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)4138410.22363/2658-4670-2024-32-2-140-153CRYMNNArticlesСтатьиResearch ArticleMarginal asymptotic diffusion analysis of two-class retrial queueing system with probabilistic priority as a model of two-modal communication networksМаргинальный асимптотически-диффузионный анализ двуклассовой RQ-системы с вероятностным приоритетом как математической модели сети связи с двумодальной информациейhttps://orcid.org/0000-0002-5097-56297201780364O-5862-2014NazarovAnatoly A.НазаровА. А.

Doctor of Technical Sciences, professor of Department of Probability Theory and Mathematical Statistic

nazarov.tsu@gmail.comhttps://orcid.org/0000-0001-8933-532256439120600E-3161-2017FedorovaEkaterina A.ФёдороваЕ. А.

PhD in Physical and Mathematical Sciences, associate professor of Department of Probability Theory and Mathematical Statistic

moiskate@mail.ruhttps://orcid.org/0000-0002-9132-012757191051392T-6377-2017IzmailovaYana E.ИзмайловаЯ. Е.

PhD in Physical and Mathematical Sciences, associate professor of Department of Probability Theory and Mathematical Statistic

evgenevna.92@mail.ruNational Research Tomsk State UniversityНациональный исследовательский Томский государственный университет15102024322VOL 32, NO2 (2024)ТОМ 32, №2 (2024)14015301112024Copyright ©; 2024, Nazarov A.A., Fedorova E.A., Izmailova Y.E.Copyright ©; 2024, Назаров А.А., Фёдорова Е.А., Измайлова Я.Е.2024Nazarov A.A., Fedorova E.A., Izmailova Y.E.Назаров А.А., Фёдорова Е.А., Измайлова Я.Е.https://creativecommons.org/licenses/by-nc/4.0https://journals.rudn.ru/miph/article/view/41384

In the paper, a retrial queueing system of \(M_2/M_2/1\) type with probabilistic priority and interruptions is considered as a model of a two-modal communication network. Two classes of customers come to the system according Poisson arrival processes. There is one service device (or channel). If a customer finds the server occupying by a customer of the same class, it goes to an orbit and makes a repeated attempt after a random delay. If an arrival customer finds the other class customer on the server, it can interrupt its service with the given probability and start servicing itself. Customers from the orbit behave the same way. There is a multiply access for customers in the orbit. Service times and inter-retrial times have exponential distributions. Customers are assumed heterogeneous, so the parameters of the distributions are different for each class. In the paper, we propose the original marginal asymptotic-diffusion method for finding of the stationary probability distributions of the number of each class customers under the long delays condition.

В работе исследуется RQ-система

В работе исследуется RQ-система \(M_2/M_2/1\) с вероятностным приоритетом и вытеснением заявок как модель двумодальной сети связи. На вход системы поступает два класса заявок, т.е. два потока. В системе имеется одно обслуживающее устройство (канал связи). Если входящая заявка застает прибор занятым заявкой того же класса, она идет на орбиту и осуществляет случайную задержку через экспоненциально распределенное случайное время. Если же на приборе находится заявка другого типа, то с некоторой вероятностью возможно прерывание обслуживания (вытеснение заявки). Необслуженная заявка уходит на орбиту. Обращаясь к прибору с орбиты, заявки действуют тем же образом. Время обслуживания каждой заявки распредлено экспоненциально. На орбите реализован протокол множественного доступа. В статье предложен оригинальный метод маргинального асимптотическидиффузионного анализа в условии большой задержки заявок на орбите для нахождения стационарных распределений вероятностей числа заявок каждого типа в системе.

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