Performance Analysis of Two Different Types of Waiting Queues with Working Vacations
This work examines a new class of working vacation queueing models that contain regular (original) and retrial waiting queues. Upon arrival, a customer either starts their service instantly if the server is available, or they join the regular queue if the server is occupied. When it is empty, the se...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/5829171 |
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| author | M. Sundararaman D. Narasimhan P. Rajadurai |
| author_facet | M. Sundararaman D. Narasimhan P. Rajadurai |
| author_sort | M. Sundararaman |
| collection | DOAJ |
| description | This work examines a new class of working vacation queueing models that contain regular (original) and retrial waiting queues. Upon arrival, a customer either starts their service instantly if the server is available, or they join the regular queue if the server is occupied. When it is empty, the server departs the system to take a working vacation (WV). The server provides services more slowly during the WV period. New customers join the retry queue (orbit), if the server is on vacation. The supplementary variable technique (SVT) examines the steady-state probability generating functions (PGFs) of queue size for different server states. Several system performances are numerically displayed, including system state probabilities, mean busy cycles, mean queue lengths, sensitivity analysis, and cost optimization values. The motivation for this model in a pandemic situation is to analyze new healthcare service systems and reflect the characteristics of patient services. |
| format | Article |
| id | doaj-art-051c3d4ca8ba43e995b40759d9c4e912 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-051c3d4ca8ba43e995b40759d9c4e9122025-02-03T06:14:52ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/5829171Performance Analysis of Two Different Types of Waiting Queues with Working VacationsM. Sundararaman0D. Narasimhan1P. Rajadurai2Department of MathematicsDepartment of MathematicsDepartment of MathematicsThis work examines a new class of working vacation queueing models that contain regular (original) and retrial waiting queues. Upon arrival, a customer either starts their service instantly if the server is available, or they join the regular queue if the server is occupied. When it is empty, the server departs the system to take a working vacation (WV). The server provides services more slowly during the WV period. New customers join the retry queue (orbit), if the server is on vacation. The supplementary variable technique (SVT) examines the steady-state probability generating functions (PGFs) of queue size for different server states. Several system performances are numerically displayed, including system state probabilities, mean busy cycles, mean queue lengths, sensitivity analysis, and cost optimization values. The motivation for this model in a pandemic situation is to analyze new healthcare service systems and reflect the characteristics of patient services.http://dx.doi.org/10.1155/2024/5829171 |
| spellingShingle | M. Sundararaman D. Narasimhan P. Rajadurai Performance Analysis of Two Different Types of Waiting Queues with Working Vacations Journal of Mathematics |
| title | Performance Analysis of Two Different Types of Waiting Queues with Working Vacations |
| title_full | Performance Analysis of Two Different Types of Waiting Queues with Working Vacations |
| title_fullStr | Performance Analysis of Two Different Types of Waiting Queues with Working Vacations |
| title_full_unstemmed | Performance Analysis of Two Different Types of Waiting Queues with Working Vacations |
| title_short | Performance Analysis of Two Different Types of Waiting Queues with Working Vacations |
| title_sort | performance analysis of two different types of waiting queues with working vacations |
| url | http://dx.doi.org/10.1155/2024/5829171 |
| work_keys_str_mv | AT msundararaman performanceanalysisoftwodifferenttypesofwaitingqueueswithworkingvacations AT dnarasimhan performanceanalysisoftwodifferenttypesofwaitingqueueswithworkingvacations AT prajadurai performanceanalysisoftwodifferenttypesofwaitingqueueswithworkingvacations |