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Analysis of Queueing Networks with Blocking

verfasst von: Simonetta Balsamo, Vittoria de Nitto Personé, Raif Onvural

Verlag: Springer US

Buchreihe : International Series in Operations Research & Management Science

Enthalten in: Professional Book Archive

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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.

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Inhaltsverzeichnis

Frontmatter

Queueing Network Models with Blocking and Applications

Frontmatter

1. Introduction

Abstract

System performance has been a major issue in the design and implementation of computer systems, production systems, communication systems, and flexible manufacturing systems. The success or failure of the design and operation of such systems is judged by the degree to which performance objective are met. Thus, tool and techniques for predicting their performance measures have received great attention in the research and development communities since early 1900s.

Simonetta Balsamo, Vittoria de Nitto Personé, Raif Onvural

2. Queueing Networks with Blocking

Abstract

In this chapter, we introduce queueing networks with finite capacity queues. When limitations are imposed on the queue capacities, a phenomenon called blocking occurs. Simply defined, blocking is forcing a departure from a queue or an arrival to a queue to stop temporarily due to lack of space in the queue. In Section 2.1 we define single class networks. There are different blocking mechanisms introduced in the literature to model different types of flow systems with finite resources. These blocking mechanisms are defined in Section 2.2. The relation between blocking and state dependent routing is introduced in Section 2.3. The extension of results presented in the context of single class networks with finite capacities to multiclass networks with blocking is presented in Section 2.4. Finally, various performance metrics of interest in the analysis of blocking networks are defined in Section 2.5. Bibliographical notes and references are presented in Section 2.6.

Simonetta Balsamo, Vittoria de Nitto Personé, Raif Onvural

3. Application Examples of Queueing Networks with Blocking

Abstract

As discussed in chapter 1, customers in real systems usually require different services provided by different servers. During this process, customers may wait in different queues in front of servers prior to start receiving services. Such complex service systems are often modeled using a network of queueing systems, referred to as a queueing network. The topology of the network represents the flow of customers from one service station to another to meet their service requirements. Hence, a queueing network is a connected directed graph whose nodes represent the service centers. The waiting area in front of a server is represented as a queue. That is, each service station has a queue associated with it. A connection between two servers indicates the one-step moves that customers may make from one service center to another service center. The route that a customer takes through the network may be deterministic or random. Customers may be of different types and may follow different routes through the network.

Simonetta Balsamo, Vittoria de Nitto Personé, Raif Onvural

Analysis of Queueing Networks with Blocking

Frontmatter

4. Exact Analysis of Markovian Networks

Abstract

In this chapter we deal with analytical solutions of a class of networks that can be represented by a continuous-time Markov process.

Simonetta Balsamo, Vittoria de Nitto Personé, Raif Onvural

5. Exact Analysis of Special Networks

Abstract

In this chapter we deal with some special classes of queueing networks with blocking for which efficient solution algorithms can be defined. The exact analysis of Markovian networks based on the Markov process underlying the network defined in Chapter 4 can be dramatically simplified for these particular networks.

Simonetta Balsamo, Vittoria de Nitto Personé, Raif Onvural

6. Approximate and Bound Analysis

Abstract

In this chapter we deal with approximate and bound methods to analyze queueing networks with blocking and to evaluate various performance indices. Section 6.1 introduces the basic ideas of the approximate method proposed in the literature. Sections 6.2 and 6.3 present some approximate solution techniques for closed and open networks with blocking, respectively. Section 6.4 deals with bound approximation methods.

Simonetta Balsamo, Vittoria de Nitto Personé, Raif Onvural

Properties of Networks with Blocking

Frontmatter

7. Equivalence, Insensitivity and Monotonicity Properties

Abstract

Equivalence, insensitivity and monotonicity are important properties of queueing network models that can be used in system performance comparison and evaluation. Insensitivity and equivalence properties provide the basis for comparing the performance of system models with different parameters and with different blocking mechanisms. These results can be applied, for example, to study the impact of the blocking type on system performance, by considering a given set of performance indices and network parameters. In particular, equivalences allow us to define more efficient algorithms to evaluate queueing networks with blocking and to extend the class of models that can be analyzed through analytical methods. Insensitivity properties lead to the identification of the factor that affect system performance and in certain cases it allow a generalization of solution methods. Some important consequence of these properties is that solution methods and algorithms already defined for a certain class of networks could be extended to other classes of networks with different blocking types and/or network parameters. For example, equivalence between networks with and without blocking immediately leads to the extension of efficient computational solution algorithms defined for BCMP networks such as MVA and Convolution algorithm to queueing networks with finite capacity queues. Monotonicity provides insights in the system behavior represented by the queueing network models.

Simonetta Balsamo, Vittoria de Nitto Personé, Raif Onvural

8. Buffer Allocation in Queueing Networks with Finite Capacities

Abstract

In this chapter we study the buffer allocation problem in queueing networks with finite capacities. We present some solution techniques proposed in the literature for queueing networks with arbitrary topology.

Simonetta Balsamo, Vittoria de Nitto Personé, Raif Onvural

Backmatter

Titel: Analysis of Queueing Networks with Blocking
verfasst von: Simonetta Balsamo
Vittoria de Nitto Personé
Raif Onvural
Copyright-Jahr: 2001
Verlag: Springer US
Electronic ISBN: 978-1-4757-3345-7
Print ISBN: 978-1-4419-5014-7
DOI: https://doi.org/10.1007/978-1-4757-3345-7