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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">msi</journal-id><journal-title-group><journal-title xml:lang="ru">Современная наука и инновации</journal-title><trans-title-group xml:lang="en"><trans-title>Modern Science and Innovations</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2307-910X</issn><publisher><publisher-name>North-Caucasus Federal University</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.37493/2307-910X.2021.4.1</article-id><article-id custom-type="elpub" pub-id-type="custom">msi-468</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ТЕХНИЧЕСКИЕ НАУКИ. ИНФОРМАТИКА, ВЫЧИСЛИТЕЛЬНАЯ ТЕХНИКА И УПРАВЛЕНИЕ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>TECHNICAL SCIENCES. INFORMATION, COMPUTING AND MANAGEMENT</subject></subj-group></article-categories><title-group><article-title>МАТЕМАТИЧЕСКАЯ МОДЕЛЬ РАСПРЕДЕЛЕНИЯ РЕСУРСОВ ВЫЧИСЛИТЕЛЬНОГО КЛАСТЕРА ОБЛАЧНЫХ ЦЕНТРОВ ОБРАБОТКИ ДАННЫХ</article-title><trans-title-group xml:lang="en"><trans-title>MATHEMATICAL MODEL OF RESOURCE DISTRIBUTION OF THE COMPUTING CLUSTER OF CLOUD DATA CENTERS</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Мочалов</surname><given-names>В. П.</given-names></name><name name-style="western" xml:lang="en"><surname>Mochalov</surname><given-names>V. P.</given-names></name></name-alternatives><email xlink:type="simple">n.b.20062@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Линец</surname><given-names>Г. И.</given-names></name><name name-style="western" xml:lang="en"><surname>Linets</surname><given-names>G. I.</given-names></name></name-alternatives><email xlink:type="simple">kbytw@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Братченко</surname><given-names>Н. Ю.</given-names></name><name name-style="western" xml:lang="en"><surname>Bratchenko</surname><given-names>N. Y.</given-names></name></name-alternatives><email xlink:type="simple">n.b.20062@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Палканов</surname><given-names>И. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Palkanov</surname><given-names>I. S.</given-names></name></name-alternatives><email xlink:type="simple">n.b.20062@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Северо-Кавказский федеральный университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>North-Caucasus Federal University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2021</year></pub-date><pub-date pub-type="epub"><day>04</day><month>08</month><year>2022</year></pub-date><volume>0</volume><issue>4</issue><fpage>10</fpage><lpage>22</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Мочалов В.П., Линец Г.И., Братченко Н.Ю., Палканов И.С., 2022</copyright-statement><copyright-year>2022</copyright-year><copyright-holder xml:lang="ru">Мочалов В.П., Линец Г.И., Братченко Н.Ю., Палканов И.С.</copyright-holder><copyright-holder xml:lang="en">Mochalov V.P., Linets G.I., Bratchenko N.Y., Palkanov I.S.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://msi.elpub.ru/jour/article/view/468">https://msi.elpub.ru/jour/article/view/468</self-uri><abstract><p>Предметом исследования являются системы распределения и балансировки нагрузки вычислительных кластеров облачных центров обработки данных (ЦОД), содержащие множество серверов, систем хранения данных, систему ввода-вывода связанных между собой коммуникационной сетью. В основе решения задачи эффективного распределения ресурсов ЦОД рассмотрен подход, в основе которого лежат эвристический жадный алгоритм с процедурой ограниченного перебора и ограничения на ресурсы его аппаратно-программного комплекса. Отмечена важность перебора, по определению максимально возможного число серверов и виртуальных машин, для которых назначается распределение. Глубина такого перебора обеспечивает необходимый баланс между качеством сервиса и временем распределения. Поэтому решение задачи распределения и балансировки нагрузки рассмотрено в виде следующих этапов: оптимального распределения программных приложений по виртуальным машинам, распределения виртуальных машин по серверам кластера ЦОД, построения схемы алгоритма балансировки нагрузки и определение основных показателей качества обработки запросов путем аналитического и имитационного моделирования. В процессе исследования проведено математическое описание системы, учитывающее состояния серверов кластера в каждый из моментов поступления заявок на обслуживание в установившемся режиме.</p></abstract><trans-abstract xml:lang="en"><p>The subject of the study is the distribution and load balancing systems of computing clusters of cloud data centers (data centers) containing a variety of servers, data storage systems, I/O system interconnected by a communication network. The solution of the problem of efficient allocation of data center resources is based on an approach based on a heuristic greedy algorithm with a limited search procedure and restrictions on the resources of its hardware and software complex. The importance of sorting is noted, by determining the maximum possible number of servers and virtual machines for which distribution is assigned. The depth of such a search provides the necessary balance between the quality of service and the distribution time. Therefore, the solution of the problem of distribution and load balancing is considered in the form of the following stages: optimal distribution of software applications across virtual machines, distribution of virtual machines across the servers of a data center cluster, and the construction of an algo scheme.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>вычислительные кластеры</kwd><kwd>виртуальные машины</kwd><kwd>физические серверы</kwd><kwd>модель распределения ресурсов</kwd><kwd>эвристические алгоритмы</kwd><kwd>модельный эксперимент</kwd></kwd-group><kwd-group xml:lang="en"><kwd>computing clusters</kwd><kwd>virtual machines</kwd><kwd>physical servers</kwd><kwd>resource allocation model</kwd><kwd>heuristic algorithms</kwd><kwd>model experiment</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Gnedenko B.V., Kovalenko I.N. 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