Analysis of a Single Server Queue in a Multi-phase Random Environment with Working Vacations and Customers' Impatience
In this paper, we analyze an M / M / 1 queueing system under both single and multiple working vacation policies, multiphase random environment, waiting server, balking and reneging. When the system is in operative phase j = 1, 2, . . ., K, customers are served one by one. Whenever the system becomes...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wrocław University of Science and Technology
2022-01-01
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| Series: | Operations Research and Decisions |
| Online Access: | https://ord.pwr.edu.pl/assets/papers_archive/ord2022vol32no2_2.pdf |
| _version_ | 1818179799512776704 |
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| author | Amina Angelika Bouchentouf Abdelhak Guendouzi Meriem Houalef Shakir Majid |
| author_facet | Amina Angelika Bouchentouf Abdelhak Guendouzi Meriem Houalef Shakir Majid |
| author_sort | Amina Angelika Bouchentouf |
| collection | DOAJ |
| description | In this paper, we analyze an M / M / 1 queueing system under both single and multiple working vacation policies, multiphase random environment, waiting server, balking and reneging. When the system is in operative phase j = 1, 2, . . ., K, customers are served one by one. Whenever the system becomes empty, the server waits a random amount of time before taking a vacation, causing the system to move to working vacation phase 0 at which new arrivals are served at a lower rate. Using the probability generating function method, we obtain the distribution for the steady-state probabilities of the system. Then, we derive important performance measures of the queueing system. Finally, some numerical examples are illustrated to show the impact of system parameters on performance measures of the queueing system. (original abstract) |
| first_indexed | 2024-12-11T21:09:37Z |
| format | Article |
| id | doaj.art-2e53d70fe8be4097b6d23f771cb35aa7 |
| institution | Directory Open Access Journal |
| issn | 2081-8858 2391-6060 |
| language | English |
| last_indexed | 2024-12-11T21:09:37Z |
| publishDate | 2022-01-01 |
| publisher | Wrocław University of Science and Technology |
| record_format | Article |
| series | Operations Research and Decisions |
| spelling | doaj.art-2e53d70fe8be4097b6d23f771cb35aa72022-12-22T00:50:46ZengWrocław University of Science and TechnologyOperations Research and Decisions2081-88582391-60602022-01-01vol. 32no. 21633171649368Analysis of a Single Server Queue in a Multi-phase Random Environment with Working Vacations and Customers' ImpatienceAmina Angelika Bouchentouf0Abdelhak Guendouzi1Meriem Houalef2Shakir Majid3Djillali Liabes University of Sidi Bel Abbes, AlgeriaDoctor Tahar Moulay University of Saida, AlgeriaUniversity of Sidi Bel Abbes, Ecole Supérieure En Sciences Appliquées, AlgeriaUniversity of Ladakh, IndiaIn this paper, we analyze an M / M / 1 queueing system under both single and multiple working vacation policies, multiphase random environment, waiting server, balking and reneging. When the system is in operative phase j = 1, 2, . . ., K, customers are served one by one. Whenever the system becomes empty, the server waits a random amount of time before taking a vacation, causing the system to move to working vacation phase 0 at which new arrivals are served at a lower rate. Using the probability generating function method, we obtain the distribution for the steady-state probabilities of the system. Then, we derive important performance measures of the queueing system. Finally, some numerical examples are illustrated to show the impact of system parameters on performance measures of the queueing system. (original abstract)https://ord.pwr.edu.pl/assets/papers_archive/ord2022vol32no2_2.pdf |
| spellingShingle | Amina Angelika Bouchentouf Abdelhak Guendouzi Meriem Houalef Shakir Majid Analysis of a Single Server Queue in a Multi-phase Random Environment with Working Vacations and Customers' Impatience Operations Research and Decisions |
| title | Analysis of a Single Server Queue in a Multi-phase Random Environment with Working Vacations and Customers' Impatience |
| title_full | Analysis of a Single Server Queue in a Multi-phase Random Environment with Working Vacations and Customers' Impatience |
| title_fullStr | Analysis of a Single Server Queue in a Multi-phase Random Environment with Working Vacations and Customers' Impatience |
| title_full_unstemmed | Analysis of a Single Server Queue in a Multi-phase Random Environment with Working Vacations and Customers' Impatience |
| title_short | Analysis of a Single Server Queue in a Multi-phase Random Environment with Working Vacations and Customers' Impatience |
| title_sort | analysis of a single server queue in a multi phase random environment with working vacations and customers impatience |
| url | https://ord.pwr.edu.pl/assets/papers_archive/ord2022vol32no2_2.pdf |
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