Academic Journal
A New Finite Approximation Method for Evaluating Steady-State Performance of a Continuous-State Markov Chain with an Application to Queues with Customer Abandonment.
| Τίτλος: | A New Finite Approximation Method for Evaluating Steady-State Performance of a Continuous-State Markov Chain with an Application to Queues with Customer Abandonment. |
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| Συγγραφείς: | Li, Shukai1 (AUTHOR) shukaili2024@u.northwestern.edu, Mehrotra, Sanjay1 (AUTHOR) mehrotra@iems.northwestern.edu |
| Πηγή: | Mathematics of Operations Research (INFORMS). May2026, Vol. 51 Issue 2, p1626-1658. 33p. |
| Θεματικοί όροι: | *Markov processes, *Queuing theory, *Approximation theory, Stochastic systems, Ergodic theory, Approximation error |
| Περίληψη: | This paper develops a new method for computing the stationary distribution and steady-state performance measures of stochastic systems that can be described as a continuous-state Markov chain supported on R. The balance equations are solved by constructing a proxy Markov chain with finite states. We show the consistency of an approximate solution and provide deterministic nonasymptotic error bounds under the supremum norm. Our method is near optimal among all approximation methods using discrete distributions. We apply the developed method to compute the stationary distribution of virtual waiting time and associated performance measures for a GI/GI/1+GI queue in which the large market assumption may not hold and the patience time may follow any bounded distribution. Numerical experiments show that our method outperforms steady-state simulation, phase-type approximation, diffusion approximation, and fluid approximation, particularly for medium or small arrival intensities in overloaded or balanced loaded queues. Funding: S. Li and S. Mehrotra were supported by the National Science Foundation grant CMMI-1763035. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematics of Operations Research (INFORMS) is the property of INFORMS: Institute for Operations Research & the Management Sciences 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.) | |
| Βάση Δεδομένων: | Business Source Index |
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| Items | – Name: Title Label: Title Group: Ti Data: A New Finite Approximation Method for Evaluating Steady-State Performance of a Continuous-State Markov Chain with an Application to Queues with Customer Abandonment. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Li%2C+Shukai%22">Li, Shukai</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> shukaili2024@u.northwestern.edu</i><br /><searchLink fieldCode="AR" term="%22Mehrotra%2C+Sanjay%22">Mehrotra, Sanjay</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mehrotra@iems.northwestern.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematics+of+Operations+Research+%28INFORMS%29%22">Mathematics of Operations Research (INFORMS)</searchLink>. May2026, Vol. 51 Issue 2, p1626-1658. 33p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Markov+processes%22">Markov processes</searchLink><br />*<searchLink fieldCode="DE" term="%22Queuing+theory%22">Queuing theory</searchLink><br />*<searchLink fieldCode="DE" term="%22Approximation+theory%22">Approximation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+systems%22">Stochastic systems</searchLink><br /><searchLink fieldCode="DE" term="%22Ergodic+theory%22">Ergodic theory</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+error%22">Approximation error</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper develops a new method for computing the stationary distribution and steady-state performance measures of stochastic systems that can be described as a continuous-state Markov chain supported on R. The balance equations are solved by constructing a proxy Markov chain with finite states. We show the consistency of an approximate solution and provide deterministic nonasymptotic error bounds under the supremum norm. Our method is near optimal among all approximation methods using discrete distributions. We apply the developed method to compute the stationary distribution of virtual waiting time and associated performance measures for a GI/GI/1+GI queue in which the large market assumption may not hold and the patience time may follow any bounded distribution. Numerical experiments show that our method outperforms steady-state simulation, phase-type approximation, diffusion approximation, and fluid approximation, particularly for medium or small arrival intensities in overloaded or balanced loaded queues. Funding: S. Li and S. Mehrotra were supported by the National Science Foundation grant CMMI-1763035. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematics of Operations Research (INFORMS) is the property of INFORMS: Institute for Operations Research & the Management Sciences 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: 10.1287/moor.2024.0468 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 33 StartPage: 1626 Subjects: – SubjectFull: Markov processes Type: general – SubjectFull: Queuing theory Type: general – SubjectFull: Approximation theory Type: general – SubjectFull: Stochastic systems Type: general – SubjectFull: Ergodic theory Type: general – SubjectFull: Approximation error Type: general Titles: – TitleFull: A New Finite Approximation Method for Evaluating Steady-State Performance of a Continuous-State Markov Chain with an Application to Queues with Customer Abandonment. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Li, Shukai – PersonEntity: Name: NameFull: Mehrotra, Sanjay IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 0364765X Numbering: – Type: volume Value: 51 – Type: issue Value: 2 Titles: – TitleFull: Mathematics of Operations Research (INFORMS) Type: main |
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