Spectral solution for a delay system with hyper-Erlang distributions
The article is devoted to the construction of a mathematical model for delaying claims in a queue in the form of a queuing system described by two flows with the laws of distribution of time intervals shifted to the right by hyper-Erlang distributions of the second order. In the queuing theory, the...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Povolzhskiy State University of Telecommunications & Informatics
2022-12-01
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| Series: | Физика волновых процессов и радиотехнические системы |
| Subjects: | |
| Online Access: | https://journals.ssau.ru/pwp/article/viewFile/10910/9301 |
| _version_ | 1797382564779917312 |
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| author | Veniamin N. Tarasov Nadezhda F. Bakhareva |
| author_facet | Veniamin N. Tarasov Nadezhda F. Bakhareva |
| author_sort | Veniamin N. Tarasov |
| collection | DOAJ |
| description | The article is devoted to the construction of a mathematical model for delaying claims in a queue in the form of a queuing system described by two flows with the laws of distribution of time intervals shifted to the right by hyper-Erlang distributions of the second order. In the queuing theory, the study of systems G/G/1 is relevant because there is no solution in the final form for the general case. Therefore, various partial distribution laws are used as an arbitrary distribution law G in the study of such systems. In this case, the use of the shifted hyper-Erlang distribution law provides the coefficient of variation of the input flow arrival intervals and service time over the entire interval (0, ). To solve the problem, we used the method of spectral solution of the Lindley integral equation, which plays an important role in the queuing theory. This method made it possible to obtain a solution for the average delay of requests in the queue for the considered system in a closed form. As is known, the remaining characteristics of the queuing system are derivatives of the average delay of requests in the queue. |
| first_indexed | 2024-03-08T21:07:16Z |
| format | Article |
| id | doaj.art-42074b8406fd41b1a8f7de7734226574 |
| institution | Directory Open Access Journal |
| issn | 1810-3189 2782-294X |
| language | English |
| last_indexed | 2024-03-08T21:07:16Z |
| publishDate | 2022-12-01 |
| publisher | Povolzhskiy State University of Telecommunications & Informatics |
| record_format | Article |
| series | Физика волновых процессов и радиотехнические системы |
| spelling | doaj.art-42074b8406fd41b1a8f7de77342265742023-12-22T10:31:41ZengPovolzhskiy State University of Telecommunications & InformaticsФизика волновых процессов и радиотехнические системы1810-31892782-294X2022-12-01254333810.18469/1810-3189.2022.25.4.33-388760Spectral solution for a delay system with hyper-Erlang distributionsVeniamin N. Tarasov0Nadezhda F. Bakhareva1Povolzhskiy State University of Telecommunications and InformaticsPovolzhskiy State University of Telecommunications and InformaticsThe article is devoted to the construction of a mathematical model for delaying claims in a queue in the form of a queuing system described by two flows with the laws of distribution of time intervals shifted to the right by hyper-Erlang distributions of the second order. In the queuing theory, the study of systems G/G/1 is relevant because there is no solution in the final form for the general case. Therefore, various partial distribution laws are used as an arbitrary distribution law G in the study of such systems. In this case, the use of the shifted hyper-Erlang distribution law provides the coefficient of variation of the input flow arrival intervals and service time over the entire interval (0, ). To solve the problem, we used the method of spectral solution of the Lindley integral equation, which plays an important role in the queuing theory. This method made it possible to obtain a solution for the average delay of requests in the queue for the considered system in a closed form. As is known, the remaining characteristics of the queuing system are derivatives of the average delay of requests in the queue.https://journals.ssau.ru/pwp/article/viewFile/10910/9301shifted hyper-erlang distributionlindley integral equationspectral decomposition methodlaplace transform |
| spellingShingle | Veniamin N. Tarasov Nadezhda F. Bakhareva Spectral solution for a delay system with hyper-Erlang distributions Физика волновых процессов и радиотехнические системы shifted hyper-erlang distribution lindley integral equation spectral decomposition method laplace transform |
| title | Spectral solution for a delay system with hyper-Erlang distributions |
| title_full | Spectral solution for a delay system with hyper-Erlang distributions |
| title_fullStr | Spectral solution for a delay system with hyper-Erlang distributions |
| title_full_unstemmed | Spectral solution for a delay system with hyper-Erlang distributions |
| title_short | Spectral solution for a delay system with hyper-Erlang distributions |
| title_sort | spectral solution for a delay system with hyper erlang distributions |
| topic | shifted hyper-erlang distribution lindley integral equation spectral decomposition method laplace transform |
| url | https://journals.ssau.ru/pwp/article/viewFile/10910/9301 |
| work_keys_str_mv | AT veniaminntarasov spectralsolutionforadelaysystemwithhypererlangdistributions AT nadezhdafbakhareva spectralsolutionforadelaysystemwithhypererlangdistributions |