Vacation Queueing Models with Server Breakdowns PDF Download
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Author: V. M. Chandrasekaran
Publisher: LAP Lambert Academic Publishing
ISBN: 9783659644115
Category :
Languages : en
Pages : 104
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Book Description
An M[x]/G/1 retrial system with two phases of heterogeneous service, where the server is subjected to breakdown at each phase of service and operates under Bernoulli vacation policy is considered. In the proposed model, any arriving batch finding the server busy, breakdown or on vacation enters an orbit. Otherwise one customer from the arriving batch enters a service immediately while the rest join the orbit. After the completion of two phases of service, the server either goes for a vacation with probability p or may continue to serve the next customer with probability 1- p. At a vacation completion epoch, the server waits for the customers, if any in the orbit, or for new customers to arrive. While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. We have constructed the mathematical model and the steady-state probability distribution of number of customers in the system when it is idle, busy, on vacation and under repair are derived. Finally, some system performance measures and the effect of various parameters measures are discussed.
Author: V. M. Chandrasekaran
Publisher: LAP Lambert Academic Publishing
ISBN: 9783659644115
Category :
Languages : en
Pages : 104
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Book Description
An M[x]/G/1 retrial system with two phases of heterogeneous service, where the server is subjected to breakdown at each phase of service and operates under Bernoulli vacation policy is considered. In the proposed model, any arriving batch finding the server busy, breakdown or on vacation enters an orbit. Otherwise one customer from the arriving batch enters a service immediately while the rest join the orbit. After the completion of two phases of service, the server either goes for a vacation with probability p or may continue to serve the next customer with probability 1- p. At a vacation completion epoch, the server waits for the customers, if any in the orbit, or for new customers to arrive. While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. We have constructed the mathematical model and the steady-state probability distribution of number of customers in the system when it is idle, busy, on vacation and under repair are derived. Finally, some system performance measures and the effect of various parameters measures are discussed.
Author: Naishuo Tian
Publisher: Springer Science & Business Media
ISBN: 0387337237
Category : Mathematics
Languages : en
Pages : 395
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Book Description
This book discusses systematically the many variations of vacation policy. The book discusses a variety of typical vacation model applications. The presentation style is unique compared with the books published in the same field – a "theorem and proof" format is used. Also, this is the first time G1/M/1 multi-server vacation models, both continuous and discrete, and the optimization and control issues have been presented in book form.
Author: J.G.C. Templeton
Publisher: Taylor & Francis
ISBN: 1351418661
Category : Mathematics
Languages : en
Pages : 344
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Book Description
Based on the careful analysis of several hundred publications, this book uniformly describes basic methods of analysis and critical results of the theory of retrial queues. Chapters discuss: analysis of single-server retrial queues, including stationary and transient distribution of the number in the system, busy period, waiting time process, limit theorems, stochastic inequalities, traffic measurement multiserver retrial queues - ergodicity, explicit formulas, algorithmic solutions, limit theorems, approximations advanced single-server and multiserver retrial queues - models with priority subscribers, non-ersistent subscribers, finite source queues Lecturers, researchers, and students in probability, statistics, operations research, telecommunications, and computer systems modeling analysis will find Retrial Queues to be an invaluable resource.
Author: Hideaki Takagi
Publisher:
ISBN:
Category : Queuing theory
Languages : en
Pages :
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Book Description
Author: Vladimir Anisimov
Publisher: John Wiley & Sons
ISBN: 1119755220
Category : Mathematics
Languages : en
Pages : 336
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Book Description
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 second volume includes eight chapters written by experts wellknown in their areas. The book conducts a stability analysis of certain types of multiserver regenerative queueing systems; a transient evaluation of Markovian queueing systems, focusing on closed-form distributions and numerical techniques; analysis of queueing models in service sectors using analytical and simulation approaches; plus an investigation of probability distributions in queueing models and their use in economics, industry, demography and environmental studies. This book also considers techniques for the control of information in queueing systems and their impact on strategic customer behavior, social welfare and the revenue of monopolists. In addition, applications of maximum entropy methods of inference for the analysis of a stable M/G/1 queue with heavy tails, and inventory models with positive service time - including perishable items and stock supplied using various algorithmic control policies ((s; S); (r;Q), etc.).
Author: J. R. Artalejo
Publisher: Springer Science & Business Media
ISBN: 3540787259
Category : Mathematics
Languages : en
Pages : 320
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Book Description
The application of auto-repeat facilities in telephone systems, as well as the use of random access protocols in computer networks, have led to growing interest in retrial queueing models. Since much of the theory of retrial queues is complex from an analytical viewpoint, with this book the authors give a comprehensive and updated text focusing on approximate techniques and algorithmic methods for solving the analytically intractable models. Retrial Queueing Systems: A Computational Approach also Presents motivating examples in telephone and computer networks. Establishes a comparative analysis of the retrial queues versus standard queues with waiting lines and queues with losses. Integrates a wide range of techniques applied to the main M/G/1 and M/M/c retrial queues, and variants with general retrial times, finite population and the discrete-time case. Surveys basic results of the matrix-analytic formalism and emphasizes the related tools employed in retrial queues. Discusses a few selected retrial queues with QBD, GI/M/1 and M/G/1 structures. Features an abundance of numerical examples, and updates the existing literature. The book is intended for an audience ranging from advanced undergraduates to researchers interested not only in queueing theory, but also in applied probability, stochastic models of the operations research, and engineering. The prerequisite is a graduate course in stochastic processes, and a positive attitude to the algorithmic probability.
Author: Naishuo Tian
Publisher: Springer
ISBN: 9780387513546
Category : Mathematics
Languages : en
Pages : 0
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Book Description
This book discusses systematically the many variations of vacation policy. The book discusses a variety of typical vacation model applications. The presentation style is unique compared with the books published in the same field – a "theorem and proof" format is used. Also, this is the first time G1/M/1 multi-server vacation models, both continuous and discrete, and the optimization and control issues have been presented in book form.
Author: Attahiru Sule Alfa
Publisher: Springer Science & Business Media
ISBN: 1441973141
Category : Computers
Languages : en
Pages : 248
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Book Description
Queueing theory applications can be discovered in many walks of life including; transportation, manufacturing, telecommunications, computer systems and more. However, the most prevalent applications of queueing theory are in the telecommunications field. Queueing Theory for Telecommunications: Discrete Time Modelling of a Single Node System focuses on discrete time modeling and illustrates that most queueing systems encountered in real life can be set up as a Markov chain. This feature is very unique because the models are set in such a way that matrix-analytic methods are used to analyze them. Queueing Theory for Telecommunications: Discrete Time Modelling of a Single Node System is the most relevant book available on queueing models designed for applications to telecommunications. This book presents clear concise theories behind how to model and analyze key single node queues in discrete time using special tools that were presented in the second chapter. The text also delves into the types of single node queues that are very frequently encountered in telecommunication systems modeling, and provides simple methods for analyzing them. Where appropriate, alternative analysis methods are also presented. This book is for advanced-level students and researchers concentrating on engineering, computer science and mathematics as a secondary text or reference book. Professionals who work in the related industries of telecommunications, industrial engineering and communications engineering will find this book useful as well.
Author: Professor Chee-Hock Ng
Publisher: John Wiley & Sons
ISBN: 9780470994665
Category : Technology & Engineering
Languages : en
Pages : 292
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Book Description
Queueing analysis is a vital tool used in the evaluation of system performance. Applications of queueing analysis cover a wide spectrum from bank automated teller machines to transportation and communications data networks. Fully revised, this second edition of a popular book contains the significant addition of a new chapter on Flow & Congestion Control and a section on Network Calculus among other new sections that have been added to remaining chapters. An introductory text, Queueing Modelling Fundamentals focuses on queueing modelling techniques and applications of data networks, examining the underlying principles of isolated queueing systems. This book introduces the complex queueing theory in simple language/proofs to enable the reader to quickly pick up an overview to queueing theory without utilizing the diverse necessary mathematical tools. It incorporates a rich set of worked examples on its applications to communication networks. Features include: Fully revised and updated edition with significant new chapter on Flow and Congestion Control as-well-as a new section on Network Calculus A comprehensive text which highlights both the theoretical models and their applications through a rich set of worked examples, examples of applications to data networks and performance curves Provides an insight into the underlying queuing principles and features step-by-step derivation of queueing results Written by experienced Professors in the field Queueing Modelling Fundamentals is an introductory text for undergraduate or entry-level post-graduate students who are taking courses on network performance analysis as well as those practicing network administrators who want to understand the essentials of network operations. The detailed step-by-step derivation of queueing results also makes it an excellent text for professional engineers.
Author: Willi-hans Steeb
Publisher: World Scientific Publishing Company
ISBN: 981310807X
Category : Mathematics
Languages : en
Pages : 323
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Book Description
This book provides a self-contained and accessible introduction to linear and multilinear algebra. Besides the standard techniques for linear and multilinear algebra many advanced topics are included. Emphasis is placed on the Kronecker product and tensor product. The Kronecker product has widespread applications in signal processing, discrete wavelets, statistical physics, computer graphics, fractals, quantum mechanics and quantum computing. All these fields are covered in detail. A key feature of the book is the many detailed worked-out examples. Computer algebra applications are also given. Each chapter includes useful exercises. The book is well suited for pure and applied mathematicians as well as theoretical physicists and engineers.New topics added to the second edition are: braid-like relations, Clebsch-Gordan expansion, nearest Kronecker product, Clifford and Pauli group, universal enveloping algebra, computer algebra and Kronecker product.
