Distribution of the peak age of information in a two-node transmission group modeled by a system with a group flow and a phase-type service time

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Abstract

This article continues the cycle of works by the authors devoted to the problem of the age of information (AoI), a metric used in information systems for monitoring and managing remote sources of information from the control center. The theoretical analysis of information transmission systems requires a quantitative assessment of the “freshness” of information delivered to the control center. The process of transferring information from peripheral sources to the center is usually modeled using queuing systems. In this paper, a queuing system with phase-type distributions is used to estimate the maximum value of the information age, called the peak age. This takes into account the special requirement of the transmission protocol, which consists in the fact that information enters the system in groups of random size. For this case, an expression is obtained for the Laplace-Stieltjes transformation of the stationary distribution function of the peak age of information and its average value. Based on the results of analytical modeling, a numerical study of the dependence of the average value of the peak age of information on the system load was carried out. The correctness of the expressions obtained was verified by comparing the analytical results with the results of simulation modeling.

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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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About the authors

Sergey I. Matyushenko

RUDN University

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

6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

Konstantin E. Samouylov

RUDN University

Author for correspondence.
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

6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

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Copyright (c) 2024 Matyushenko S.I., Samouylov K.E.

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