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| Format: | Recurso digital |
| Language: | English |
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2026
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| Online Access: | https://doi.org/10.5281/zenodo.19248113 |
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| _version_ | 1866901086051237888 |
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| author | M. Seenivasan, N. Siva Sankari |
| author_facet | M. Seenivasan, N. Siva Sankari |
| contents | <p>Abstract:<br>This paper examines an investigation an M/M/1 Queueing System with Balking and Impatient<br>Customers under Differentiated Working Vacations. The Poisson Process is used to determine the<br>arrival, and the services are distributed exponentially. FCFS was used to serve the customer. There are<br>two different kinds of vacations: the first kind begins after a busy duration, and the second kind starts<br>when there are no customers waiting for the server to get back from vacation. The two vacations are<br>exponentially distributed and independent. During the first kind and the second kind of vacations,<br>services are exponentially distributed. Additionally, the impatience of the waiting consumer during the<br>vacation period is taken into consideration. Balking customer is one who decides not to enter the queue<br>after observing its length. Considering the Stochastic Processes {( ( ), ( )): ≥ 0}. This was solved<br>using the matrix geometric method. Some parameters are used in the calculation of performance<br>metrics. Additionally, certain graphical and numerical tables are produced.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19248113 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | An M/M/1 Queueing System with Balking and Impatient Customers under Differentiated Working Vacations M. Seenivasan, N. Siva Sankari Arrival rate, Service rate, first kind and second kind – Two types working vacation, Impatience Customers, Balking, Matrix Geometric Method <p>Abstract:<br>This paper examines an investigation an M/M/1 Queueing System with Balking and Impatient<br>Customers under Differentiated Working Vacations. The Poisson Process is used to determine the<br>arrival, and the services are distributed exponentially. FCFS was used to serve the customer. There are<br>two different kinds of vacations: the first kind begins after a busy duration, and the second kind starts<br>when there are no customers waiting for the server to get back from vacation. The two vacations are<br>exponentially distributed and independent. During the first kind and the second kind of vacations,<br>services are exponentially distributed. Additionally, the impatience of the waiting consumer during the<br>vacation period is taken into consideration. Balking customer is one who decides not to enter the queue<br>after observing its length. Considering the Stochastic Processes {( ( ), ( )): ≥ 0}. This was solved<br>using the matrix geometric method. Some parameters are used in the calculation of performance<br>metrics. Additionally, certain graphical and numerical tables are produced.</p> |
| title | An M/M/1 Queueing System with Balking and Impatient Customers under Differentiated Working Vacations |
| topic | Arrival rate, Service rate, first kind and second kind – Two types working vacation, Impatience Customers, Balking, Matrix Geometric Method |
| url | https://doi.org/10.5281/zenodo.19248113 |