Skip to main content
SpringerLink
Log in

Mathematical Tools for the Internet of Things Analysis

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

An overview of recent publications on the use of mathematical methods and models for the analysis of the Internet of Things is given. It is shown that IoT modeling uses such sections of mathematics as game theory, probability theory, theory of random processes, Boolean and matrix algebra, graph theory, number theory, complex variable theory, measure theory, optimization theory, simulation modeling, cluster analysis, and numerical and mathematical analysis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ahmed Waleed Al-Khafaji, “Development of PSMECA analysis technique applying IoT components in physical security systems,” Radioelectronic and Computer Systems, No 3(87), 63–73 (2018). https://doi.org/10.32620/reks.2018.3.07.

  2. Î. F. Òarasov and S. S. Turlakova, “Mathematical modelling of advanced engineering technologies for smart enterprises: An overview of approaches and ways of implementation,” Economy of Industry, No. 3 (83), 57–75 (2018). https://doi.org/10.15407/econindustry2018.03.057.

  3. A. Lekidis and P. Katsaros, “Model-based design of energy-efficient applications for IoT systems,” in: S. Bliudze and S. Bensalem (eds.), Methods and Tools for Rigorous System Design (MeTRiD 2018) EPTCS 272, (2018) pp. 24–38. https://doi.org/10.4204/EPTCS.272.3.

  4. Md Sadek Ali, Y. Li, Md Kh. H. Jewel, O. J. Famoriji, and F. Lin, “Channel estimation and peak-to-average power ratio analysis of narrowband internet of things uplink systems,” Wireless Communications and Mobile Computing, Vol. 2018, Article ID 2570165 (2018). https://doi.org/10.1155/2018/2570165.

  5. R. M. Alonso, D. Plets, E. F. Pupo, M. Deruyck, L. Martens, G. G. Nieto, and W. Joseph, “IoT-based management platform for real-time spectrum and energy optimization of broadcasting networks,” Wireless Communications and Mobile Computing, Vol. 2018, Article ID 7287641 (2018). https://doi.org/10.1155/2018/7287641.

  6. J. S. Kumar and M. A. Zaveri, “Clustering approaches for pragmatic two-layer IoT architecture,” Wireless Communications and Mobile Computing, Vol. 2018, Article ID 8739203 (2018). https://doi.org/10.1155/2018/8739203.

  7. O. N. Lodneva and E. P. Romasevich, “Analysis of devices traffic of the Internet of Things,” Modern Information Technology and IT-Education, Vol. 14, No. 1, 149–169 (2018). https://doi.org/10.25559/SITITO.14.201801.149-169.

    Google Scholar 

  8. S. S. Turlakova, “Information and communication technologies for the development of “smart” industries,” Economy of Industry, No. 1(85), 101–123 (2019). https://doi.org/10.15407/econindustry2019.01.101.

  9. M. Seliem, Kh. Elgazzar, and K. Khalil, “Towards privacy preserving IoT environments: A survey,” Wireless Communications and Mobile Computing, Vol. 2018, Article ID 1032761 (2018). https://doi.org/10.1155/2018/1032761.

  10. A. Triantafyllou, P. Sarigiannidis, and T. D. Lagkas, “Network protocols, schemes, and mechanisms for Internet of Things (IoT): Features, open challenges, and trends,” Wireless Communications and Mobile Computing, Vol. 2018, Article ID 5349894 (2018). https://doi.org/10.1155/2018/5349894.

  11. M. Pasha and S. M. W. Shah, “Framework for E-health systems in IoT-based environments,” Wireless Communications and Mobile Computing, Vol. 2018, Article ID 6183732 (2018). https://doi.org/10.1155/2018/6183732.

  12. S. Ali, M. G. Kibria, M. A. Jarwar, H. K. Lee, and I. Chong, “A model of socially connected web objects for IoT applications,” Wireless Communications and Mobile Computing, Vol. 2018, Article ID 6309509 (2018). https://doi.org/10.1155/2018/6309509.

  13. J. Seo, K. Kim, Mookyu Park, Moosung Park, and K. Lee, “An analysis of economic impact on IoT industry under GDPR,” Mobile Information Systems, Vol. 2018, Article ID 6792028 (2018). https://doi.org/10.1155/2018/6792028.

  14. P. Salva-Garciamailto, J. M. Alcaraz-Calero, Q. Wang, J. B. Bernabe, and A. Skarmeta, “5G NB-IoT: Efficient network traffic filtering for multitenant IoT cellular networks,” Security and Communication Networks, Vol. 2018, Article ID 9291506 (2018). https://doi.org/10.1155/2018/9291506.

  15. S. Hameed, F. I. Khan, and B. Hameed, “Understanding security requirements and challenges in internet of things (IoT): A review,” J. of Computer Networks and Communications, Vol. 2019, Article ID 9629381 (2019). https://doi.org/10.1155 /2019/9629381.

  16. M. A. Elizarov, “ Models and algorithms of information interaction in Internet of Things networks,” Author’s Abstracts of Ph.D. Theses, St. Petersburg (2017).

  17. S. Breiner, E. Subrahmanian, and R. D. Sriram, “Modeling the internet of things: A foundational approach,” in: WoT’16: Proc. of the Seventh International Workshop on the Web of Things (Stuttgart, Germany, November 2016), (2016), pp. 38–41. https://doi.org/10.1145/3017995.3018003.

  18. P. Bogdan, M. Pajic, P. P. Pande, and V. Raghunathan, “Making the Internet-of-things a reality: from smart models, sensing and actuation to energy-efficient architectures,” in CODES’16: Proc. of the Eleventh IEEE/ACM/IFIP International Conference on Hardware/Software Codesign and System Synthesis (Pittsburgh, Pennsylvania, October 2016), Article No. 25 (2016). https://doi.org/10.1145/2968456.2973272.

  19. G. D’Angelo, S. Ferretti , V. Ghini, “Modeling the Internet of Things: A simulation perspective,” arXiv:1707.00832v2 [cs.DC], 20 Sep 2017. URL: https://arxiv.org/abs/1707.00832v2.

  20. G. Margelis, X. Fafoutis, G. Oikonomou, R. Piechocki, T. Tryfonas, and P. Thomas, “Efficient DCT-based secret key generation for the Internet of Things,” Ad Hoc Networks, Vol. 92, 101744 (2019).

    Article  Google Scholar 

  21. M. S. Mahdavinejad, M. Rezvan, M. Barekatain, P. Adibi, P. Barnaghi, and Amit P. Sheth, “Machine learning for Internet of Things data analysis: A survey,” Digital Communications and Networks, Vol. 4, Iss. 3, 161–175 (2018).

    Article  Google Scholar 

  22. G. Ding, L. Wang, and Q. Wu, “Big data analytics in future Internet of things,” arXiv:1311.4112v1 [cs.DC], 17 Nov 2013. URL: https://arxiv.org/abs/1311.4112.

  23. P. J. Ryan and R. B. Watson, “Research challenges for the Internet of things: What role can or play?” Systems, Vol. 5, Iss. 24 (2017). https://doi.org/10.3390/systems5010024.

Download references

Author information

Authors and Affiliations

  1. Kyiv National Economic University named after Vadym Hetman, Kyiv, Ukraine

    G. Mamonova

  2. International Scientific and Training Center of Information Technologies and Systems, National Academy of Sciences of Ukraine and Ministry of Education and Science of Ukraine, Kyiv, Ukraine

    N. Maidaniuk

Authors
  1. G. Mamonova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. Maidaniuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. Mamonova.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 4, July–August, 2020, pp. 119–127.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mamonova, G., Maidaniuk, N. Mathematical Tools for the Internet of Things Analysis. Cybern Syst Anal 56, 621–627 (2020). https://doi.org/10.1007/s10559-020-00279-w

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-020-00279-w

Keywords

Search

Navigation