The Laplace–Stieltjes Transformation of the Distribution Function of the Peak Age of Information in a Multichannel Transmission Group
DOI:
https://doi.org/10.14529/cmse240104Keywords:
age of information, peak age of information, multi-channel queuing system, reordering of applicationsAbstract
This article continues the author’s cycle of works 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. In this paper, we consider a model of a two-node transmission group consisting of an information source (sender node), a control center (recipient node) and several communication channels between them. It is assumed that the channel capacities may be different. At the same time, the network protocol requires that the information received by the recipient node be read in the same sequence as it was transmitted from the sending node. As a result, packets that violate the established order are delayed at the sending node for the time required to restore order. In this paper, the information transfer process is modeled using a multichannel queuing system with a limited storage, Poisson flow of applications, exponential maintenance and reordering of applications. At the same time, applications simulate packets of transmitted information, the system storage is a queue of packets for transmission, the service of applications on devices of varying intensity is the process of transmitting packets over communication channels. This model was used for the first time to estimate the age of information. As a result of the conducted research, expressions for the Laplace–Stieltjes transformation of the stationary distribution function and the initial moments of the maximum value of the information age, called the peak age, were obtained. A numerical study of system performance indicators has been conducted, including an analysis of the peak age of information at various system loads. The correctness of the analytical results is confirmed by the results of simulation modeling.References
Sultan A. Ultra Reliable and Low Latency Communications. 3GPP. 2023. URL: https://www.3gpp.org/technologies/urlcc-2022 (accessed: 15.09.2023).
Kaul S., Yates R., Gruteser M. Real-time status: How often should one update? 2012 Proceedings IEEE INFOCOM. 2012. P. 2731–2735. DOI: 10.1109/INFCOM.2012.6195689.
Costa M., Codreanu M., Ephremides A. On the Age of Information in Status Update Systems With Packet Management. IEEE Transactions on Information Theory. 2016. Vol. 62, no. 4. P. 1897–1910. DOI: 10.1109/TIT.2016.2533395.
Kaul S.K., Yates R.D., Gruteser M. Status updates through queues. 2012 46th Annual Conference on Information Sciences and Systems (CISS). 2012. P. 1–6. DOI: 10.1109/CISS.2012.6310931.
Kaul S., Gruteser M., Rai V., Kenney J. Minimizing age of information in vehicular networks. 2011 8th Annual IEEE Communications Society Conference on Sensor, Mesh and Ad Hoc Communications and Networks. 2011. P. 350–358. DOI: 10.1109/SAHCN.2011.5984917.
Kosta A., Pappas N., Angelakis V. Angelakis. Age of Information: A New Concept, Metric and Tools. Foundations and Trends in Networking. 2017. Vol. 12, no. 3. P. 162–259.
Chiariotti F., Soret B., Popovski P. Peak Age of Information Distribution Bounds for Multi-Connectivity Transmissions. 2021 IEEE 22nd International Workshop on Signal Processing Advances in Wireless Communications (SPAWC). 2021. P. 321–325. DOI: 10.1109/SPAWC51858.2021.9593271.
Liu Q., Zeng H., Chen M. Minimizing AoI With Throughput Requirements in Multi-Path Network Communication. IEEE/ACM Transactions on Networking. 2022. Vol. 30, no. 3. P. 1203–1216. DOI: 10.1109/TNET.2021.3135494.
Qian Z., Wu F., Pan J., et al. Minimizing Age of Information in Multi-channel Timesensitive Information Update Systems. IEEE INFOCOM 2020—IEEE Conference on Computer Communications. 2020. P. 446–455. DOI: 10.1109/INFOCOM41043.2020.9155420.
Beytur H.B., Uysal-Biyikoglu E. Minimizing age of information on multi-flow networks. 2018 26th Signal Processing and Communications Applications Conference (SIU). 2018. P. 1–4. DOI: 10.1109/SIU.2018.8404772.
Liu Q., Zeng H., Chen M. Minimizing Age-of-Information with Throughput Requirements in Multi-Path Network Communication. Proceedings of the Twentieth ACM International Symposium on Mobile Ad Hoc Networking and Computing. New York, NY, USA: Association for Computing Machinery, 2019. P. 41–50. DOI: 10.1145/3323679.3326502.
Matyushenko S.I. Analysis of a multichannel service system with limited storage and reordering of applications. Vestnik TvGU. Seriya: Prikladnaya matematika. 2010. No. 19. P. 55–70. (in Russian).
Matyushenko S., Ermolayeva A. On stationary characteristics of a multiserver exponential queuing system with reordering of requests. 2021 13th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT). 2021. P. 98–103. DOI: 10.1109/ICUMT54235.2021.9631709.
Naumov V.A. On the limiting probabilities of a semi-Markov process. Sovremennie zadachi v tochnih naukah. M.: Universitet drugbi narodov, 1975. P. 35–39. (in Russian).
