Extreme values in closed networks.
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| Title: | Extreme values in closed networks. |
|---|---|
| Authors: | Jelenković, Predrag1 (AUTHOR) predrag@ee.columbia.edu, Momčilović, Petar2 (AUTHOR) petar@tamu.edu |
| Source: | Queueing Systems. Mar2026, Vol. 110 Issue 1, p1-24. 24p. |
| Subjects: | Queueing networks, Queuing theory, Large deviations (Mathematics), Stochastic models |
| Abstract: | For a widely used hub-and-spoke closed product-form network consisting of an infinite-server node and several single-server queues, we characterize the maximum queue-length distribution in various operational regimes by leveraging a novel probabilistic representation of the joint queue-length distribution and scaling where the number of customers grows. In these limiting regimes, we derive explicit characterizations of the maximum that are asymptotically equivalent to the maximum of independent random variables with the same geometric marginal distribution as queue lengths. In particular, when both the number of customers and queues grow, the parameters of the marginal distribution depend on the global characteristics of the network and are explicitly computed from a quadratic equation that arises from the corresponding large-deviation rate functions. Explicit computation of global characteristics of product-form distribution beyond the marginals, e.g., the maximum, appears novel, and our methodology may apply to other global measures of interest. [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 | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 189910467 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Extreme values in closed networks. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Jelenković%2C+Predrag%22">Jelenković, Predrag</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> predrag@ee.columbia.edu</i><br /><searchLink fieldCode="AR" term="%22Momčilović%2C+Petar%22">Momčilović, Petar</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> petar@tamu.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Queueing+Systems%22">Queueing Systems</searchLink>. Mar2026, Vol. 110 Issue 1, p1-24. 24p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Queueing+networks%22">Queueing networks</searchLink><br /><searchLink fieldCode="DE" term="%22Queuing+theory%22">Queuing theory</searchLink><br /><searchLink fieldCode="DE" term="%22Large+deviations+%28Mathematics%29%22">Large deviations (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+models%22">Stochastic models</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: For a widely used hub-and-spoke closed product-form network consisting of an infinite-server node and several single-server queues, we characterize the maximum queue-length distribution in various operational regimes by leveraging a novel probabilistic representation of the joint queue-length distribution and scaling where the number of customers grows. In these limiting regimes, we derive explicit characterizations of the maximum that are asymptotically equivalent to the maximum of independent random variables with the same geometric marginal distribution as queue lengths. In particular, when both the number of customers and queues grow, the parameters of the marginal distribution depend on the global characteristics of the network and are explicitly computed from a quadratic equation that arises from the corresponding large-deviation rate functions. Explicit computation of global characteristics of product-form distribution beyond the marginals, e.g., the maximum, appears novel, and our methodology may apply to other global measures of interest. [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/s11134-025-09962-1 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 24 StartPage: 1 Subjects: – SubjectFull: Queueing networks Type: general – SubjectFull: Queuing theory Type: general – SubjectFull: Large deviations (Mathematics) Type: general – SubjectFull: Stochastic models Type: general Titles: – TitleFull: Extreme values in closed networks. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Jelenković, Predrag – PersonEntity: Name: NameFull: Momčilović, Petar IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 02570130 Numbering: – Type: volume Value: 110 – Type: issue Value: 1 Titles: – TitleFull: Queueing Systems Type: main |
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