A matrix geometric solution of a multi-server queue with waiting servers and customers’ impatience under variant working vacation and vacation interruption
This paper deals with a M/M/c queueing system with waiting servers, balking, reneging, and K-variant working vacations subjected to Bernoulli schedule vacation interruption. Whenever the system is emptied, the servers wait for a while before synchronously going on vacation during which services are...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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University of Belgrade
2023-01-01
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| Series: | Yugoslav Journal of Operations Research |
| Subjects: | |
| Online Access: | https://doiserbia.nb.rs/img/doi/0354-0243/2023/0354-02432300001Z.pdf |
| _version_ | 1797680692590542848 |
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| author | Ziad Ines Laxmi Vijaya P. Bhavani Girija E. Bouchentouf Amina Angelika Majid Shakir |
| author_facet | Ziad Ines Laxmi Vijaya P. Bhavani Girija E. Bouchentouf Amina Angelika Majid Shakir |
| author_sort | Ziad Ines |
| collection | DOAJ |
| description | This paper deals with a M/M/c queueing system with waiting servers, balking, reneging, and K-variant working vacations subjected to Bernoulli schedule vacation interruption. Whenever the system is emptied, the servers wait for a while before synchronously going on vacation during which services are offered with a lower rate. We obtain the steady-state probabilities of the system using the matrix-geometric method. In addition, we derive important performance measures of the queueing model. Moreover, we construct a cost model and apply a direct search method to get the optimum service rates during both working vacation and regular working periods at lowest cost. Finally, numerical results are provided. |
| first_indexed | 2024-03-11T23:33:44Z |
| format | Article |
| id | doaj.art-65331b8f6a88434792cca1780a76b7b5 |
| institution | Directory Open Access Journal |
| issn | 0354-0243 1820-743X |
| language | English |
| last_indexed | 2024-03-11T23:33:44Z |
| publishDate | 2023-01-01 |
| publisher | University of Belgrade |
| record_format | Article |
| series | Yugoslav Journal of Operations Research |
| spelling | doaj.art-65331b8f6a88434792cca1780a76b7b52023-09-20T06:02:48ZengUniversity of BelgradeYugoslav Journal of Operations Research0354-02431820-743X2023-01-0133338940710.2298/YJOR220315001Z0354-02432300001ZA matrix geometric solution of a multi-server queue with waiting servers and customers’ impatience under variant working vacation and vacation interruptionZiad Ines0Laxmi Vijaya P.1Bhavani Girija E.2Bouchentouf Amina Angelika3Majid Shakir4Laboratory of Mathematics of Sidi Bel Abbes, Kasdi Merbah University, Ouargla, AlgeriaDepartment of Applied mathematics, Andhra University, Visakhapatnam, IndiaDepartment of Applied mathematics, Andhra University, Visakhapatnam, IndiaMathematics Laboratory, Djillali Liabes University of Sidi Bel Abbes, Algeria + Laboratory of Stochastic Models, Statistic and Applications, University of Saida-Dr. Moulay Tahar, AlgeriaDepartment of Mathematics, University of Ladakh, IndiaThis paper deals with a M/M/c queueing system with waiting servers, balking, reneging, and K-variant working vacations subjected to Bernoulli schedule vacation interruption. Whenever the system is emptied, the servers wait for a while before synchronously going on vacation during which services are offered with a lower rate. We obtain the steady-state probabilities of the system using the matrix-geometric method. In addition, we derive important performance measures of the queueing model. Moreover, we construct a cost model and apply a direct search method to get the optimum service rates during both working vacation and regular working periods at lowest cost. Finally, numerical results are provided.https://doiserbia.nb.rs/img/doi/0354-0243/2023/0354-02432300001Z.pdfqueueing modelsmatrix analytic methodperformance measurescost modeloptimisation |
| spellingShingle | Ziad Ines Laxmi Vijaya P. Bhavani Girija E. Bouchentouf Amina Angelika Majid Shakir A matrix geometric solution of a multi-server queue with waiting servers and customers’ impatience under variant working vacation and vacation interruption Yugoslav Journal of Operations Research queueing models matrix analytic method performance measures cost model optimisation |
| title | A matrix geometric solution of a multi-server queue with waiting servers and customers’ impatience under variant working vacation and vacation interruption |
| title_full | A matrix geometric solution of a multi-server queue with waiting servers and customers’ impatience under variant working vacation and vacation interruption |
| title_fullStr | A matrix geometric solution of a multi-server queue with waiting servers and customers’ impatience under variant working vacation and vacation interruption |
| title_full_unstemmed | A matrix geometric solution of a multi-server queue with waiting servers and customers’ impatience under variant working vacation and vacation interruption |
| title_short | A matrix geometric solution of a multi-server queue with waiting servers and customers’ impatience under variant working vacation and vacation interruption |
| title_sort | matrix geometric solution of a multi server queue with waiting servers and customers impatience under variant working vacation and vacation interruption |
| topic | queueing models matrix analytic method performance measures cost model optimisation |
| url | https://doiserbia.nb.rs/img/doi/0354-0243/2023/0354-02432300001Z.pdf |
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