Optimal Scheduling of Critically Loaded Multiclass GI/M/n+M Queues in an Alternating Renewal Environment.
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| Title: | Optimal Scheduling of Critically Loaded Multiclass GI/M/n+M Queues in an Alternating Renewal Environment. |
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| Authors: | Arapostathis, Ari1 (AUTHOR), Pang, Guodong2 (AUTHOR) gup3@psu.edu, Zheng, Yi2 (AUTHOR) |
| Source: | Applied Mathematics & Optimization. Oct2021, Vol. 84 Issue 2, p1857-1901. 45p. |
| Subjects: | Diffusion processes, Poisson processes, Jump processes, Scheduling, Diffusion control |
| Abstract: | In this paper, we study optimal control problems for multiclass G I / M / n + M queues in an alternating renewal (up–down) random environment in the Halfin–Whitt regime. Assuming that the downtimes are asymptotically negligible and only the service processes are affected, we show that the limits of the diffusion-scaled state processes under non-anticipative, preemptive, work-conserving scheduling policies, are controlled jump diffusions driven by a compound Poisson jump process. We establish the asymptotic optimality of the infinite-horizon discounted and long-run average (ergodic) problems for the queueing dynamics. Since the process counting the number of customers in each class is not Markov, the usual martingale arguments for convergence of mean empirical measures cannot be applied. We surmount this obstacle by demonstrating the convergence of the generators of an augmented Markovian model which incorporates the age processes of the renewal interarrival times and downtimes. We also establish long-run average moment bounds of the diffusion-scaled queueing processes under some (modified) priority scheduling policies. This is accomplished via Foster–Lyapunov equations for the augmented Markovian model. [ABSTRACT FROM AUTHOR] |
| Copyright of Applied Mathematics & Optimization 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 |
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| Items | – Name: Title Label: Title Group: Ti Data: Optimal Scheduling of Critically Loaded Multiclass GI/M/n+M Queues in an Alternating Renewal Environment. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Arapostathis%2C+Ari%22">Arapostathis, Ari</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Pang%2C+Guodong%22">Pang, Guodong</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> gup3@psu.edu</i><br /><searchLink fieldCode="AR" term="%22Zheng%2C+Yi%22">Zheng, Yi</searchLink><relatesTo>2</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Applied+Mathematics+%26+Optimization%22">Applied Mathematics & Optimization</searchLink>. Oct2021, Vol. 84 Issue 2, p1857-1901. 45p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Diffusion+processes%22">Diffusion processes</searchLink><br /><searchLink fieldCode="DE" term="%22Poisson+processes%22">Poisson processes</searchLink><br /><searchLink fieldCode="DE" term="%22Jump+processes%22">Jump processes</searchLink><br /><searchLink fieldCode="DE" term="%22Scheduling%22">Scheduling</searchLink><br /><searchLink fieldCode="DE" term="%22Diffusion+control%22">Diffusion control</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this paper, we study optimal control problems for multiclass G I / M / n + M queues in an alternating renewal (up–down) random environment in the Halfin–Whitt regime. Assuming that the downtimes are asymptotically negligible and only the service processes are affected, we show that the limits of the diffusion-scaled state processes under non-anticipative, preemptive, work-conserving scheduling policies, are controlled jump diffusions driven by a compound Poisson jump process. We establish the asymptotic optimality of the infinite-horizon discounted and long-run average (ergodic) problems for the queueing dynamics. Since the process counting the number of customers in each class is not Markov, the usual martingale arguments for convergence of mean empirical measures cannot be applied. We surmount this obstacle by demonstrating the convergence of the generators of an augmented Markovian model which incorporates the age processes of the renewal interarrival times and downtimes. We also establish long-run average moment bounds of the diffusion-scaled queueing processes under some (modified) priority scheduling policies. This is accomplished via Foster–Lyapunov equations for the augmented Markovian model. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Applied Mathematics & Optimization 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/s00245-020-09698-9 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 45 StartPage: 1857 Subjects: – SubjectFull: Diffusion processes Type: general – SubjectFull: Poisson processes Type: general – SubjectFull: Jump processes Type: general – SubjectFull: Scheduling Type: general – SubjectFull: Diffusion control Type: general Titles: – TitleFull: Optimal Scheduling of Critically Loaded Multiclass GI/M/n+M Queues in an Alternating Renewal Environment. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Arapostathis, Ari – PersonEntity: Name: NameFull: Pang, Guodong – PersonEntity: Name: NameFull: Zheng, Yi IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: Oct2021 Type: published Y: 2021 Identifiers: – Type: issn-print Value: 00954616 Numbering: – Type: volume Value: 84 – Type: issue Value: 2 Titles: – TitleFull: Applied Mathematics & Optimization Type: main |
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