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)3095410.22363/2658-4670-2022-30-2-160-182ArticlesСтатьиResearch ArticleAnalysis of queuing systems with threshold renovation mechanism and inverse service disciplineАнализ систем массового обслуживания с пороговым механизмом обновления и инверсионной дисциплиной обслуживанияhttps://orcid.org/0000-0002-7909-6396ZaryadovIvan S.ЗарядовИ. 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.ruVianaHilquias C. C.ВианаИлкиаш К. К.PHD student of Department of Applied Probability and Informaticshilvianamat1@gmail.comhttps://orcid.org/0000-0002-9388-9499MilovanovaTatiana A.МиловановаТ. 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» РАН03052022302VOL 30, NO2 (2022)ТОМ 30, №2 (2022)16018203052022Copyright ©; 2022, Zaryadov I.S., Viana H.C., Milovanova T.A.Copyright ©; 2022, Зарядов И.С., Виана И.К., Милованова Т.А.2022Zaryadov I.S., Viana H.C., Milovanova T.A.Зарядов И.С., Виана И.К., Милованова Т.А.http://creativecommons.org/licenses/by/4.0https://journals.rudn.ru/miph/article/view/30954

The paper presents a study of three queuing systems with a threshold renovation mechanism and an inverse service discipline. In the model of the first type, the threshold value is only responsible for activating the renovation mechanism (the mechanism for probabilistic reset of claims). In the second model, the threshold value not only turns on the renovation mechanism, but also determines the boundaries of the area in the queue from which claims that have entered the system cannot be dropped. In the model of the third type (generalizing the previous two models), two threshold values are used: one to activate the mechanism for dropping requests, the second - to set a safe zone in the queue. Based on the results obtained earlier, the main time-probabilistic characteristics of these models are presented. With the help of simulation modeling, the analysis and comparison of the behavior of the considered models were carried out.

В работе представлено исследование трёх систем массового обслуживания с пороговым механизмом обновления и инверсионной дисциплиной обслуживания. В модели первого типа пороговое значение отвечает только за активацию механизма обновления - механизма вероятностного сброса заявок. Во второй модели пороговое значение не только включает механизм обновления, но и определяет в накопителе границы области, из которой поступившие в систему заявки не могут быть сброшены. В модели третьего типа, обобщающей предыдущие две модели, используются два пороговых значения: одно для активации механизма сброса заявок, второе - для задания безопасной зоны в накопителе. На основе полученных ранее результатов представлены основные вероятностновременные характеристики рассмотренных моделей. С помощью имитационного моделирования проведён анализ и сравнение поведения изученных моделей.

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