Preemptive Priority Markovian Queue Subject to Server Breakdown with Imperfect Coverage and Working Vacation Interruption
This work considers a preemptive priority queueing system with vacation, where the single server may break down with imperfect coverage. Various combinations of server vacation priority queueing models have been studied by many scholars. A common assumption in these models is that the server will on...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Computation |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2079-3197/11/5/89 |
| _version_ | 1827741719712497664 |
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| author | Tzu-Hsin Liu He-Yao Hsu Jau-Chuan Ke Fu-Min Chang |
| author_facet | Tzu-Hsin Liu He-Yao Hsu Jau-Chuan Ke Fu-Min Chang |
| author_sort | Tzu-Hsin Liu |
| collection | DOAJ |
| description | This work considers a preemptive priority queueing system with vacation, where the single server may break down with imperfect coverage. Various combinations of server vacation priority queueing models have been studied by many scholars. A common assumption in these models is that the server will only resume its normal service rate after the vacation is over. However, such speculation is more limited in real-world situations. Hence, in this study, the vacation will be interrupted if a customer waits for service in the system at the moment of completion of service during vacation. The stationary probability distribution is derived by using the probability generating function approach. We also develop varieties of performance measures and provide a simple numerical example to illustrate these measures. Optimization analysis is finally carried out, including cost optimization and tri-object optimization. |
| first_indexed | 2024-03-11T03:50:06Z |
| format | Article |
| id | doaj.art-c52f729d78284baebaee0ece5c8d9810 |
| institution | Directory Open Access Journal |
| issn | 2079-3197 |
| language | English |
| last_indexed | 2024-03-11T03:50:06Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computation |
| spelling | doaj.art-c52f729d78284baebaee0ece5c8d98102023-11-18T00:58:02ZengMDPI AGComputation2079-31972023-04-011158910.3390/computation11050089Preemptive Priority Markovian Queue Subject to Server Breakdown with Imperfect Coverage and Working Vacation InterruptionTzu-Hsin Liu0He-Yao Hsu1Jau-Chuan Ke2Fu-Min Chang3Department of Finance, Chaoyang University of Technology, 168, Jifeng E. Rd., Wufeng District, Taichung City 41349, TaiwanPh.D. Program of Business Administration in Industrial Development, Department of Business Administration, Chaoyang University of Technology, 168, Jifeng E. Rd., Wufeng District, Taichung City 41349, TaiwanDepartment of Applied Statistics, National Taichung University of Science and Technology, No. 129, Sec. 3, Sanmin Rd., North District, Taichung City 404336, TaiwanDepartment of Finance, Chaoyang University of Technology, 168, Jifeng E. Rd., Wufeng District, Taichung City 41349, TaiwanThis work considers a preemptive priority queueing system with vacation, where the single server may break down with imperfect coverage. Various combinations of server vacation priority queueing models have been studied by many scholars. A common assumption in these models is that the server will only resume its normal service rate after the vacation is over. However, such speculation is more limited in real-world situations. Hence, in this study, the vacation will be interrupted if a customer waits for service in the system at the moment of completion of service during vacation. The stationary probability distribution is derived by using the probability generating function approach. We also develop varieties of performance measures and provide a simple numerical example to illustrate these measures. Optimization analysis is finally carried out, including cost optimization and tri-object optimization.https://www.mdpi.com/2079-3197/11/5/89preemptive priority queueworking vacationvacation interruptionunreliable serverimperfect coverage |
| spellingShingle | Tzu-Hsin Liu He-Yao Hsu Jau-Chuan Ke Fu-Min Chang Preemptive Priority Markovian Queue Subject to Server Breakdown with Imperfect Coverage and Working Vacation Interruption Computation preemptive priority queue working vacation vacation interruption unreliable server imperfect coverage |
| title | Preemptive Priority Markovian Queue Subject to Server Breakdown with Imperfect Coverage and Working Vacation Interruption |
| title_full | Preemptive Priority Markovian Queue Subject to Server Breakdown with Imperfect Coverage and Working Vacation Interruption |
| title_fullStr | Preemptive Priority Markovian Queue Subject to Server Breakdown with Imperfect Coverage and Working Vacation Interruption |
| title_full_unstemmed | Preemptive Priority Markovian Queue Subject to Server Breakdown with Imperfect Coverage and Working Vacation Interruption |
| title_short | Preemptive Priority Markovian Queue Subject to Server Breakdown with Imperfect Coverage and Working Vacation Interruption |
| title_sort | preemptive priority markovian queue subject to server breakdown with imperfect coverage and working vacation interruption |
| topic | preemptive priority queue working vacation vacation interruption unreliable server imperfect coverage |
| url | https://www.mdpi.com/2079-3197/11/5/89 |
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