M/M/1 Retrial Queue with Working Vacation Interruption and Feedback under N-Policy
We consider an M/M/1 retrial queue with working vacations, vacation interruption, Bernoulli feedback, and N-policy simultaneously. During the working vacation period, customers can be served at a lower rate. Using the matrix-analytic method, we get the necessary and sufficient condition for the syst...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/414739 |
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| _version_ | 1832566243868016640 |
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| author | Li Tao Liyuan Zhang Shan Gao |
| author_facet | Li Tao Liyuan Zhang Shan Gao |
| author_sort | Li Tao |
| collection | DOAJ |
| description | We consider an M/M/1 retrial queue with working vacations, vacation interruption, Bernoulli feedback, and N-policy simultaneously. During the working vacation period, customers can be served at a lower rate. Using the matrix-analytic method, we get the necessary and sufficient condition for the system to be stable. Furthermore, the stationary probability distribution and some performance measures are also derived. Moreover, we prove the conditional stochastic decomposition for the queue length in the orbit. Finally, we present some numerical examples and use the parabolic method to search the optimum value of service rate in working vacation period. |
| format | Article |
| id | doaj-art-f916c95bb9894f60bb808da17bbdf69c |
| 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-f916c95bb9894f60bb808da17bbdf69c2025-02-03T01:04:49ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/414739414739M/M/1 Retrial Queue with Working Vacation Interruption and Feedback under N-PolicyLi Tao0Liyuan Zhang1Shan Gao2School of Science, Shandong University of Technology, Zibo 255049, ChinaSchool of Business, Shandong University of Technology, Zibo 255049, ChinaDepartment of Mathematics, Beijing Jiaotong University, Beijing 100044, ChinaWe consider an M/M/1 retrial queue with working vacations, vacation interruption, Bernoulli feedback, and N-policy simultaneously. During the working vacation period, customers can be served at a lower rate. Using the matrix-analytic method, we get the necessary and sufficient condition for the system to be stable. Furthermore, the stationary probability distribution and some performance measures are also derived. Moreover, we prove the conditional stochastic decomposition for the queue length in the orbit. Finally, we present some numerical examples and use the parabolic method to search the optimum value of service rate in working vacation period.http://dx.doi.org/10.1155/2014/414739 |
| spellingShingle | Li Tao Liyuan Zhang Shan Gao M/M/1 Retrial Queue with Working Vacation Interruption and Feedback under N-Policy Journal of Applied Mathematics |
| title | M/M/1 Retrial Queue with Working Vacation Interruption and Feedback under N-Policy |
| title_full | M/M/1 Retrial Queue with Working Vacation Interruption and Feedback under N-Policy |
| title_fullStr | M/M/1 Retrial Queue with Working Vacation Interruption and Feedback under N-Policy |
| title_full_unstemmed | M/M/1 Retrial Queue with Working Vacation Interruption and Feedback under N-Policy |
| title_short | M/M/1 Retrial Queue with Working Vacation Interruption and Feedback under N-Policy |
| title_sort | m m 1 retrial queue with working vacation interruption and feedback under n policy |
| url | http://dx.doi.org/10.1155/2014/414739 |
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