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 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
Analysis of Queueing Systems
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.