Multi-Server Two-Way Communication Retrial Queue Subject to Disaster and Synchronous Working Vacation
This research analyzes a multi-server retrial queue with two types of calls: working vacation and working breakdown. The incoming call may enter the retrial queue and attempt to seize a server after a random delay if all the servers are unavailable upon arrival. In its idle time, the server makes ou...
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MDPI AG
2025-01-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/18/1/24 |
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| author | Tzu-Hsin Liu He-Yao Hsu Fu-Min Chang |
| author_facet | Tzu-Hsin Liu He-Yao Hsu Fu-Min Chang |
| author_sort | Tzu-Hsin Liu |
| collection | DOAJ |
| description | This research analyzes a multi-server retrial queue with two types of calls: working vacation and working breakdown. The incoming call may enter the retrial queue and attempt to seize a server after a random delay if all the servers are unavailable upon arrival. In its idle time, the server makes outgoing calls. All the servers take a synchronous working vacation when the system empties after regular service. The system may fail at any time due to disasters, forcing all the calls within the service area to leave the system and causing all the main servers to fail. When the main servers fail, the repair process begins immediately. The standby servers serve arriving customers at a lower level of service during the working breakdown or working vacation. For this model, we derive an explicit expression for the stationary distribution with the help of the quasi-birth-and-death process and the matrix geometric method. Further, the formulas of various system performance indices are developed. An application example is given and several numerical experiments are performed to verify the analytical results. We also perform the comparative analysis of retrial queues with/without two-way communication and two-way communication retrial queues with/without disasters. The results reveal that the proper consideration of outgoing calls to the server can reduce the average time spent in the buffer. Furthermore, a more reliable server reduces the server idle rate. |
| format | Article |
| id | doaj-art-a79872ed76c44ca9a37a3b20e85bac4f |
| institution | Kabale University |
| issn | 1999-4893 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj-art-a79872ed76c44ca9a37a3b20e85bac4f2025-01-24T13:17:31ZengMDPI AGAlgorithms1999-48932025-01-011812410.3390/a18010024Multi-Server Two-Way Communication Retrial Queue Subject to Disaster and Synchronous Working VacationTzu-Hsin Liu0He-Yao Hsu1Fu-Min Chang2Department of Finance, Chaoyang University of Technology, 168, Jifeng East Road, Wufeng District, Taichung City 41349, TaiwanPh.D. Program of Business Administration in Industrial Development, Department of Business Administration, Chaoyang University of Technology, 168, Jifeng East Road, Wufeng District, Taichung City 41349, TaiwanDepartment of Finance, Chaoyang University of Technology, 168, Jifeng East Road, Wufeng District, Taichung City 41349, TaiwanThis research analyzes a multi-server retrial queue with two types of calls: working vacation and working breakdown. The incoming call may enter the retrial queue and attempt to seize a server after a random delay if all the servers are unavailable upon arrival. In its idle time, the server makes outgoing calls. All the servers take a synchronous working vacation when the system empties after regular service. The system may fail at any time due to disasters, forcing all the calls within the service area to leave the system and causing all the main servers to fail. When the main servers fail, the repair process begins immediately. The standby servers serve arriving customers at a lower level of service during the working breakdown or working vacation. For this model, we derive an explicit expression for the stationary distribution with the help of the quasi-birth-and-death process and the matrix geometric method. Further, the formulas of various system performance indices are developed. An application example is given and several numerical experiments are performed to verify the analytical results. We also perform the comparative analysis of retrial queues with/without two-way communication and two-way communication retrial queues with/without disasters. The results reveal that the proper consideration of outgoing calls to the server can reduce the average time spent in the buffer. Furthermore, a more reliable server reduces the server idle rate.https://www.mdpi.com/1999-4893/18/1/24disastermulti-server retrial queuerepairsynchronous working vacationtwo-way communication |
| spellingShingle | Tzu-Hsin Liu He-Yao Hsu Fu-Min Chang Multi-Server Two-Way Communication Retrial Queue Subject to Disaster and Synchronous Working Vacation Algorithms disaster multi-server retrial queue repair synchronous working vacation two-way communication |
| title | Multi-Server Two-Way Communication Retrial Queue Subject to Disaster and Synchronous Working Vacation |
| title_full | Multi-Server Two-Way Communication Retrial Queue Subject to Disaster and Synchronous Working Vacation |
| title_fullStr | Multi-Server Two-Way Communication Retrial Queue Subject to Disaster and Synchronous Working Vacation |
| title_full_unstemmed | Multi-Server Two-Way Communication Retrial Queue Subject to Disaster and Synchronous Working Vacation |
| title_short | Multi-Server Two-Way Communication Retrial Queue Subject to Disaster and Synchronous Working Vacation |
| title_sort | multi server two way communication retrial queue subject to disaster and synchronous working vacation |
| topic | disaster multi-server retrial queue repair synchronous working vacation two-way communication |
| url | https://www.mdpi.com/1999-4893/18/1/24 |
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