An Introduction To Queueing Systems
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An Introduction to Queueing Systems
Author: Sanjay K. Bose
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-12-01
Queueing is an aspect of modern life that we encounter at every step in our daily activities. Whether it happens at the checkout counter in the supermarket or in accessing the Internet, the basic phenomenon of queueing arises whenever a shared facility needs to be accessed for service by a ]arge number of jobs or customers. The study of queueing is important as it gravides both a theoretical background to the kind of service that we may expect from such a facility and the way in which the facility itself may be designed to provide some specified grade of service to its customers. Our study of queueing was basically motivated by its use in the study of communication systems and computer networks. The various computers, routers and switches in such a network may be modelled as individual queues. The whole system may itself be modelled as a queueing network providing the required service to the messages, packets or cells that need to be carried. Application of queueing theory provides the theoretical framework for the design and study of such networks. The purpose of this book is to support a course on queueing systems at the senior undergraduate or graduate Ievels. Such a course would then provide the theoretical background on which a subsequent course on the performance modeHing and analysis of computer networks may be based.
An Introduction to Queueing Theory
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
An Elementary Introduction to Queueing Systems
Author: Wah Chun Chan
language: en
Publisher: World Scientific Publishing Company
Release Date: 2014
Ch. 1. Modeling of queueing systems. 1.1. Mathematical modeling. 1.2. The Poisson input process. 1.3. Superposition of independent Poisson processes. 1.4. Decomposition of a Poisson process. 1.5. The exponential interarrival time distribution. 1.6. The Markov property or memoryless property. 1.7. Relationship between the Poisson distribution and the exponential distribution. 1.8. The service time distribution. 1.9. The residual service time distribution. 1.10. The birth and death process. 1.11. The outside observer's distribution and the arriving customer's distribution -- ch. 2. Queueing systems with losses. 2.1. Introduction. 2.2. The Erlang loss system. 2.3. The Erlang loss formula -- ch. 3. Queueing systems allowing waiting. 3.1. Introduction. 3.2. The Erlang delay system. 3.3. The distribution function of the waiting time. 3.4. Little's formula -- ch. 4. The Engset loss and delay systems. 4.1. Introduction. 4.2. The Engset loss system. 4.3. The arriving customer's distribution for the Engset loss system. 4.4. The offered load and carried load in the Engset loss system. 4.5. The Engset delay system. 4.6. The waiting time distribution function for the Engset delay system. 4.7. The mean waiting time in the Engset delay system. 4.8. The offered load and carried load in the Engset delay system -- ch. 5. Queueing systems with a single server. 5.1. Introduction. 5.2. The M/M/1 queue. 5.3. The M/G/1 queue and the Pollaczek-Khinchin formula for the mean waiting time. 5.4. The M/G/1 queue with vacations. 5.5. The M/G/1 queue with priority discipline. 5.6. The GI/M/1 queue