Problem Overview $$\varOmega {\bigl (G(V,E)\bigr )}$$

Smith, J. MacGregor

doi:10.1007/978-3-319-78822-7_2

J. MacGregor Smith⁵

Part of the book series: Springer Series in Operations Research and Financial Engineering ((ORFE))

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Overview

Finite queueing models and blocking systems and their traffic problems originated with A. K. Erlang and the Danish telephone system in Copenhagen, Denmark, around 1909. In this chapter, we present an introduction to Stochastic Processes together with the notation used in queueing and congestion problems. We will trace the evolution of queue and queueing network models and their optimization for traffic congestion and performance. We also articulate the framework as depicted in Figure 2.1 and outline of topics around which the models in the Volume will be developed.

The best thing to do is create a lagom (Swedish for “just the right amount”) number of processes.

—A. K. Erlang

So yes, much of my work has had a theoretical bent, but it has almost always been driven by a strong link with engineering requirements or by observations from nature.

—Erol Gelenbe

(1) “What is the question?;” and (2) “if you know enough mathematics, you will know when not to use it.”

—G.F. Newell

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Notes

1.
John Little was Philip Morse’s Ph.D. student at MIT.
2.
Erlang was reported to have jumped down the manholes in Copenhagen to help fix the telephone network.

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Department of Mechanical & Industrial Engineering, University of Massachusetts, Amherst, MA, USA
J. MacGregor Smith

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Smith, J.M. (2018). Problem Overview $\varOmega {\bigl (G(V,E)\bigr )}$. In: Introduction to Queueing Networks. Springer Series in Operations Research and Financial Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-78822-7_2

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DOI: https://doi.org/10.1007/978-3-319-78822-7_2
Published: 29 August 2018
Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-78822-7
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