On joint distributions of general bulk service Poisson queue with infinite buffer and group optional service.
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| Title: | On joint distributions of general bulk service Poisson queue with infinite buffer and group optional service. |
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| Authors: | Verma, Kunal1 (AUTHOR) anuradha.mat@iitbhu.ac.in, Banerjee, Anuradha1 (AUTHOR) anuradha.mat@iitbhu.ac.in, Maurya, Amita1 (AUTHOR), Lata, Priti1 (AUTHOR) |
| Source: | RAIRO: Operations Research (2804-7303). 2026, Vol. 60 Issue 1, p383-405. 23p. |
| Subjects: | Poisson processes, Queuing theory |
| Abstract: | This paper investigates a batch-service queueing model where a single-server operates in two service stages. Clients arrive at the system according to the Poisson process. The server first provides the First Essential Service (FES) in batches, with batch sizes constrained between a lower limit a and an upper limit b. On completion of FES, the same server may offer a Second Optional Service (SOS), where some or all clients from the previous batch may participate, again in batches limited between 1 and b, based on a certain probability. If, after completing the SOS, the number of clients in the queue is less than a, the server remains idle until the queue length reaches a; otherwise, it proceeds to the next FES batch. Service times for both FES and SOS follow exponential distributions. The system assumes an infinite-buffer, allowing unrestricted waiting space for incoming clients. Such a queueing structure can model real-world systems like public transportation or communication networks. Using the probability generating function (PGF) approach, we derive steady-state joint distributions of the number of clients in the queue and those being served during both FES and SOS. Key performance metrics and numerical results are provided to support further research. The paper concludes with a healthcare-associated cost-minimization problem through service rates optimization using metaheuristic PSO technique. [ABSTRACT FROM AUTHOR] |
| Copyright of RAIRO: Operations Research (2804-7303) is the property of EDP 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.) | |
| Database: | Engineering Source |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 192633511 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: On joint distributions of general bulk service Poisson queue with infinite buffer and group optional service. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Verma%2C+Kunal%22">Verma, Kunal</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> anuradha.mat@iitbhu.ac.in</i><br /><searchLink fieldCode="AR" term="%22Banerjee%2C+Anuradha%22">Banerjee, Anuradha</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> anuradha.mat@iitbhu.ac.in</i><br /><searchLink fieldCode="AR" term="%22Maurya%2C+Amita%22">Maurya, Amita</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Lata%2C+Priti%22">Lata, Priti</searchLink><relatesTo>1</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22RAIRO%3A+Operations+Research+%282804-7303%29%22">RAIRO: Operations Research (2804-7303)</searchLink>. 2026, Vol. 60 Issue 1, p383-405. 23p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Poisson+processes%22">Poisson processes</searchLink><br /><searchLink fieldCode="DE" term="%22Queuing+theory%22">Queuing theory</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper investigates a batch-service queueing model where a single-server operates in two service stages. Clients arrive at the system according to the Poisson process. The server first provides the First Essential Service (FES) in batches, with batch sizes constrained between a lower limit a and an upper limit b. On completion of FES, the same server may offer a Second Optional Service (SOS), where some or all clients from the previous batch may participate, again in batches limited between 1 and b, based on a certain probability. If, after completing the SOS, the number of clients in the queue is less than a, the server remains idle until the queue length reaches a; otherwise, it proceeds to the next FES batch. Service times for both FES and SOS follow exponential distributions. The system assumes an infinite-buffer, allowing unrestricted waiting space for incoming clients. Such a queueing structure can model real-world systems like public transportation or communication networks. Using the probability generating function (PGF) approach, we derive steady-state joint distributions of the number of clients in the queue and those being served during both FES and SOS. Key performance metrics and numerical results are provided to support further research. The paper concludes with a healthcare-associated cost-minimization problem through service rates optimization using metaheuristic PSO technique. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of RAIRO: Operations Research (2804-7303) is the property of EDP 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.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=192633511 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1051/ro/2026003 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 23 StartPage: 383 Subjects: – SubjectFull: Poisson processes Type: general – SubjectFull: Queuing theory Type: general Titles: – TitleFull: On joint distributions of general bulk service Poisson queue with infinite buffer and group optional service. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Verma, Kunal – PersonEntity: Name: NameFull: Banerjee, Anuradha – PersonEntity: Name: NameFull: Maurya, Amita – PersonEntity: Name: NameFull: Lata, Priti IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: 2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 28047303 Numbering: – Type: volume Value: 60 – Type: issue Value: 1 Titles: – TitleFull: RAIRO: Operations Research (2804-7303) Type: main |
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