Waiting Time Control Chart for M/G/1 Retrial Queue
Retrial queues are used extensively to model many practical problems in service systems, call centers, data centers, and computer network systems. The average waiting time is the main observable characteristic of the retrial queues. Long queues may cause negative impacts such as waste of manpower an...
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| Language: | English |
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MDPI AG
2024-09-01
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| Series: | Computation |
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| Online Access: | https://www.mdpi.com/2079-3197/12/9/191 |
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| author | Yih-Bey Lin Tzu-Hsin Liu Yu-Cheng Tsai Fu-Min Chang |
| author_facet | Yih-Bey Lin Tzu-Hsin Liu Yu-Cheng Tsai Fu-Min Chang |
| author_sort | Yih-Bey Lin |
| collection | DOAJ |
| description | Retrial queues are used extensively to model many practical problems in service systems, call centers, data centers, and computer network systems. The average waiting time is the main observable characteristic of the retrial queues. Long queues may cause negative impacts such as waste of manpower and unnecessary crowding leading to suffocation, and can even cause trouble for customers and institutions. Applying control chart technology can help managers analyze customers’ waiting times to improve the effective performance of service and attention. This paper pioneers the developing and detailed study of a waiting time control chart for a retrial queue with general service times. Two waiting time control charts, the Shewhart control chart, and a control chart using the weighted variance method are constructed in this paper. We present three cases for the Shewhart control chart in which the service time obeys special distributions, such as exponential, Erlang, and hyper-exponential distributions. The case of an exponentially distributed service time is also presented for the control chart using the weighted variance method. Based on the numerical simulations conducted herein, managers can better monitor and analyze the customers’ waiting times for their service systems and take preventive measures. |
| format | Article |
| id | doaj-art-a7a261cc89314ecdb9d24c2aa6da3b08 |
| institution | OA Journals |
| issn | 2079-3197 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computation |
| spelling | doaj-art-a7a261cc89314ecdb9d24c2aa6da3b082025-08-20T01:55:22ZengMDPI AGComputation2079-31972024-09-0112919110.3390/computation12090191Waiting Time Control Chart for M/G/1 Retrial QueueYih-Bey Lin0Tzu-Hsin Liu1Yu-Cheng Tsai2Fu-Min Chang3Department of Finance, Chaoyang University of Technology, Taichung City 41349, TaiwanDepartment of Finance, Chaoyang University of Technology, Taichung City 41349, TaiwanPh.D. Program of Business Administration in Industrial Development, Department of Business Administration, Chaoyang University of Technology, Taichung City 41349, TaiwanDepartment of Finance, Chaoyang University of Technology, Taichung City 41349, TaiwanRetrial queues are used extensively to model many practical problems in service systems, call centers, data centers, and computer network systems. The average waiting time is the main observable characteristic of the retrial queues. Long queues may cause negative impacts such as waste of manpower and unnecessary crowding leading to suffocation, and can even cause trouble for customers and institutions. Applying control chart technology can help managers analyze customers’ waiting times to improve the effective performance of service and attention. This paper pioneers the developing and detailed study of a waiting time control chart for a retrial queue with general service times. Two waiting time control charts, the Shewhart control chart, and a control chart using the weighted variance method are constructed in this paper. We present three cases for the Shewhart control chart in which the service time obeys special distributions, such as exponential, Erlang, and hyper-exponential distributions. The case of an exponentially distributed service time is also presented for the control chart using the weighted variance method. Based on the numerical simulations conducted herein, managers can better monitor and analyze the customers’ waiting times for their service systems and take preventive measures.https://www.mdpi.com/2079-3197/12/9/191waiting timecontrol chartretrial queuegeneral service times |
| spellingShingle | Yih-Bey Lin Tzu-Hsin Liu Yu-Cheng Tsai Fu-Min Chang Waiting Time Control Chart for M/G/1 Retrial Queue Computation waiting time control chart retrial queue general service times |
| title | Waiting Time Control Chart for M/G/1 Retrial Queue |
| title_full | Waiting Time Control Chart for M/G/1 Retrial Queue |
| title_fullStr | Waiting Time Control Chart for M/G/1 Retrial Queue |
| title_full_unstemmed | Waiting Time Control Chart for M/G/1 Retrial Queue |
| title_short | Waiting Time Control Chart for M/G/1 Retrial Queue |
| title_sort | waiting time control chart for m g 1 retrial queue |
| topic | waiting time control chart retrial queue general service times |
| url | https://www.mdpi.com/2079-3197/12/9/191 |
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