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2002 | Buch

An Introduction to Queueing Systems

verfasst von: Sanjay K. Bose

Verlag: Springer US

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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Introduction
Abstract
Queueing systems are models of systems providing service. Such a model may represent any system where jobs or customers arrive looking for service of some kind and depart after such service has been provided. We can model systems of this type as either single queues or a system of interconnected queues forming a queueing network. These are the kinds of systems that are dealt with here and our objective is to describe the analytical techniques that may be applied to study their performance. An example of a simple queueing model has been shown in Figure 1.1 . Such a model may be used to represent a typical queueing situation where jobs arrive, wait if all servers are busy, eventually get served by an available server and leave after the required service is obtained.
Sanjay K. Bose
Chapter 2. Basic Queueing Theory
Fundamentals of Analyzing Single Queues
Abstract
As shown in the simple example of the previous chapter, the basic approach to the analysis of simple queueing models would begin by defining an appropriate system state for the queue. The analysis of the queue would then essentially be the study of the way this system state would evolve. The transient solution would be the solution obtained for this system state, given the various input parameters, and the initial conditions with which the queue starts operation. In this text, we are however interested in the performance analysis of the queue once equilibrium conditions have been reached. Analyses of some basic queues where the arrivals come from a Poisson process and the service times are exponentially distributed will be considered in this chapter. Before we consider such analysis, it would be useful to review some of the basics of the theory of Markov Chains and Birth-Death Processes. These are considered next. Further details on this may be found in [Fel65], [Kle75] or [Wol89].
Sanjay K. Bose
Chapter 3. Analysis of the M/G/1 Queue in Equilibrium
Performance Analysis Using Residual Life and Imbedded Markov Chain Approaches
Abstract
In the previous chapter, we were primarily concerned with queues where the service times were exponentially distributed. Queues with nonexponential service times were not really considered, except in a limited fashion in Section 2.9 while describing the Method of Stages. In this chapter, we consider the detailed analysis of single server queues with infinite buffers where the service times can have any general distribution. The arrival process is still assumed to be Poisson in nature.
Sanjay K. Bose
Chapter 4. Advanced Queueing Theory
Vacations, Bulk Arrivals and Priorities in a M/G/1 Queue and the Geo/G/1 Queue
Abstract
Exact analytical methods are available for studying open and closed queueing networks with product-form solutions. Examples of such networks and the methods for obtaining exact analytical results for them were considered in Chapter 5. These results are applicable only if the queues satisfy all the restrictive conditions that are required on their respective arrival and service processes. These conditions may be quite restrictive and may not allow us to use these techniques under more general conditions.
Sanjay K. Bose
Chapter 5. Fundamentals of Queueing Networks
Open and Closed Networks with Product-Form Solutions
Abstract
In this chapter, we consider service models, where the service to be provided may be represented as a sequence of services provided by several servers. Such a service scenario may be conveniently represented as Networks of Queues as shown in Figures 5.1 and 5.2. In these models, customers/jobs which finish service at a queue may either move on for the next stage of service to another queue (or even re-enter the earlier queue) or may leave the network altogether.
Sanjay K. Bose
Chapter 6. Advanced Queueing Networks
Approximation Techniques and Algorithms for Open and Closed Queueing Networks
Abstract
In the previous chapter, we were primarily concerned with queues where the service times were exponentially distributed. Queues with nonexponential service times were not really considered, except in a limited fashion in Section 2.9 while describing the Method of Stages. In this chapter, we consider the detailed analysis of single server queues with infinite buffers where the service times can have any general distribution. The arrival process is still assumed to be Poisson in nature.
Sanjay K. Bose
Chapter 7. Simulation Techniques for Queues and Queueing Networks
Basic Principles for the Design of Queueing Simulators
Abstract
Exact analytical methods are available for studying open and closed queueing networks with product-form solutions. Examples of such networks and the methods for obtaining exact analytical results for them were considered in Chapter 5. These results are applicable only if the queues satisfy all the restrictive conditions that are required on their respective arrival and service processes. These conditions may be quite restrictive and may not allow us to use these techniques under more general conditions.
Sanjay K. Bose
Backmatter
Metadaten
Titel
An Introduction to Queueing Systems
verfasst von
Sanjay K. Bose
Copyright-Jahr
2002
Verlag
Springer US
Electronic ISBN
978-1-4615-0001-8
Print ISBN
978-1-4613-4880-1
DOI
https://doi.org/10.1007/978-1-4615-0001-8