Scipediacontent: Scipediacontent moved page Draft Content 588639849 to Berg et al 2007a

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Scipediacontent moved page Draft Content 588639849 to Berg et al 2007a

Scipediacontent: Created page with " == Abstract == c-congestion period of an m/m/ ∞-queue is a period during which the number of customers in the system is continuously above level c. Interesting quantities..."

2021-02-16T09:04:13Z

Created page with " == Abstract == c-congestion period of an m/m/ ∞-queue is a period during which the number of customers in the system is continuously above level c. Interesting quantities..."

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== Abstract ==

c-congestion period of an m/m/ ∞-queue is a period during which the number of customers in the system is continuously above level c. Interesting quantities related to a c-congestion period are, besides its duration Dc, the total area Ac above c, and the number of arrived customers Nc. In the literature Laplace transforms for these quantities have been derived, as well as explicit formulae for their means. Explicit expressions for higher moments and covariances (between Dc, Nc and Ac), however, have not been found so far. This paper presents recursive relations through which all moments and covariances can be obtained. Up to a starting condition, we explicitly solve these equations; for instance, we write E Dc2 explicitly in terms of E D02. We then find formulae for these starting conditions (which directly relate to the busy period in the m/m/ ∞ queue). Finally, a c-intercongestion period is defined as the period during which the number of customers is continuously below level c. Also for this situation a recursive scheme allows us to explicitly compute higher moments and covariances. Additionally we present the Laplace transform of a so-called intercongestion triple of the three performance quantities. It is also shown that expressions for the quantities of a c-intercongestion period can be used in an approximation for the c-congestion period. This is especially useful as the expressions for the c-intercongestion period are numerically more stable than those for the c-congestion period. © 2007 Elsevier Ltd. All rights reserved.

== Original document ==

The different versions of the original document can be found in:

* [http://dx.doi.org/10.1016/j.peva.2006.12.001 http://dx.doi.org/10.1016/j.peva.2006.12.001]

* [http://resolver.tudelft.nl/uuid:c0eba3ac-024a-426e-8e70-481cad1e9e18 http://resolver.tudelft.nl/uuid:c0eba3ac-024a-426e-8e70-481cad1e9e18]

* [https://research.utwente.nl/en/publications/analysis-of-congestion-periods-of-an-mmqueue(e9dbf46f-3139-4249-9a9b-d2df465b602e).html https://research.utwente.nl/en/publications/analysis-of-congestion-periods-of-an-mmqueue(e9dbf46f-3139-4249-9a9b-d2df465b602e).html]

* [https://api.elsevier.com/content/article/PII:S0166531606001246?httpAccept=text/xml https://api.elsevier.com/content/article/PII:S0166531606001246?httpAccept=text/xml],
: [https://api.elsevier.com/content/article/PII:S0166531606001246?httpAccept=text/plain https://api.elsevier.com/content/article/PII:S0166531606001246?httpAccept=text/plain],
: [http://dx.doi.org/10.1016/j.peva.2006.12.001 http://dx.doi.org/10.1016/j.peva.2006.12.001] under the license https://www.elsevier.com/tdm/userlicense/1.0/

* [https://research.utwente.nl/en/publications/analysis-of-congestion-periods-of-an-mm-queue https://research.utwente.nl/en/publications/analysis-of-congestion-periods-of-an-mm-queue],
: [https://www.sciencedirect.com/science/article/pii/S0166531606001246 https://www.sciencedirect.com/science/article/pii/S0166531606001246],
: [https://repository.tudelft.nl/view/tno/uuid:c0eba3ac-024a-426e-8e70-481cad1e9e18 https://repository.tudelft.nl/view/tno/uuid:c0eba3ac-024a-426e-8e70-481cad1e9e18],
: [https://www.narcis.nl/publication/RecordID/oai%3Acwi.nl%3A14173 https://www.narcis.nl/publication/RecordID/oai%3Acwi.nl%3A14173],
: [http://core.ac.uk/display/11481934 http://core.ac.uk/display/11481934],
: [https://dblp.uni-trier.de/db/journals/pe/pe64.html#RoijersMB07 https://dblp.uni-trier.de/db/journals/pe/pe64.html#RoijersMB07],
: [https://ir.cwi.nl/pub/10841 https://ir.cwi.nl/pub/10841],
: [https://doi.org/10.1016/j.peva.2006.12.001 https://doi.org/10.1016/j.peva.2006.12.001],
: [https://academic.microsoft.com/#/detail/2114260442 https://academic.microsoft.com/#/detail/2114260442]

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Berg et al 2007a - Revision history

Scipediacontent: Scipediacontent moved page Draft Content 588639849 to Berg et al 2007a

Scipediacontent: Created page with " == Abstract == c-congestion period of an m/m/ ∞-queue is a period during which the number of customers in the system is continuously above level c. Interesting quantities..."