Petri—Markov networks in university management: Stochastic modeling of successful discipline mastery

The article examines the problem of improving the efficiency of educational process management at a university using the mathematical apparatus of Petri—Markov networks (PMN). The proposed model formalizes the key contradiction of the educational process — the “competition” between the fixed calendar time allocated by the curriculum for mastering a course and the stochastic nature of student learning. The article presents a hierarchy of models: from a basic PMN, describing the mastery of a single course by a single student, to a complex network simulating the academic performance of an entire student group throughout the entire period of study. The proposed learning function is the Erlang distribution, whose parameters vary to account for individual student characteristics and the quality of teaching. Based on the model, an algorithm for university management has been developed that allows for assessing the achievability of performance targets and planning corrective actions. The “Results” section presents an example of the algorithm’s application to the “Fundamentals of project activities” course, demonstrating the assessment of student readiness and the calculation of the probabilities of academic risks. It is shown that the use of PMN allows for a transition from reactive to proactive management based on forecasting and simulating various scenarios of the educational process.

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