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A Tutorial on Queuing and Trunking with Applications to CommunicationsNetworks of Queues

A Tutorial on Queuing and Trunking with Applications to Communications: Networks of Queues [In previous chapters, we only considered individual queues in isolation. That is, we considered systems that consist of an arrival process, a single queue with a particular queuing discipline, and one or more servers. Modern data networks, however, consist of many queues that interact in complex ways. While many of these interactions defy analysis, in this chapter we introduce a model of a network of queues in which, after being served in one queue, customers may join another queue. The key result for this model is known as Jackson’s Theorem. However, we first present Burke’s Theorem, which provides some of the intuition behind Jackson’s Theorem, and then derive a simple version of Jackson’s Theorem. Next, we state some extensions of Jackson’s Theorem and the BCMP Theorem, which can also be viewed as a further extension of Jackson’s Theorem. It is important to carefully consider the statement of Jackson’s Theorem and the well-prescribed limits of its application. To this end, we carefully discuss “Kleinrock’s Assumption” throughout the chapter.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Tutorial on Queuing and Trunking with Applications to CommunicationsNetworks of Queues

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Publisher
Springer International Publishing
Copyright
© Springer Nature Switzerland AG 2012
ISBN
978-3-031-00551-0
Pages
65 –88
DOI
10.1007/978-3-031-01679-0_5
Publisher site
See Chapter on Publisher Site

Abstract

[In previous chapters, we only considered individual queues in isolation. That is, we considered systems that consist of an arrival process, a single queue with a particular queuing discipline, and one or more servers. Modern data networks, however, consist of many queues that interact in complex ways. While many of these interactions defy analysis, in this chapter we introduce a model of a network of queues in which, after being served in one queue, customers may join another queue. The key result for this model is known as Jackson’s Theorem. However, we first present Burke’s Theorem, which provides some of the intuition behind Jackson’s Theorem, and then derive a simple version of Jackson’s Theorem. Next, we state some extensions of Jackson’s Theorem and the BCMP Theorem, which can also be viewed as a further extension of Jackson’s Theorem. It is important to carefully consider the statement of Jackson’s Theorem and the well-prescribed limits of its application. To this end, we carefully discuss “Kleinrock’s Assumption” throughout the chapter.]

Published: Jan 1, 2012

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