Methodological Aspects of Integrating and Mathematically Modeling a Cyber Range as an Innovative IT Solution for Cybersecurity Education in Higher Education Institutions

Abstract

The increasing complexity of cyber threats necessitates scalable and practice-oriented approaches to cybersecurity education. This paper presents the design and evaluation of a virtual cyber range integrated into bachelor’s and master’s cybersecurity programs at a Ukrainian university. The proposed platform is based on a multi-layer virtualized architecture that incorporates Red, Blue, and White team environments, enabling offensive, defensive, and administrative training within a unified infrastructure. The study combines competency-based curriculum mapping with Capture the Flag (CTF) exercises and pre-/post-training assessment. Experimental results demonstrate statistically significant learning improvements, with an average Learning Gain Index (LGI) above 0.6, confirming the effectiveness of the proposed approach in developing incident response, penetration testing, and secure system configuration skills. In addition to the architectural and educational contributions, the paper introduces a stochastic discrete-time dynamic model with Markov- modulated random coefficients to evaluate cyber range effectiveness under uncertainty. The model enables quantitative assessment of long-term performance, risk levels, and resource management strategies, accounting for variability in attack intensity, system reliability, and user behavior. The proposed model is formulated independently of a specific cyber range implementation, enabling its application to a broad class of cybersecurity training and simulation platforms. The results confirm that cyber range integration strengthens competency development and aligns with international practices in cybersecurity education.