Analysis of Queues

Analysis of Queues

Exploring a broad range of applications, the book contains plenty of solved problems, exercises, case studies, paradoxes, and numerical examples.

Author: Natarajan Gautam

Publisher: CRC Press

ISBN: 9781439806586

Category: Business & Economics

Page: 802

View: 565

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.
Categories: Business & Economics

Sample Path Analysis of Queueing Systems

Sample Path Analysis of Queueing Systems

Stidham and El-Taha [182] unify and extend previous work on sample-path analysis of queues; they investigate the behavior of a discrete-state, continuous-time process with an imbedded point process and derive relations between various ...

Author: Muhammad El-Taha

Publisher: Springer Science & Business Media

ISBN: 9781461557210

Category: Business & Economics

Page: 295

View: 328

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.
Categories: Business & Economics

Analysis of Queueing Networks with Blocking

Analysis of Queueing Networks with Blocking

Almost all queueing networks with product form queue length distributions require infinite queues, that is, it is assumed that there is always a space in the queue for arriving customers. In real life systems, the storage space is ...

Author: Simonetta Balsamo

Publisher: Springer Science & Business Media

ISBN: 9781475733457

Category: Business & Economics

Page: 255

View: 936

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.
Categories: Business & Economics

Analysis of Queueing Systems

Analysis of Queueing Systems

As seen in Table 4.1, we analyze a variety of queues using the method of stages approach. ... TABLE 4.1 Summary of non-Poisson queues analyzed via method of stages Case Classification Solution 1 (M |E|, |1): (GD|oo oo) general 2 (M |E|, ...

Author: J.A. White

Publisher: Elsevier

ISBN: 9780323146609

Category: Mathematics

Page: 542

View: 219

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.
Categories: Mathematics

Performance Analysis of Queuing and Computer Networks

Performance Analysis of Queuing and Computer Networks

307 8.2 The Imbedded Markov Chain for G/M/1/∞ Queue . . . . . . . . . 307 8.3 Analysis of the Parameter α . . . . . . . . . . . . . . . . . . . . . 313 8.3.1 Stability criterion in terms of the parameters of the queue .

Author: G.R. Dattatreya

Publisher: CRC Press

ISBN: 158488987X

Category: Computers

Page: 472

View: 457

Performance Analysis of Queuing and Computer Networks develops simple models and analytical methods from first principles to evaluate performance metrics of various configurations of computer systems and networks. It presents many concepts and results of probability theory and stochastic processes. After an introduction to queues in computer networks, this self-contained book covers important random variables, such as Pareto and Poisson, that constitute models for arrival and service disciplines. It then deals with the equilibrium M/M/1/∞queue, which is the simplest queue that is amenable for analysis. Subsequent chapters explore applications of continuous time, state-dependent single Markovian queues, the M/G/1 system, and discrete time queues in computer networks. The author then proceeds to study networks of queues with exponential servers and Poisson external arrivals as well as the G/M/1 queue and Pareto interarrival times in a G/M/1 queue. The last two chapters analyze bursty, self-similar traffic, and fluid flow models and their effects on queues.
Categories: Computers

Some New Results in the Statistical Analysis of Queues

Some New Results in the Statistical Analysis of Queues

In the paper some new results are presented for the statistical analysis of queues.

Author: Carl M. Harris

Publisher:

ISBN: OCLC:227543238

Category: Estimation theory

Page: 35

View: 770

In the paper some new results are presented for the statistical analysis of queues. Special emphasis is placed on the estimation of input and service parameters and/or distributions in various queueing contexts. A fair amount of background material is quoted from the literature in order to provide an appropriate setting for the discussion of the new results. (Author).
Categories: Estimation theory

Performance Analysis of Closed Queueing Networks

Performance Analysis of Closed Queueing Networks

Mean value analysis for blocking queueing networks. IEEE Transaction on Software Engineering, 14(4), 418–428. Akyildiz, I. F. (1988c). On the exact and approximate throughput analysis of closed queueing networks with blocking.

Author: Svenja Lagershausen

Publisher: Springer Science & Business Media

ISBN: 9783642322143

Category: Business & Economics

Page: 169

View: 761

This book deals with the performance analysis of closed queueing networks with general processing times and finite buffer spaces. It offers a detailed introduction to the problem and a comprehensive literature review. Two approaches to the performance of closed queueing networks are presented. One is an approximate decomposition approach, while the second is the first exact approach for finite-capacity networks with general processing times. In this Markov chain approach, queueing networks are analyzed by modeling the entire system as one Markov chain. As this approach is exact, it is well-suited both as a reference quantity for approximate procedures and as extension to other queueing networks. Moreover, for the first time, the exact distribution of the time between processing starts is provided.
Categories: Business & Economics

Performance Analysis of Queuing and Computer Networks

Performance Analysis of Queuing and Computer Networks

After an introduction to queues in computer networks, this self-contained book covers important random variables, such as Pareto and Poisson, that constitute models for arrival and service disciplines.

Author: G.R. Dattatreya

Publisher: Chapman and Hall/CRC

ISBN: 1584889861

Category: Computers

Page: 472

View: 681

Performance Analysis of Queuing and Computer Networks develops simple models and analytical methods from first principles to evaluate performance metrics of various configurations of computer systems and networks. It presents many concepts and results of probability theory and stochastic processes. After an introduction to queues in computer networks, this self-contained book covers important random variables, such as Pareto and Poisson, that constitute models for arrival and service disciplines. It then deals with the equilibrium M/M/1/∞queue, which is the simplest queue that is amenable for analysis. Subsequent chapters explore applications of continuous time, state-dependent single Markovian queues, the M/G/1 system, and discrete time queues in computer networks. The author then proceeds to study networks of queues with exponential servers and Poisson external arrivals as well as the G/M/1 queue and Pareto interarrival times in a G/M/1 queue. The last two chapters analyze bursty, self-similar traffic, and fluid flow models and their effects on queues.
Categories: Computers

An Introduction to Queueing Theory

An Introduction to Queueing Theory

This edition includes additional topics in methodology and applications.

Author: U. Narayan Bhat

Publisher: Birkhäuser

ISBN: 0817684204

Category: Mathematics

Page: 339

View: 859

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
Categories: Mathematics

Queues Inventories and Maintenance

Queues  Inventories and Maintenance

A seminal work by one of the founders of the science of operations research, this text for upper-level undergraduates and graduate students examines general queuing problems, discusses the effect of changes of arrival and service ...

Author: Philip McCord Morse

Publisher: Courier Corporation

ISBN: 0486439143

Category: Mathematics

Page: 202

View: 845

A seminal work by one of the founders of the science of operations research, this text for upper-level undergraduates and graduate students examines general queuing problems, discusses the effect of changes of arrival and service distributions on queuing results, and describes the application of queuing theory to maintenance and inventory problems.
Categories: Mathematics

Queueing Theory 1

Queueing Theory 1

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.

Author: Vladimir Anisimov

Publisher: John Wiley & Sons

ISBN: 9781789450019

Category: Mathematics

Page: 336

View: 304

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.
Categories: Mathematics

Fundamentals of Queueing Theory

Fundamentals of Queueing Theory

This book is also a valuable reference for practitioners in applied mathematics, operations research, engineering, and industrial engineering.

Author: John F. Shortle

Publisher: John Wiley & Sons

ISBN: 9781118943526

Category: Business & Economics

Page: 576

View: 716

The definitive guide to queueing theory and its practical applications—features numerous real-world examples of scientific, engineering, and business applications Thoroughly updated and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fifth Edition presents the statistical principles and processes involved in the analysis of the probabilistic nature of queues. Rather than focus narrowly on a particular application area, the authors illustrate the theory in practice across a range of fields, from computer science and various engineering disciplines to business and operations research. Critically, the text also provides a numerical approach to understanding and making estimations with queueing theory and provides comprehensive coverage of both simple and advanced queueing models. As with all preceding editions, this latest update of the classic text features a unique blend of the theoretical and timely real-world applications. The introductory section has been reorganized with expanded coverage of qualitative/non-mathematical approaches to queueing theory, including a high-level description of queues in everyday life. New sections on non-stationary fluid queues, fairness in queueing, and Little’s Law have been added, as has expanded coverage of stochastic processes, including the Poisson process and Markov chains. • Each chapter provides a self-contained presentation of key concepts and formulas, to allow readers to focus independently on topics relevant to their interests • A summary table at the end of the book outlines the queues that have been discussed and the types of results that have been obtained for each queue • Examples from a range of disciplines highlight practical issues often encountered when applying the theory to real-world problems • A companion website features QtsPlus, an Excel-based software platform that provides computer-based solutions for most queueing models presented in the book. Featuring chapter-end exercises and problems—all of which have been classroom-tested and refined by the authors in advanced undergraduate and graduate-level courses—Fundamentals of Queueing Theory, Fifth Edition is an ideal textbook for courses in applied mathematics, queueing theory, probability and statistics, and stochastic processes. This book is also a valuable reference for practitioners in applied mathematics, operations research, engineering, and industrial engineering.
Categories: Business & Economics

Discrete Time Analysis of Multi Queue Systems with Multiple Departure Streams in Material Handling and Production under Different Service Rules

Discrete Time Analysis of Multi Queue Systems with Multiple Departure Streams in Material Handling and Production under Different Service Rules

Cooper and Murray (1969) study an exhaustive service and a gated service model. The queues of the polling model are served in cycle order. Based on a Poisson arrival process, the mean number of waiting customers and the mean cycle time ...

Author: Baumann, Marion

Publisher: KIT Scientific Publishing

ISBN: 9783731509844

Category: Technology & Engineering

Page: 272

View: 240

Categories: Technology & Engineering

Stability Analysis of Regenerative Queueing Models

Stability Analysis of Regenerative Queueing Models

An important study presented in [4] contains both the stability conditions and the bounds on the rate of convergence to stationarity for ... The stability analysis of a single-class GI/G/m/0-type retrial queue has been developed in [2].

Author: Evsey Morozov

Publisher: Springer Nature

ISBN: 9783030824389

Category:

Page:

View: 870

Categories:

Some Problems in the Analysis of Queuing Systems

Some Problems in the Analysis of Queuing Systems

This is followed by discussion of several independent problems: (1) a two counter problem, where arrivals join the shorter queue; (2) some numerical methods for determining the transient behavior of finite queues; (3) double queues, with ...

Author: Maurice W. Sasieni

Publisher:

ISBN: OCLC:500867530

Category: Differential equations

Page: 116

View: 453

A summary is given of the main techniques which have been used in the analysis of queuing systems. This is followed by discussion of several independent problems: (1) a two counter problem, where arrivals join the shorter queue; (2) some numerical methods for determining the transient behavior of finite queues; (3) double queues, with impatient customers and service clerks -- typified by a taxi-stand with queues of passengers and taxis; (4) the use of Laplace transforms in analysis of queues; (5) the relation among the mean arrival rate, the mean number in the system, and the mean waiting time of an arrival; (6) the application of queuing theory to job-shop analysis; and (7) the estimation of system parameters from observations on the behavior of the queue. A bibliography is enclosed.
Categories: Differential equations

Practical Queueing Analysis

Practical Queueing Analysis

This text enables the reader to use queuing analysis to solve practical problems without needing sophisticated mathematics.

Author: Mike Tanner

Publisher: McGraw-Hill Companies

ISBN: UOM:39015032186481

Category: Queuing theory

Page: 391

View: 835

Queuing theory is a highly complex, but essential part of computer communications which deals with the efficient use of networked resources. This text enables the reader to use queuing analysis to solve practical problems without needing sophisticated mathematics. After discussing fundamental issues and characteristics, the book focuses on useful results and formulae, rather than background theory. A library of subroutines for building analysis programs is provided, as is a menu-driven program on the optional diskette.
Categories: Queuing theory

Discrete Time Analysis of Multi Server Queueing Systems in Material Handling and Service

Discrete Time Analysis of Multi Server Queueing Systems in Material Handling and Service

We give a summary of the existing discrete time queueing models in chapter 3. A literature review of relevant publications about multi-server queues is provided in the same chapter. The conclusion of our literature review leads to the ...

Author: Judith M. Matzka

Publisher: KIT Scientific Publishing

ISBN: 9783866446885

Category:

Page: 104

View: 947

Categories:

Queueing Theory in Manufacturing Systems Analysis and Design

Queueing Theory in Manufacturing Systems Analysis and Design

... Laplace Transforms and Generating Functions A.2.1 Laplace Transforms A.2.2 Laplace - Stieltjes Transforms A.2.3 Generating Functions 360 360 361 361 B Summary of Important Results for Single - Station Queueing Systems B.1 Results ...

Author: H.T. Papadopolous

Publisher: Springer Science & Business Media

ISBN: 0412387204

Category: Technology & Engineering

Page: 394

View: 395

The objective of the book is to acquaint the reader with the use of queueing theory in the analysis of manufacturing systems.
Categories: Technology & Engineering

Traffic Highway Engineering

Traffic   Highway Engineering

The theory of queuing therefore concerns the use of mathematical algorithms to describe the processes that result in the ... The analysis of queues can be undertaken by assuming either deterministic or stochastic queue characteristics.

Author: Nicholas J. Garber

Publisher: Cengage Learning

ISBN: 9781111800833

Category: Technology & Engineering

Page: 1230

View: 224

The new edition of Garber and Hoel's best-selling text focuses on giving students insight into all facets of traffic and highway engineering. Students generally come to this course with little knowledge or understanding of the importance of transportation, much less of the extensive career opportunities within the field. Transportation is an extremely broad field, and courses must either cover all transportation modes or focus on specifics. While many topics can be covered with a survey approach, this often lacks sufficient depth and students leave the course without a full understanding of any of the fields. This text focuses exclusively on traffic and highway engineering beginning with a discussion of the pivotal role transportation plays in our society, including employment opportunities, historical impact, and the impact of transportation on our daily lives. This approach gives students a sense of what the field is about as well as an opportunity to consider some of its challenges. Later chapters focus on specific issues facing transportation engineers. The text uses pedagogical tools such as worked problems, diagrams and tables, reference material, and realistic examples to demonstrate how the material is applied. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Categories: Technology & Engineering