Determination of the Spectral Index of Ergodicity of a Birth-and-Death Process
We obtain a new explicit relation for the calculation of the spectral index of ergodicity of a birth-and-death process with continuous time. The calculation of the index is reduced to the solution of an optimization problem of nonlinear programming that contains the infinitesimal matrix of the proce...
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| Datum: | 2000 |
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| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
2000
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4488 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510615772069888 |
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| author | Kartashov, M. V. Карташов, Н. В. Карташов, Н. В. |
| author_facet | Kartashov, M. V. Карташов, Н. В. Карташов, Н. В. |
| author_sort | Kartashov, M. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:30:08Z |
| description | We obtain a new explicit relation for the calculation of the spectral index of ergodicity of a birth-and-death process with continuous time. The calculation of the index is reduced to the solution of an optimization problem of nonlinear programming that contains the infinitesimal matrix of the process. As an example, we use the proposed method for finding the exact values of the indices of exponential ergodicity for certain Markov queuing systems. |
| first_indexed | 2026-03-24T02:59:49Z |
| format | Article |
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| id | umjimathkievua-article-4488 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:59:49Z |
| publishDate | 2000 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/21/a611bc5af731f44347399494b3962a21.pdf |
| spelling | umjimathkievua-article-44882020-03-18T20:30:08Z Determination of the Spectral Index of Ergodicity of a Birth-and-Death Process Вычисление спектрального показателя эргодичности процесса рождения и гибели Kartashov, M. V. Карташов, Н. В. Карташов, Н. В. We obtain a new explicit relation for the calculation of the spectral index of ergodicity of a birth-and-death process with continuous time. The calculation of the index is reduced to the solution of an optimization problem of nonlinear programming that contains the infinitesimal matrix of the process. As an example, we use the proposed method for finding the exact values of the indices of exponential ergodicity for certain Markov queuing systems. Отримано нову явну формулу для обчислення спектрального показника ергодичності процесу народження та загибелі з неперервним часом. Обчислення показника зведено до розв'язку оптимізаційної задачі нелінійного програмування, яка містить інфінітезимальну матрицю процесу. Як приклад новим методом знайдено точні значення показників експоненціальної ергодичності для деяких марковських-систем масового обслуговування. Institute of Mathematics, NAS of Ukraine 2000-07-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4488 Ukrains’kyi Matematychnyi Zhurnal; Vol. 52 No. 7 (2000); 889-897 Український математичний журнал; Том 52 № 7 (2000); 889-897 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4488/5680 https://umj.imath.kiev.ua/index.php/umj/article/view/4488/5681 Copyright (c) 2000 Kartashov M. V. |
| spellingShingle | Kartashov, M. V. Карташов, Н. В. Карташов, Н. В. Determination of the Spectral Index of Ergodicity of a Birth-and-Death Process |
| title | Determination of the Spectral Index of Ergodicity of a Birth-and-Death Process |
| title_alt | Вычисление спектрального показателя эргодичности процесса рождения и гибели |
| title_full | Determination of the Spectral Index of Ergodicity of a Birth-and-Death Process |
| title_fullStr | Determination of the Spectral Index of Ergodicity of a Birth-and-Death Process |
| title_full_unstemmed | Determination of the Spectral Index of Ergodicity of a Birth-and-Death Process |
| title_short | Determination of the Spectral Index of Ergodicity of a Birth-and-Death Process |
| title_sort | determination of the spectral index of ergodicity of a birth-and-death process |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4488 |
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