and further research. "...This book has brought a freshness and novelty as it deals mainly with modeling and analysis in applications as well as with statistical inference for queueing problems. With his 40 years of valuable experience in teaching and high level research in this subject area, Professor Bhat has been able to achieve what he aimed: to make [the work] somewhat different in content and approach from other books." - Assam Statistical Review of the first edition

Advances in Queueing Theory, Methods, and Open Problems

Advances in Queueing Theory, Methods, and Open Problems

Author: Jewgeni H. Dshalalow

Publisher: CRC Press

Published: 2023-07-21

Total Pages: 530

ISBN-13: 1000949931

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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.


Book Synopsis Advances in Queueing Theory, Methods, and Open Problems by : Jewgeni H. Dshalalow

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 2023-07-21 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.

Analysis of Queueing Systems

Analysis of Queueing Systems

Author: J.A. White

Publisher: Elsevier

Published: 2012-12-02

Total Pages: 543

ISBN-13: 0323146600

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Analysis and Queueing Systems is a nine-chapter introductory text that considers the applied problem of analyzing queueing systems. This book outlines a sequence of steps, which if properly executed yield an improved design of the system. This book deals first with the development of the necessary background in probability theory and transforms methods. These topics are followed by a presentation of queueing models and how these simple models can be applied in more complex situations. The subsequent chapters survey the development of prescriptive models of queueing systems; the principles of transient analysis; and the modeling techniques for use in analyzing more complex queueing systems. The discussion then shifts to the design of data collection systems and the analysis of data. The last chapter focuses on the development of simulation models.


Book Synopsis Analysis of Queueing Systems by : J.A. White

Download or read book Analysis of Queueing Systems written by J.A. White and published by Elsevier. This book was released on 2012-12-02 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis and Queueing Systems is a nine-chapter introductory text that considers the applied problem of analyzing queueing systems. This book outlines a sequence of steps, which if properly executed yield an improved design of the system. This book deals first with the development of the necessary background in probability theory and transforms methods. These topics are followed by a presentation of queueing models and how these simple models can be applied in more complex situations. The subsequent chapters survey the development of prescriptive models of queueing systems; the principles of transient analysis; and the modeling techniques for use in analyzing more complex queueing systems. The discussion then shifts to the design of data collection systems and the analysis of data. The last chapter focuses on the development of simulation models.

Frontiers in Queueing

Frontiers in Queueing

Author: Jewgeni H. Dshalalow

Publisher: CRC Press

Published: 1997-01-21

Total Pages: 482

ISBN-13: 9780849380761

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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.


Book Synopsis Frontiers in Queueing by : Jewgeni H. Dshalalow

Download or read book Frontiers in Queueing written by Jewgeni H. Dshalalow and published by CRC Press. This book was released on 1997-01-21 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Analysis of Queues

Analysis of Queues

Author: Natarajan Gautam

Publisher: CRC Press

Published: 2012-04-26

Total Pages: 804

ISBN-13: 1439806586

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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.


Book Synopsis Analysis of Queues by : Natarajan Gautam

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.