On the Discrete-Time Geo/G/1 Queue with Vacations in Random Environment
A discrete-time Geo/G/1 queue with vacations in random environment is analyzed. Using the method of supplementary variable, we give the probability generating function (PGF) of the stationary queue length distribution at arbitrary epoch. The PGF of the stationary sojourn time distribution is also de...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2016-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2016/4029415 |
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| _version_ | 1832560444029534208 |
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| author | Jianjun Li Liwei Liu |
| author_facet | Jianjun Li Liwei Liu |
| author_sort | Jianjun Li |
| collection | DOAJ |
| description | A discrete-time Geo/G/1 queue with vacations in random environment is analyzed. Using the method of supplementary variable, we give the probability generating function (PGF) of the stationary queue length distribution at arbitrary epoch. The PGF of the stationary sojourn time distribution is also derived. And we present the various performance measures such as mean number of customers in the system, mean length of the type-i cycle, and mean time that the system resides in phase 0. In addition, we show that the M/G/1 queue with vacations in random environment can be approximated by its discrete-time counterpart. Finally, we present some special cases of the model and numerical examples. |
| format | Article |
| id | doaj-art-68f07d6ad2684fdf9de5b3200b9bcc61 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-68f07d6ad2684fdf9de5b3200b9bcc612025-02-03T01:27:34ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/40294154029415On the Discrete-Time Geo/G/1 Queue with Vacations in Random EnvironmentJianjun Li0Liwei Liu1School of Science, Nanjing University of Science and Technology, Nanjing 210094, ChinaSchool of Science, Nanjing University of Science and Technology, Nanjing 210094, ChinaA discrete-time Geo/G/1 queue with vacations in random environment is analyzed. Using the method of supplementary variable, we give the probability generating function (PGF) of the stationary queue length distribution at arbitrary epoch. The PGF of the stationary sojourn time distribution is also derived. And we present the various performance measures such as mean number of customers in the system, mean length of the type-i cycle, and mean time that the system resides in phase 0. In addition, we show that the M/G/1 queue with vacations in random environment can be approximated by its discrete-time counterpart. Finally, we present some special cases of the model and numerical examples.http://dx.doi.org/10.1155/2016/4029415 |
| spellingShingle | Jianjun Li Liwei Liu On the Discrete-Time Geo/G/1 Queue with Vacations in Random Environment Discrete Dynamics in Nature and Society |
| title | On the Discrete-Time Geo/G/1 Queue with Vacations in Random Environment |
| title_full | On the Discrete-Time Geo/G/1 Queue with Vacations in Random Environment |
| title_fullStr | On the Discrete-Time Geo/G/1 Queue with Vacations in Random Environment |
| title_full_unstemmed | On the Discrete-Time Geo/G/1 Queue with Vacations in Random Environment |
| title_short | On the Discrete-Time Geo/G/1 Queue with Vacations in Random Environment |
| title_sort | on the discrete time geo g 1 queue with vacations in random environment |
| url | http://dx.doi.org/10.1155/2016/4029415 |
| work_keys_str_mv | AT jianjunli onthediscretetimegeog1queuewithvacationsinrandomenvironment AT liweiliu onthediscretetimegeog1queuewithvacationsinrandomenvironment |