Control in Technology and Process Control

Laplace - Stieltjes transform of the peak age of information for the case when packet transmission is modeled by a PH|PH|1|r queueing system with FCFS discipline

S. Matyushenko^a, K. E. Samouylov<sup>ab

a</sup> Peoples’ Friendship University of Russia (RUDN University), Moscow
^b Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow

Abstract: This work is devoted to the analysis of Peak Age of Information (PAoI) – the metric used in 5G mobile cellular communications for remote groups monitoring and mamgement at the control center. Currently, in the operation of the queuing system PH|PH|1|r, the Laplace – Stieltjes transform of the PAoI has been obtained. The PAoI presents the time between the generation of updates at the source and the delay in their delivery across the network and assumes that only timely received updates can reflect the current state of the system. When analyzing technical information transmission systems, it should be taken into account that the PAoI metric is significantly different from the delay measured at the time instants when the packet reaches its destination. The new PAoI metric is defined for an alternative time, that complicates its analysis. To check the correctness of the analytical results, they were compared with special cases of the queueing system M|M|1|1, as well as with the results of a simulation analysis of the queueing system with distributed cases of phase type.

Keywords: AoI, age of information, peak age of information, PH-distribution

UDC: 519.872
BBK: 22.18

Received: November 22, 2023
Published: November 30, 2023

DOI: 10.25728/ubs.2023.106.11