Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)2517810.22363/2658-4670-2020-28-4-305-318ArticlesСтатьиResearch ArticleQueueing systems with different types of renovation mechanism and thresholds as the mathematical models of active queue management mechanismСистемы массового обслуживания с различными видами обновления и порогами как математические модели алгоритмов активного управления очередямиViana Carvalho CravidHilquiasВиана Карвалью КравидИлкиаш

post-graduate student of Department of Applied Probability and Informatics

hilvianamat1@gmail.comZaryadovIvan S.ЗарядовИван С.

Candidate of Physical and Mathematical Sciences, assistant professor of Department of Applied Probability and Informatics of Peoples’ Friendship University of Russia (RUDN University); Senior Researcher of Institute of Informatics Problems of Federal Research Center “Computer Science and Control” Russian Academy of Sciences

zaryadov-is@rudn.ruMilovanovaTatiana A.МиловановаТатьяна А.

Candidate of Physical and Mathematical Sciences, lecturer of Department of Applied Probability and Informatics

milovanova-ta@rudn.ruPeoples’ Friendship University of Russia (RUDN University)Российский университет дружбы народовInstitute of Informatics Problems, FRC CSC RASИнститут проблем информатики Федеральный исследовательский центр «Информатика и управление» РАН15122020284VOL 28, NO4 (2020)ТОМ 28, №4 (2020)30531809122020Copyright ©; 2020, Viana Carvalho Cravid H., Zaryadov I.S., Milovanova T.A.Copyright ©; 2020, Виана Карвалью Кравид И., Зарядов И.С., Милованова Т.А.2020Viana Carvalho Cravid H., Zaryadov I.S., Milovanova T.A.Виана Карвалью Кравид И., Зарядов И.С., Милованова Т.А.http://creativecommons.org/licenses/by/4.0https://journals.rudn.ru/miph/article/view/25178

This article is devoted to some aspects of using the renovation mechanism (different types of renovation are considered, definitions and brief overview are also given) with one or several thresholds as the mathematical models of active queue management mechanisms. The attention is paid to the queuing systems in which a threshold mechanism with renovation is implemented. This mechanism allows to adjust the number of packets in the system by dropping (resetting) them from the queue depending on the ratio of a certain control parameter with specified thresholds at the moment of the end of service on the device (server) (in contrast to standard RED-like algorithms, when a possible drop of a packet occurs at the time of arrivals of next packets in the system). The models with one, two and three thresholds with different types of renovation are under consideration. It is worth noting that the thresholds determine not only from which place in the buffer the packets are dropped, but also to which the reset of packets occurs. For some of the models certain analytical and numerical results are obtained (the references are given), some of them are only under investigation, so only the mathematical model and current results may be considered. Some results of comparing classic RED algorithm with renovation mechanism are presented.

Работа посвящена некоторым аспектам использования механизма обновления (различные варианты обновления рассмотрены, определения и краткий обзор представлены) с одним или несколькими порогами в качестве математических моделей механизмов активного управления очередями. Описаны системы массового обслуживания, в которых реализован механизм обновления с порогами, позволяющий управлять числом заявок в системе путем их сброса из накопителя в зависимости от значения некоторого управляющего параметра и пороговых значений. Сброс заявок из накопителя происходит в момент окончания обслуживания заявки на приборе, что отличает данный механизм сброса от RED-подобных алгоритмов, для которых сброс возможен в момент поступления в систему. Представлены модели с одним, двумя или тремя порогами. В этих моделях пороговые значения определяют не только место, с которого в накопителе начинается сброс заявок, но и до какой позиции заявки могут быть сброшены. Для некоторых из описываемых моделей уже получены аналитические и численные результаты (ссылки на работы представлены), но большая часть моделей находится в процессе изучения, поэтому представлены только описания и некоторые текущие данные. Приведены некоторые результаты сравнения классического алгоритма RED с механизмом обновления.

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