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<article 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" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" article-type="research-article" dtd-version="1.2" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">Infokommunikacionnye tehnologii</journal-id><journal-title-group><journal-title xml:lang="en">Infokommunikacionnye tehnologii</journal-title><trans-title-group xml:lang="ru"><trans-title>Инфокоммуникационные технологии</trans-title></trans-title-group></journal-title-group><issn publication-format="print">2073-3909</issn><publisher><publisher-name xml:lang="en">Povolzhskiy State University of Telecommunications and Informatics</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">689818</article-id><article-id pub-id-type="doi">10.18469/ikt.2024.22.1.04</article-id><article-categories><subj-group subj-group-type="toc-heading" xml:lang="en"><subject>Telecommunication Systems and Devices</subject></subj-group><subj-group subj-group-type="toc-heading" xml:lang="ru"><subject>Системы и устройства телекоммуникаций</subject></subj-group><subj-group subj-group-type="article-type"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title xml:lang="en">Mathematical modeling of secure multipoint video conference sessions using multilayer graphs</article-title><trans-title-group xml:lang="ru"><trans-title>Математическое моделирование защищенных многоточечных сеансов видеоконференцсвязи многоуровневыми графами</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Gladkikh</surname><given-names>А. А.</given-names></name><name xml:lang="ru"><surname>Гладких</surname><given-names>А. А.</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><bio xml:lang="en"><p>Professor of Radio Engineering, Telecommunications and Information Security Department, Doctor of Technical Sciences</p></bio><bio xml:lang="ru"><p>д.т.н., профессор, профессор кафедры радиотехники, телекоммуникации и защиты информации</p></bio><email>a_gladkikh@mail.ru</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Mishin</surname><given-names>D. V.</given-names></name><name xml:lang="ru"><surname>Мишин</surname><given-names>Д. В.</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><bio xml:lang="en"><p>Professor of Radio Electronic Systems Department, Doctor of Technical Sciences</p></bio><bio xml:lang="ru"><p>д.т.н., профессор кафедры радиоэлектронных систем</p></bio><email>d.mishin@psuti.ru</email><xref ref-type="aff" rid="aff2"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Driagin</surname><given-names>S. А.</given-names></name><name xml:lang="ru"><surname>Дрягин</surname><given-names>С. А.</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><bio xml:lang="en"><p>Deputy Chief Designer</p></bio><bio xml:lang="ru"><p>заместитель главного конструктора научно-производственного объединения</p></bio><email>s_drg@mail.ru</email><xref ref-type="aff" rid="aff3"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Korsunskii</surname><given-names>A. S.</given-names></name><name xml:lang="ru"><surname>Корсунский</surname><given-names>А. С.</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><bio xml:lang="en"><p>Deputy Chief Designer, PhD in Technical Sciences</p></bio><bio xml:lang="ru"><p>к.т.н., главный конструктор</p></bio><email>aksspb@mail.ru</email><xref ref-type="aff" rid="aff3"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">Ulyanovsk State Technical University</institution></aff><aff><institution xml:lang="ru">Ульяновский государственный технический университет</institution></aff></aff-alternatives><aff-alternatives id="aff2"><aff><institution xml:lang="en">Povolzhskiy State University of Telecommunications and Informatics</institution></aff><aff><institution xml:lang="ru">Поволжский государственный университет телекоммуникаций и информатики</institution></aff></aff-alternatives><aff-alternatives id="aff3"><aff><institution xml:lang="en">Research-and-Production Association «Mars»</institution></aff><aff><institution xml:lang="ru">Научно-производственный центр «Марс»</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2025-03-09" publication-format="electronic"><day>09</day><month>03</month><year>2025</year></pub-date><volume>22</volume><issue>1</issue><issue-title xml:lang="en"/><issue-title xml:lang="ru"/><fpage>31</fpage><lpage>42</lpage><history><date date-type="received" iso-8601-date="2025-08-23"><day>23</day><month>08</month><year>2025</year></date><date date-type="accepted" iso-8601-date="2025-08-23"><day>23</day><month>08</month><year>2025</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2025, Gladkikh А.А., Mishin D.V., Driagin S.А., Korsunskii A.S.</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2025, Гладких А.А., Мишин Д.В., Дрягин С.А., Корсунский А.С.</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="en">Gladkikh А.А., Mishin D.V., Driagin S.А., Korsunskii A.S.</copyright-holder><copyright-holder xml:lang="ru">Гладких А.А., Мишин Д.В., Дрягин С.А., Корсунский А.С.</copyright-holder><ali:free_to_read xmlns:ali="http://www.niso.org/schemas/ali/1.0/"/><license><ali:license_ref xmlns:ali="http://www.niso.org/schemas/ali/1.0/">https://creativecommons.org/licenses/by-nc-nd/4.0</ali:license_ref></license></permissions><self-uri xlink:href="https://journals.eco-vector.com/2073-3909/article/view/689818">https://journals.eco-vector.com/2073-3909/article/view/689818</self-uri><abstract xml:lang="en"><p>The article describes a multilayer graph model for multipoint videoconference sessions. The model presented in this study allows to specify requirements for quality of video capture quality when transferred between terminals and multipoint control unit at the service layer, as well as assessing bandwidth performance and delay of datalink channels at the secure and transport network layer. The given multilayer graph model for videoconference system is designed taking into account the features of secure network configuration, in which several overlay network layers are distinguished over transportation networks. This model specifies a structure of multipoint videoconference session at service layer, at which videoconferencing terminals interoperate through server. Traffic flows generated during session are distributed according to routing rules at the secure network layer. A purpose to select the most optimal route configuration for the entire session includes a number of alternative methods to distribute traffic for each pair of client-server communication seems to be rather complicated. The study proposes an algorithm for searching the shortest path in the graph of a secure overlay network with a step-by-step projection fer each individual route section onto the underlying level of the transport network to find the shortest path within its boundaries. An example for solving a problem on finding route in regard to the overlay network requirements and the actual traffic flow through the transportation network is given. Minimization of the capacity usage of leased channels was chosen as the optimality criterion. Experiments were conducted to evaluate the session quality based on the objective methods for various video-stream parameters, and corresponding quantitative estimates of the required bandwidth in order to organize a session.</p></abstract><trans-abstract xml:lang="ru"><p>В работе рассматривается модель многоточечного сеанса видеоконференцсвязи на основе многоуровневого графа. Предлагаемая модель позволяет задавать на сервисном уровне требования к качеству передаваемых видеоизображений между множеством терминалов и сервером многоточечной связи, а на уровнях защищенной и транспортной сети оценивать пропускную способность и задержки каналов передачи данных. Предложена модель многоуровневого графа системы видеоконференцсвязи, учитывающая особенности построения и организации защищенных сетей, в которых выделяется несколько уровней наложенных сетей поверх транспортной сети. В данной модели на сервисном уровне задается структура многоточечного сеанса, при котором терминалы видеоконференции взаимодействует через сервер. Формируемые в ходе сеанса потоки трафика распределяются в соответствии с правилами маршрутизации на уровне защищенной сети. Учитывая множество альтернативных способов распределения трафика для каждой пары клиент-серверного взаимодействия, выбор наиболее оптимальной конфигурации маршрутов для сеанса в целом оказывается достаточно сложной задачей. В исследовании предложен алгоритм нахождения кратчайшего пути в графе защищенной наложенной сети с поэтапным проецированием каждого отдельного участка маршрута на нижележащий уровень транспортной сети для поиска кратчайшего пути в его пределах. Приведен пример решения задачи поиска маршрутов для каждого абонента с учетом правил наложенной сети и фактического продвижения трафика по транспортной сети. В качестве критерия оптимальности выбрана минимизация использования емкости арендуемых каналов. Проведены эксперименты для получения оценок качества сеанса на основе объективных методов при различных параметрах видеопотока и соответствующие им количественные оценки требуемой пропускной способности для организации сеанса.</p></trans-abstract><kwd-group xml:lang="en"><kwd>multilayer graph</kwd><kwd>videoconference</kwd><kwd>multipoint videoconference sessions</kwd><kwd>quality evaluation of videoconference sessions</kwd><kwd>data transmission network</kwd><kwd>calculation of required channel resources</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>многоуровневый граф</kwd><kwd>видеоконференцсвязь</kwd><kwd>многоточечные сеансы видеоконференцсвязи</kwd><kwd>оценка качества видеоконференцсвязи</kwd><kwd>сеть передачи данных</kwd><kwd>расчет загруженности каналов</kwd></kwd-group><funding-group/></article-meta></front><body></body><back><ref-list><ref id="B1"><label>1.</label><citation-alternatives><mixed-citation xml:lang="en">Recommendations ITU-T E.800 (09/2008). 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