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Асимптотически диффузионный анализ RQ-системы с обратными связями и неординарным входящим потоком
- Авторы: Назаров А.А.1, Рожкова С.В.1,2, Титаренко Е.Ю.2
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Учреждения:
- Томский государственный университет
- Томский политехнический университет
- Выпуск: Том 31, № 3 (2023)
- Страницы: 205-217
- Раздел: Статьи
- URL: https://journals.rudn.ru/miph/article/view/35917
- DOI: https://doi.org/10.22363/2658-4670-2023-31-3-205-217
- EDN: https://elibrary.ru/LACMZU
- ID: 35917
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Аннотация
В работе исследована \(M^{[n]}/M/1\) RQ-система с неординарным пуассоновским входящим потоком. Заявки на вход системы поступают группами. В каждый момент времени обслуживается не более одной заявки, остальные попадают на орбиту. Заявка, обслуживание которой завершено, либо покидает систему, либо повторно поступает на обслуживание, либо переходит на орбиту. Методом асимптотически диффузионного анализа при асимптотическом условии растущего среднего времени ожидания на орбите построена аппроксимация распределения вероятностей числа заявок на орбите. Показано, что точность диффузионной аппроксимации превышает точность гауссовской аппроксимации.
Полный текст
Introduction There are situations in practice where an arriving customer that sees the server being occupied temporarily leaves the system or goes to orbit. In some random time customer retries to occupy a server again. These situations are modeled as retrial queuing systems. In addition, there are queuing systems in which a customer that has already received service requires a second service. It depends on the quality of the received service or external factors. Classical examples are communication networks in which erroneously transmitted data is retransmitted. The functioning of such systems is described by retrial queuing systems with feedback. There are many reviews on the study of queuing systems with repeated calls, for example [1, 2]. Models with feedback, instantaneous and delayed, have also been intensively studied in the last two decades [3-5]. At the same time, classical methods do not allow us to evaluate the characteristics of such systems. The application of asymptotic analysis methods makes it possible to obtain the asymptotic characteristics of the system under various limiting conditions. For example, in [6], a stationary probability distribution of the number of customers in orbit was obtained under conditions of a large delay of customers in orbit. To perform more detailed and accurate analysis of the model a method of asymptotic diffusion analysis is applied [7]. In this paper, we study retrial queuing systems with single server, batch Poisson arrival process, instantaneous and delayed feedback. The retrial and service times are exponentially distributed. A diffusion approximation of the probability distribution of the number of customers in orbit is constructed. It is shown that the accuracy of the diffusion approximation is higher then the accuracy of Gaussian approximation obtained in [6]. 2. System description We consider the queuing systemОб авторах
А. А. Назаров
Томский государственный университет
Email: nazarov.tsu@gmail.com
ORCID iD: 0000-0002-5097-5629
Doctor of Technical Sciences, Professor of Department of Probability Theory and Mathematical Statistics, Institute of Applied Mathematics and Computer Science
пр. Ленина, д. 36, Томск, 634050, РоссияС. В. Рожкова
Томский государственный университет; Томский политехнический университет
Email: rozhkova@tpu.ru
ORCID iD: 0000-0002-8888-9291
Doctor of Physical and Mathematical Sciences, Professor of Department of Mathematics and Computer Science, School of Core Engineering Education, 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
пр. Ленина, д. 36, Томск, 634050, Россия; ул. Советская, д. 73 стр.1, Томск, 634050, РоссияЕ. Ю. Титаренко
Томский политехнический университет
Автор, ответственный за переписку.
Email: teu@tpu.ru
ORCID iD: 0000-0002-0478-8232
Lecturer of Mathematics and Computer Science, School of Core Engineering Education
ул. Советская, д. 73 стр.1, Томск, 634050, РоссияСписок литературы
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