Analysis of an M/M/c Queueing System with Impatient Customers and Synchronous Vacations
We consider an M/M/c queueing system with impatient customers and a synchronous vacation policy, where customer impatience is due to the servers’ vacation. Whenever a system becomes empty, all the servers take a vacation. If the system is still empty, when the vacation ends, all the servers take ano...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/893094 |
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| _version_ | 1832561873018421248 |
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| author | Dequan Yue Wuyi Yue Guoxi Zhao |
| author_facet | Dequan Yue Wuyi Yue Guoxi Zhao |
| author_sort | Dequan Yue |
| collection | DOAJ |
| description | We consider an M/M/c queueing system with impatient customers and a synchronous vacation policy, where customer impatience is due to the servers’ vacation. Whenever a system becomes empty, all the servers take a vacation. If the system is still empty, when the vacation ends, all the servers take another vacation; otherwise, they return to serve the queue. We develop the balance equations for the steady-state probabilities and solve the equations by using the probability generating function method. We obtain explicit expressions of some important performance measures by means of the two indexes. Based on these, we obtain some results about limiting behavior for some performance measures. We derive closed-form expressions of some important performance measures for two special cases. Finally, some numerical results are also presented. |
| format | Article |
| id | doaj-art-c8e0d46319e1456aa8d6c44776ee840c |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-c8e0d46319e1456aa8d6c44776ee840c2025-02-03T01:24:06ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/893094893094Analysis of an M/M/c Queueing System with Impatient Customers and Synchronous VacationsDequan Yue0Wuyi Yue1Guoxi Zhao2College of Science, Yanshan University, Qinhuangdao 066004, ChinaDepartment of Intelligence and Informatics, Konan University, Kobe 658-8501, JapanSchool of Economics and Management, Yanshan University, Qinhuangdao 066004, ChinaWe consider an M/M/c queueing system with impatient customers and a synchronous vacation policy, where customer impatience is due to the servers’ vacation. Whenever a system becomes empty, all the servers take a vacation. If the system is still empty, when the vacation ends, all the servers take another vacation; otherwise, they return to serve the queue. We develop the balance equations for the steady-state probabilities and solve the equations by using the probability generating function method. We obtain explicit expressions of some important performance measures by means of the two indexes. Based on these, we obtain some results about limiting behavior for some performance measures. We derive closed-form expressions of some important performance measures for two special cases. Finally, some numerical results are also presented.http://dx.doi.org/10.1155/2014/893094 |
| spellingShingle | Dequan Yue Wuyi Yue Guoxi Zhao Analysis of an M/M/c Queueing System with Impatient Customers and Synchronous Vacations Journal of Applied Mathematics |
| title | Analysis of an M/M/c Queueing System with Impatient Customers and Synchronous Vacations |
| title_full | Analysis of an M/M/c Queueing System with Impatient Customers and Synchronous Vacations |
| title_fullStr | Analysis of an M/M/c Queueing System with Impatient Customers and Synchronous Vacations |
| title_full_unstemmed | Analysis of an M/M/c Queueing System with Impatient Customers and Synchronous Vacations |
| title_short | Analysis of an M/M/c Queueing System with Impatient Customers and Synchronous Vacations |
| title_sort | analysis of an m m c queueing system with impatient customers and synchronous vacations |
| url | http://dx.doi.org/10.1155/2014/893094 |
| work_keys_str_mv | AT dequanyue analysisofanmmcqueueingsystemwithimpatientcustomersandsynchronousvacations AT wuyiyue analysisofanmmcqueueingsystemwithimpatientcustomersandsynchronousvacations AT guoxizhao analysisofanmmcqueueingsystemwithimpatientcustomersandsynchronousvacations |