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)4340810.22363/2658-4670-2024-32-3-271-282BAUGITComputer ScienceИнформатика и вычислительная техникаResearch ArticleAnalysis of a queuing system of a single capacity with phase-type distributions and queue updatingАнализ системы обслуживания единичной ёмкости с распределениями фазового типа и обновлением очередиhttps://orcid.org/0000-0001-8247-8988MatyushenkoSergey I.МатюшенкоС. И.

Candidate of Physical and Mathematical Sciences, Assistant professor of Department of Probability Theory and Cyber Security

matyushenko-si@rudn.ruhttps://orcid.org/0000-0002-6368-9680SamouylovKonstantin E.СамуйловК. Е.

Professor, Doctor of Technical Sciences, Head of the Department of Probability Theory and Cyber Security

samuylov-ke@rudn.ruGritsenkoNikolai Yu.ГриценкоН. Ю.PhD student of Department of Probability Theory and Cyber Security1142221032@rudn.ruRUDN UniversityРоссийский университет дружбы народов15122024323VOL 32, NO3 (2024)ТОМ 32, №3 (2024)27128225032025Copyright ©; 2024, Matyushenko S.I., Samouylov K.E., Gritsenko N.Y.Copyright ©; 2024, Матюшенко С.И., Самуйлов К.Е., Гриценко Н.Ю.2024Matyushenko S.I., Samouylov K.E., Gritsenko N.Y.Матюшенко С.И., Самуйлов К.Е., Гриценко Н.Ю.https://creativecommons.org/licenses/by-nc/4.0https://journals.rudn.ru/miph/article/view/43408

In this paper, we study a queuing system with a single-capacity storage device and queue updating. An update is understood as the following mechanism: an application that enters the system and finds another application in the drive destroys it, taking its place in the drive. It should be noted that systems with one or another update mechanism have long attracted the attention of researchers, since they have important applied significance. Recently, interest in systems of this kind has grown in connection with the tasks of assessing and managing the age of information. A system with a queue update mechanism similar to the one we are considering has already been studied earlier in the works of other authors. However, in these works we were talking about the simplest version of the system with Poisson flow and exponential maintenance. In this paper, we consider a phase-type flow and maintenance system. As a result of our research, we developed a recurrent matrix algorithm for calculating the stationary distribution of states of a Markov process describing the stochastic behavior of the system in question, and obtained expressions for the main indicators of its performance.

В данной работе исследуется однолинейная система массового обслуживания с накопителем единичной ёмкости и обновлением очереди. Под обновлением понимается следующий механизм: заявка, поступающая в систему и застающая в накопителе другую заявку, уничтожает её, занимая её место в накопителе. Следует заметить, что системы с тем или иным механизмом обновления давно привлекают внимание исследователей, поскольку имеют важное прикладное значение. В последнее время интерес к системам подобного рода вырос в связи с задачами оценки и управления возрастом информации. Система с механизмом обновления очереди, подобная рассматриваемой нами, уже исследовалась ранее в работах других авторов. Однако в этих работах речь шла о простейшем варианте системы с пуассоновским потоком и экспоненциальным обслуживанием. В данной работе мы рассматриваем систему с потоком и обслуживанием фазового типа. В результате проведённого исследования нами был разработан рекуррентный матричный алгоритм для расчёта стационарного распределения состояний марковского процесса, описывающего стохастическое поведение рассматриваемой системы, и получены выражения для основных показателей её производительности.

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