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)4366710.22363/2658-4670-2024-32-4-380-394DDNAPRComputer ScienceИнформатика и вычислительная техникаResearch ArticleAsymptotic diffusion analysis of RQ system M/M/1 with unreliable serverАсимптотически диффузионный анализ RQ системы с ненадёжным приборомhttps://orcid.org/0000-0001-9044-521157802914700AAD-2035-2019VoroninaNataliya M.ВоронинаН. М.

Senior Lecturer of Department of Information Technology of School of Information Technology and Robotics Engineering

vnm@tpu.ruhttps://orcid.org/0000-0002-8888-92916603581666F-5512-2017RozhkovaSvetlana V.РожковаС. В.

Doctor of Physics and Mathematics Sciences, Professor of Department of Mathematics and Mathematical Physics of School of Nuclear Technology Engineering, National Research Tomsk Polytechnic University, Professor of Department of Probability Theory and Mathematical Statistics Institute of Applied Mathematics and Computer Science, National Research Tomsk State University

rozhkova@tpu.ruNational Research Tomsk Polytechnic UniversityНациональный исследовательский Томский политехнический университетNational Research Tomsk State UniversityНациональный исследовательский Томский государственный университет15122024324VOL 32, NO4 (2024)ТОМ 32, №4 (2024)38039405042025Copyright ©; 2024, Voronina N.M., Rozhkova S.V.Copyright ©; 2024, Воронина Н.М., Рожкова С.В.2024Voronina N.M., Rozhkova S.V.Воронина Н.М., Рожкова С.В.https://creativecommons.org/licenses/by-nc/4.0https://journals.rudn.ru/miph/article/view/43667

The paper considers a single-line retrial queueing system with an unreliable server. Queuing systems are called unreliable if their servers may fail from time to time and require restoration (repair), only after which they can resume servicing customers. The input of the system is a simple Poisson flow of customers. The service time and uptime of the server are distributed exponentially. An incoming customer try to get service. The server can be free, busy or under repair. The customer is serviced immediately if the server is free. If it is busy or under repair, the customer goes into orbit. And after a random time it tries to get service again. The study is carried out by the method of asymptotically diffusion analysis under the condition of a large delay of requests in orbit. In this work, the transfer coefficient and diffusion coefficient were found and a diffusion approximation

В работе рассматривается однолинейная RQ-система массового обслуживания с ненадёжным прибором. Системы массового обслуживания называются ненадёжными, если их приборы могут время от времени выходить из строя и требовать восстановления (ремонта), только после которого они могут возобновить обслуживание запросов. Исследование проводится методом асимптотически диффузионного анализа в условии большой задержки заявок на орбите. Найдены стационарное распределение состояний прибора, коэффициент переноса и коэффициент диффузии. Построена диффузионная аппроксимация. Доказано, что точность диффузионной аппроксимации превышает точность гауссовской аппроксимации.

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