Распределение пикового возраста информации в двухузловой группе передачи, моделируемой системой обслуживания с групповым потоком и обслуживанием фазового типа

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Данная статья продолжает цикл работ авторов, посвященных проблеме возраста информации (AoI) - метрики, используемой в информационных системах для мониторинга и управления удаленными источниками информации со стороны центра управления. Теоретический анализ систем передачи информации требует количественной оценки «свежести» информации, доставляемой в центр управления. Процесс передачи информации от периферийных источников к центру обычно моделируется с помощью систем массового обслуживания. В данной работе для оценки максимального значения возраста информации, называемого пиковым возрастом, используется система массового обслуживания с распределениями фазового типа. При этом учитывается специальное требование протокола передачи, состоящее в том, что информация в систему поступает группами случайного размера. Для данного случая получено выражение для преобразования Лапласа-Стилтьеса стационарной функции распределения пикового возраста информации и его среднего значения. По результатам аналитического моделирования проведено численное исследование зависимости среднего значения пикового возраста информации от загрузки системы. Корректность полученных выражений проверена путем сравнения аналитических результатов с результатами имитационного моделирования.

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1. Introduction The problem of timely delivery of information to the control and management center arises in various spheres of human activity: in energy systems, in the industrial Internet of things, in the field of autonomous transport, in video surveillance systems, etc. [1-3]. In 2011, to quantify the freshness of information received by the control and monitoring center, the Age of Information (AoI) metric was proposed, which is a function of the time between the generation of updates at the sending node and the delay in their delivery over the network to the control and monitoring center (recipient node) [4- 13]. The most convenient device for studying the problem of information age is the device of queuing systems and networks. An overview of the works in which the analysis of the age of information is proposed to be carried out using this device can be found, for example, in [14]. It should be noted that most specialists limit themselves to simple models, for example, with an exponential distribution of time between the moments of generation of updates at the sending node and an exponential or deterministic distribution of the duration of update processing at the receiving node [15-17]. However, the simplest models of queuing systems allow us to obtain only a rough estimate of the age of information, since single-parameter distributions do not make it possible to take into account all the features of the protocols of modern dispatch control and data collection systems. In this paper, the process of transferring information from the sending node to the receiving node is modeled using a queuing system with phase-type distributions, the choice of phase parameters of which allows flexibly modeling complex dependencies that arise in modern data transmission systems. 2. Description of the model Let’s consider a group of information transmission (GT) consisting of a sender node (SN), a recipient node (RN) and a communication channel between them (Fig. 1). Transmission from the SN to the RN is carried out by groups of packets of random length over a single communication channel. If the channel is busy, groups of packages line up in a queue with a limited number of waiting places. If there are no places in the queue, the group is lost and no longer has an impact on the information transfer process. A group is considered transferred if the last packet of this group is transmitted. By the peak age of the
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Об авторах

С. И. Матюшенко

Российский университет дружбы народов им. П. Лумумбы

Email: matyushenko-si@rudn.ru
ORCID iD: 0000-0001-8247-8988

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

ул. Миклухо-Маклая, д. 6, Москва, 117198, Российская Федерация

К. Е. Самуйлов

Российский университет дружбы народов им. П. Лумумбы

Автор, ответственный за переписку.
Email: samuylov-ke@rudn.ru
ORCID iD: 0000-0002-6368-9680

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

ул. Миклухо-Маклая, д. 6, Москва, 117198, Российская Федерация

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© Матюшенко С.И., Самуйлов К.Е., 2024

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