Sharp and simple bounds for the Erlang delay and loss formulae.
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| Title: | Sharp and simple bounds for the Erlang delay and loss formulae. |
|---|---|
| Authors: | Harel, Arie1 Arie.Harel@baruch.cuny.edu |
| Source: | Queueing Systems. Feb2010, Vol. 64 Issue 2, p119-143. 25p. 7 Charts, 3 Graphs. |
| Subjects: | ERLANG (Computer program language), Programming languages, Convex functions, Real variables, Probability theory |
| Abstract: | We prove some simple and sharp lower and upper bounds for the Erlang delay and loss formulae and for the number of servers that invert the Erlang delay and loss formulae. We also suggest simple and sharp approximations for the number of servers that invert the Erlang delay and loss formulae. We illustrate the importance of these bounds by using them to establish convexity proofs. We show that the probability that the M/ M/ s queue is empty is a decreasing and convex function of the traffic intensity. We also give a very short proof to show that the Erlang delay formula is convex in the traffic intensity when the number of servers is held constant. The complete proof of this classical result has never been published. We also give a very short proof to show that the Erlang delay formula is a convex function of the (positive integer) number of servers. One of our results is then used to get a sharp bound to the Flow Assignment Problem. [ABSTRACT FROM AUTHOR] |
| Copyright of Queueing Systems is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 47734895 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Sharp and simple bounds for the Erlang delay and loss formulae. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Harel%2C+Arie%22">Harel, Arie</searchLink><relatesTo>1</relatesTo><i> Arie.Harel@baruch.cuny.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Queueing+Systems%22">Queueing Systems</searchLink>. Feb2010, Vol. 64 Issue 2, p119-143. 25p. 7 Charts, 3 Graphs. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22ERLANG+%28Computer+program+language%29%22">ERLANG (Computer program language)</searchLink><br /><searchLink fieldCode="DE" term="%22Programming+languages%22">Programming languages</searchLink><br /><searchLink fieldCode="DE" term="%22Convex+functions%22">Convex functions</searchLink><br /><searchLink fieldCode="DE" term="%22Real+variables%22">Real variables</searchLink><br /><searchLink fieldCode="DE" term="%22Probability+theory%22">Probability theory</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We prove some simple and sharp lower and upper bounds for the Erlang delay and loss formulae and for the number of servers that invert the Erlang delay and loss formulae. We also suggest simple and sharp approximations for the number of servers that invert the Erlang delay and loss formulae. We illustrate the importance of these bounds by using them to establish convexity proofs. We show that the probability that the M/ M/ s queue is empty is a decreasing and convex function of the traffic intensity. We also give a very short proof to show that the Erlang delay formula is convex in the traffic intensity when the number of servers is held constant. The complete proof of this classical result has never been published. We also give a very short proof to show that the Erlang delay formula is a convex function of the (positive integer) number of servers. One of our results is then used to get a sharp bound to the Flow Assignment Problem. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Queueing Systems is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s11134-009-9152-7 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 25 StartPage: 119 Subjects: – SubjectFull: ERLANG (Computer program language) Type: general – SubjectFull: Programming languages Type: general – SubjectFull: Convex functions Type: general – SubjectFull: Real variables Type: general – SubjectFull: Probability theory Type: general Titles: – TitleFull: Sharp and simple bounds for the Erlang delay and loss formulae. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Harel, Arie IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 02 Text: Feb2010 Type: published Y: 2010 Identifiers: – Type: issn-print Value: 02570130 Numbering: – Type: volume Value: 64 – Type: issue Value: 2 Titles: – TitleFull: Queueing Systems Type: main |
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