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Delayed and Network Queues by Dimitar P. Mishev, Aliakbar Montazer Haghighi

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Chapter 6Networks of Queues with Delay

6.1 Introduction to Networks of Queues

As the modern world has become highly technological with the advent of the Internet and wireless communication, as well as advancements in manufacturing and production systems, public transportation, logistics, and health care, performance evaluation of such systems is best possible by modeling them as a network of queues, in which many theoretical ideas have been developed during the past six decades. A network of queues is applied to model a real-world system when a set of resources is shared by some components of the system. In other words, a network of queues is a flow system, which indicates that a task flows (transfers or moves) through two or more finite- or infinite-capacity stations to receive a complete service. Several examples of networks of queues appear in our day-to-day lives and perhaps we do not notice them. Assembly of an automobile in a car manufactory is a simple example. The digital computer developed in the early 1960s highlighted more applications of queueing theory. Examples are in a sequence of application in the field of information processing and queueing networks of various types. Applications demanded expansion of analytical and numerical methodologies of various queueing models. The solution of Riemann–Hilbert problems is an example. In many cases, however, exact analysis of networks is impossible and, thus, it is necessary to introduce assumptions to offer solution for ...

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