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

Cover Page

Cite item

Full Text

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.

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

References

  1. Sultan, A. Ultra Reliable and Low Latency Communications. 3GPP 2023.
  2. Kamoun, F. & Kleinrock, L. Analysis of Shared Finite Storage in a Computer Network Node Environment Under General Traffic Conditions. IEEE Transactions on Communications 28, 992- 1003. doi: 10.1109/TCOM.1980.1094756 (1980).
  3. Baskett, F., Chandy, K. M., Muntz, R. R. & Palacios, F. G. Open, Closed, and Mixed Networks of Queues with Different Classes of Customers. Journal of the ACM 22, 248-260. doi: 10.1145/321879.321887 (1975).
  4. Bedewy, A. M., Sun, Y. & Shroff, N. B. Age-optimal information updates in multihop networks in 2017 IEEE International Symposium on Information Theory (ISIT) (2017), 576-580. doi: 10.1109/ISIT.2017.8006593.
  5. Bojan, T. M., Kumar, U. R. & Bojan, V. M. An internet of things based intelligent transportation system in 2014 IEEE International Conference on Vehicular Electronics and Safety (2014), 174-179. doi: 10.1109/ICVES.2014.7063743.
  6. Hu, C. & Dong, Y. Age of information of two-way data exchanging systems with power-splitting. Journal of Communications and Networks 21, 295-306. doi: 10.1109/JCN.2019.000037 (2019).
  7. Costa, М., Codreanu, М. & Ephremides, А. Age of information with packet management in IEEE International Symposium on Information Theory (ISIT) (2014), 1583-1587.
  8. Chiariotti, F., Vikhrova, O., Soret, B. & Popovski, P. Peak Age of Information Distribution for Edge Computing With Wireless Links. IEEE Transactions on Communications 69, 3176-3191. doi: 10.1109/TCOMM.2021.3053038 (2021).
  9. Kadota, I., Uysal-Biyikoglu, E., Singh, R. & Modiano, E. Minimizing the Age of Information in broadcast wireless networks in 2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton) (2016), 844-851. doi: 10.1109/ALLERTON.2016.7852321.
  10. Kosta, A., Pappas, N., Ephremides, A. & Angelakis, V. Non-linear Age of Information in a Discrete Time Queue: Stationary Distribution and Average Performance Analysis in ICC 2020 - 2020 IEEE International Conference on Communications (ICC) (2020), 1-6. doi: 10.1109/ICC40277.2020.9148775.
  11. Talak, R., Karaman, S. & Modiano, E. Improving Age of Information in Wireless Networks With Perfect Channel State Information. IEEE/ACM Transactions on Networking 28, 1765-1778. doi: 10.1109/TNET.2020.2996237 (2020).
  12. Tripathi, V., Talak, R. & Modiano, E. Age of information for discrete time queues 2019.
  13. Wijerathna Basnayaka, C. M., Jayakody, D. N. K., Ponnimbaduge Perera, T. D. & Vidal Ribeiro, M. Age of Information in an URLLC-enabled Decode-and-Forward Wireless Communication System in 2021 IEEE 93rd Vehicular Technology Conference (VTC2021-Spring) (2021), 1-6. doi: 10.1109/VTC2021Spring51267.2021.9449007.
  14. Zhbankova, E., Khakimov, A., Markova, E. & Gaidamaka, Y. The Age of Information in Wireless Cellular Systems: Gaps, Open Problems, and Research Challenges. Sensors 23. doi: 10.3390/s23198238 (2023).
  15. Kaul, S., Yates, R. & Gruteser, M. Real-time status: How often should one update? in 2012 Proceedings IEEE INFOCOM (2012), 2731-2735. doi: 10.1109/INFCOM.2012.6195689.
  16. Costa, M., Codreanu, M. & Ephremides, A. On the Age of Information in Status Update Systems With Packet Management. IEEE Transactions on Information Theory 62, 1897-1910. doi: 10.1109/TIT.2016.2533395 (2016).
  17. Kaul, S. K., Yates, R. D. & Gruteser, M. Status updates through queues in 2012 46th Annual Conference on Information Sciences and Systems (CISS) (2012), 1-6. doi: 10.1109/CISS.2012.6310931.
  18. Bocharov, P. P. & Pechinkin, A. V. Queueing Theory [Teoriya massovogo obsluzhivaniya] in Russian. 529 pp. (Izd-vo RUDN, Moscow, 1995).
  19. Bocharov, P. P. & Yakutina, S. V. Stationary queue distribution in a finite capacity service system with group flow and phase-type service time [Stacionarnoe raspredelenie ocheredi v sisteme obslugivaniya konechnoy emkosty s gruppovim potokom i vremenem obslugivaniya fazovogo tipa]. Avtomatika i Telemekhanika. in Russian, 106-119 (1994).
  20. Naumov, V. A. O predelnih veroyatnostyah polumarkovskogo processa [On the limiting probabilities of a semi-Markov process] in Russian. 35-39 (Universitet drugbi narodov, Moscow, 1975).

Supplementary files

Supplementary Files
Action
1. JATS XML
Download