Modeling the dynamics of the servers load by stochastic Petri nets with priorities (on the example of a video conferencing system)

Modern forms of education in higher educational institutions determine the increased load on the servers of higher educational institutions. This is especially true for video conferencing systems implemented on the basis of the University's information infrastructure. To improve the reliability and stability of these systems, it is necessary to analyze the load distribution on the system as a whole and its individual components in accordance with the existing schedule. The main task of the article is to predict the load peaks, which are determined by the graph, but also depend on a number of random factors. The article proposes a dynamic model that simulates the formation of the load on the servers of the video conferencing system depending on the available schedule of classes, taking into account random factors. The solution of the problem of modeling and predicting the behavior of a dynamic system is based on the use of the stochastic apparatus of Petri nets with priorities. As an additional mechanism for ensuring the adequacy of the model, the time intervals of Petri net transitions are determined, within which they can be active, which allows you to link the functioning of the entire network with real time intervals in the class schedule. The adequacy of the proposed model is proved by the correspondence of the predicted load servers distribution based on the results computational experiment to real video conferencing system data

1. Naeve A., Yli-Luoma P., Kravcik M., Lytras M.D. A modelling approach to study learning processes with a focus on knowledge creation. Int. J. Technology Enhanced Learning. 2008;1(1/2):1–34. Available at: https://core.ac.uk/download/pdf/191008631.pdf (accessed 12.08.2020).

2. Kuhrmann M., Fernández D.M., Münch J. Teaching Software Process Modeling. Proceedings – International Conference on Software Engineering. 2013, DOI: 10.1109/ICSE.2013.6606665

3. Solomon B. Models and concepts of curriculum implementation, some definitions and influence of implementation. Conference proceedings. Curriculum change and evaluation. 2019. DOI: 10.13140/RG.2.2.17850.24009

4. Picciano A. G. Theories and frameworks for online education: Seeking an integrated model. Online Learning. 2017;21(3):166-190. DOI: 10.24059/olj.v21i3.1225

5. Huang, Y., Chung, T.: Modeling and Analysis of Urban Traffic Lights Control Systems Using Timed CP-nets. Journal of information science and engineering. 2008;24:875-890. Available at: http://www.iis.sinica.edu.tw/page/jise/2008/200805_13.pdf (accessed: 05.10.2020).

6. DiCesare F., Kulp P.T., Gile M., List G. The application of Petri nets to the modeling, analysis and control of intelligent urban traffic networks. Valette R. (eds) Application and Theory of Petri Nets. Lecture Notes in Computer Science. 1994;815. Available at: https://link.springer.com/chapter/10.1007%2F3-540-58152-9_2 (accessed: 21.11.2020)

7. Benarbia T., Labadi K., Moumen D., Chayet M. Modeling and Control of Self-Service Public Bicycle Systems by Using Petri Nets. International Journal of Modelling Identification and Control. 2012;17:173-194.

8. Malkov M. V., Maligina S. N. Petri nets and modeling. Proceedings of the Kolsk science center RAS. 2010;3:35-40 (In Russ).

9. Verbeek H.M.W., Wynn M.T., van der Aalst W.M.P., Hofstede A.H.M. Reduction rules for reset/inhibitor nets. Journal of Computer and System Sciences. 2010;76(2):125-143.

10. Best E., Koutny M. Petri net semantics of priority systems. Theoretical Computer Science. 1992,96(1):175-215.

11. Lomazova I., Popova-Zeugmann L.: Controlling Petri net behavior using priorities for transitions. Fundamenta Informatica. 2016;143(1-2):101-112.

12. Ryabtsev V., Utkina T.: Information technology for design of automated control of technological processes systems. Control, communication and security systems. 2016;1:207-239 (In Russ).

13. Naumov V. Petri nets in modeling the process of freight forwarding services. Automobile Transport (Kharkov). 2009;24:120-124 (In Russ).

14. Anagnostopoulos T., Zaslavsky A., Medvedev A., Khoruzhnikov S. Top-k Query based Dynamic Scheduling for IoT-enabled Smart City Waste Collection. Proceedings of the 16th IEEE International Conference on Mobile Data Management (MDM 2015), Pittsburgh, US 2015.

15. Dolinina O., Pechenkin V., Gubin N. Combined Intellectual and Petri Net with Priorities Approach to the Waste Disposal in the Smart City. Recent Research in Control Engineering and Decision Making. Studies in Systems, Decision and Control. 2019;199:755-767 DOI: 10.1007/978-3-030-12072-6_61