Analytically Simple and Computationally Efficient Results for the GIX/Geo/c Queues
A simple solution to determine the distributions of queue-lengths at different observation epochs for the model GIX/Geo/c is presented. In the past, various discrete-time queueing models, particularly the multiserver bulk-arrival queues, have been solved using complicated methods that lead to incomp...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2019/6480139 |
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| author | Mohan L. Chaudhry James J. Kim Abhijit D. Banik |
| author_facet | Mohan L. Chaudhry James J. Kim Abhijit D. Banik |
| author_sort | Mohan L. Chaudhry |
| collection | DOAJ |
| description | A simple solution to determine the distributions of queue-lengths at different observation epochs for the model GIX/Geo/c is presented. In the past, various discrete-time queueing models, particularly the multiserver bulk-arrival queues, have been solved using complicated methods that lead to incomplete results. The purpose of this paper is to use the roots method to solve the model GIX/Geo/c that leads to a result that is analytically elegant and computationally efficient. This method works well even for the case when the inter-batch-arrival times follow heavy-tailed distributions. The roots of the underlying characteristic equation form the basis for all distributions of queue-lengths at different time epochs. |
| format | Article |
| id | doaj-art-f957a2389ab14cd98e4e84e3fdf18211 |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-f957a2389ab14cd98e4e84e3fdf182112025-02-03T01:32:15ZengWileyJournal of Probability and Statistics1687-952X1687-95382019-01-01201910.1155/2019/64801396480139Analytically Simple and Computationally Efficient Results for the GIX/Geo/c QueuesMohan L. Chaudhry0James J. Kim1Abhijit D. Banik2Department of Mathematics and Computer Science, Royal Military College of Canada, P.O. Box 17000, STN Forces, Kingston Ont, K7K 7B4, CanadaRoyal Canadian Air Force (RCAF), 86 Moreuil Wood Blvd, Petawawa Ont, K8H 1A5, CanadaSchool of Basic Sciences, Indian Institute of Technology Bhubaneswar, Permanent Campus Argul, Jatni, Khurda-725 050, Odisha, IndiaA simple solution to determine the distributions of queue-lengths at different observation epochs for the model GIX/Geo/c is presented. In the past, various discrete-time queueing models, particularly the multiserver bulk-arrival queues, have been solved using complicated methods that lead to incomplete results. The purpose of this paper is to use the roots method to solve the model GIX/Geo/c that leads to a result that is analytically elegant and computationally efficient. This method works well even for the case when the inter-batch-arrival times follow heavy-tailed distributions. The roots of the underlying characteristic equation form the basis for all distributions of queue-lengths at different time epochs.http://dx.doi.org/10.1155/2019/6480139 |
| spellingShingle | Mohan L. Chaudhry James J. Kim Abhijit D. Banik Analytically Simple and Computationally Efficient Results for the GIX/Geo/c Queues Journal of Probability and Statistics |
| title | Analytically Simple and Computationally Efficient Results for the GIX/Geo/c Queues |
| title_full | Analytically Simple and Computationally Efficient Results for the GIX/Geo/c Queues |
| title_fullStr | Analytically Simple and Computationally Efficient Results for the GIX/Geo/c Queues |
| title_full_unstemmed | Analytically Simple and Computationally Efficient Results for the GIX/Geo/c Queues |
| title_short | Analytically Simple and Computationally Efficient Results for the GIX/Geo/c Queues |
| title_sort | analytically simple and computationally efficient results for the gix geo c queues |
| url | http://dx.doi.org/10.1155/2019/6480139 |
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