Асимптотически диффузионный анализ RQ системы с ненадёжным прибором

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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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1. Introduction Queuing systems with repeated requests are quite often used in various areas of telecommunications. Modern information processing systems often encounter unstable operating conditions, such as overloads, failures, and resource limitations. Under these conditions, conventional retrial queuing (RQ) systems may not be able to process all incoming requests, resulting in lost information and poor performance [1-4]. Repetitive request systems offer a solution to this problem by providing a mechanism for processing requests that cannot be fulfilled immediately. Instead of discarding such requests, they are resubmitted to the queue after a certain time, increasing the likelihood of successful completion of service. The most complete and detailed description of RQ systems and their detailed comparison with classical queuing systems was reflected in [5-7]. There are different types of unreliability. For example, the works [8-10] consider the unreliability of the server as a breakdown. The authors in [11-14] consider an unreliable server with collisions or conflicts during simultaneous access to the server. Figure 1. Model of retrial queueing system M/M/1 with unreliable server This problem is especially relevant when it comes to unreliable servers that can fail due to software errors, hardware malfunctions or external factors. Server failures can lead to data loss, interruption of services, and decreased performance. If the server fails while servicing the request, it goes to repair. A request under maintenance goes into orbit and awaits recovery of the server. A fairly large number of works are devoted to systems with unreliable server [15-20]. To understand the behavior of systems with repeated requests and evaluate their performance, it is necessary to use analytical methods. In this paper, we consider a single-line queuing system with an unreliable server. We will conduct the study using the method of asymptotic diffusion analysis. It has been proven that the accuracy of the diffusion approximation exceeds the accuracy of the Gaussian approximation calculated in [21]. 2. System description Any data network, having generated customers, sends them to a shared resource (server). If the server is free, then the customer is served. If the server fails while servicing a customer, it is sent for repair, and the customers go into orbit. Let’s consider an RQ system with an unreliable server, the input of which receives a simple flow of customers with parameter
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Об авторах

Н. М. Воронина

Национальный исследовательский Томский политехнический университет

Email: vnm@tpu.ru
ORCID iD: 0000-0001-9044-5211
Scopus Author ID: 57802914700
ResearcherId: AAD-2035-2019

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

пр. Ленина, д. 30, Томск, 634050, Российская Федерация

С. В. Рожкова

Национальный исследовательский Томский политехнический университет; Национальный исследовательский Томский государственный университет

Автор, ответственный за переписку.
Email: rozhkova@tpu.ru
ORCID iD: 0000-0002-8888-9291
Scopus Author ID: 6603581666
ResearcherId: F-5512-2017

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

пр. Ленина, д. 30, Томск, 634050, Российская Федерация; пр. Ленина, д. 36, Томск, 634050, Российская Федерация

Список литературы

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© Воронина Н.М., Рожкова С.В., 2024

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