Information and Telecommunication Sciences https://infotelesc.kpi.ua/ <p><strong>Information</strong> <strong>and</strong> <strong>Telecommunication</strong> <strong>Sciences </strong>was founded in 2010, ISSN 2312-4121 (Print), ISSN 2411-2976 (Online). ITS is an international peer-reviewed scientific journal. </p> <p>The journal is published 2 times a year (June, December).</p> <p>Founder: National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”.</p> <p>Publisher: National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”.</p> <p>We accept papers in following language: English.</p> <p>Cite the title as: Inform Telecom Sci.</p> <p>Readership: telecommunications, computer science, artificial intelligence, cybersecurity, wireless technologies, fiber-optic systems, microwave technologies, web technologies.</p> <p>Keywords: Internet of Things, cloud computing, Sensor Networks, Service Delivery Platforms Design, information efficiency, artificial intelligence, radio monitoring.</p> <p>Indexing: DOAJ, Google Scholar, OpenAIRE, BASE, WorldCat </p> <p>This is an open access journal, meaning that all content is freely available to the user or his/her institution without any payment. Users are permitted to read, download, copy, distribute, print, search, or link to the full text of articles, and to use them for any other lawful purpose without prior permission from the publisher or author.</p> National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" en-US Information and Telecommunication Sciences 2312-4121 <p>The ownership of copyright remains with the Authors.</p> <p>Authors may use their own material in other publications provided that the Journal is acknowledged as the original place of publication and National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute” as the Publisher.</p> <p>ITS articles are published under Creative Commons licence:</p> <ul> <li> Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under <a href="https://creativecommons.org/licenses/by/4.0/">CC BY 4.0</a>that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.</li> <li>Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.</li> <li>Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.</li> </ul> PROSPECTIVE RESEARCH DIRECTIONS IN THE ELECTRONIC COMMUNICATIONS INDUSTRY https://infotelesc.kpi.ua/article/view/346460 <p><strong>Background. </strong>At the present stage, electronic communications must provide: ultra-fast data exchange between production systems, which increases productivity and safety; the use of robotic systems and artificial intelligence to support people in production processes. Reliable electronic communications ensure the security of industrial networks and personal data; intelligent factories with network sensors and automated data processing systems. In this context, new challenges are facing electronic communications and, accordingly, new problems are identified, the solution of which requires conducting promising scientific research.</p> <p><strong>Objective</strong>. The purpose of this work is to generalise and highlight the key areas of development of electronic communications, which determine the current and future state of the industry. It is aimed at outlining scientific challenges and prospects associated with the digitalisation of society, the growth of demand for fast, reliable and secure data transmission.</p> <p><strong>Methods</strong>. Analysis of factors and technologies that influence the growth of needs for the further development of electronic communications, the quality of telecommunications services in fifth and next generation networks, the introduction of new types of electronic communications and their integration with advanced information technologies.</p> <p><strong>Results</strong>. The presented research directions determine the future of electronic communications. Research in these areas will ensure the sustainable development of the industry, taking into account the growing needs of modern society in fast, secure and reliable data transmission technologies.</p> <p><strong>Conclusions</strong>. The main goal of the 6G direction and future generations of networks is to create ultra-fast, ultra-reliable and intelligent networks capable of supporting new types of services and applications, from autonomous control and remote medicine to full-scale multimedia communications. The direction of quantum communications is a revolutionary direction that promises to ensure absolute security of information transmission and open up new opportunities for communication. The direction of IoT scaling is a key direction that determines the future of many communication technologies. The research area that includes artificial intelligence (AI) and machine learning (ML) calls for further integration of AI and ML into all aspects of electronic communications, leading to smarter, more efficient and secure networks. Security and privacy in electronic communications is a dynamic area that is constantly evolving due to the growth of cyber threats and technological advancements. Edge and Fog Computing are key technologies for the future of electronic communications, and their development requires an interdisciplinary approach that combines computer science, telecommunications, AI and IoT. Research in the field of NFV and SDN is necessary to improve the performance, automation and security of networks. They play a key role in the future of 5G/6G, cloud computing, IoT and industrial networks. Green communications is an important research area that aims to improve the energy efficiency and sustainability of telecommunications networks. Networks for critical applications are a key element of modern infrastructures, and their development requires an interdisciplinary approach that combines telecommunications, cybersecurity, artificial intelligence and other fields. Holographic and tactile communication interaction technologies will become the basis of future digital communications, changing the way people and machines interact.</p> Serhii Kravchuk Iryna Kravchuk Copyright (c) 2025 http://creativecommons.org/licenses/by/4.0 2025-12-29 2025-12-29 2 4 18 10.20535/2411-2976.22025.4-18 METHODOLOGY FOR ASSESSING THE SENSITIVITY OF QUEUING SYSTEM PARAMETERS WITH SELF-SIMILARITY PROPERTIES TO SUBSCRIBER ACCESS CHARACTERISTICS https://infotelesc.kpi.ua/article/view/346463 <p><strong>Background.</strong> The last decades were marked by a significant achievement in the field of teletraffic theory – the discovery of self-similar properties of processes occurring in modern networks. Modern telecommunication networks and information systems are complex, dynamic structures in which data flows are formed by a large number of independent sources. Studies show that traffic in such systems exhibits the property of correlation on different time scales. This means that changes in network load can affect its operation not only in the short term, but also over significant time intervals.</p> <p><strong>Objective.</strong> The purpose of the paper is to investigate how the queuing systems’ (QS) characteristics sensitivity changes in the Hurst parameter (H) under conditions of self-similar traffic. Additionally, it aims to assess the impact of the traffic correlation properties on the quality indicators of the telecommunication networks’ functioning.</p> <p><strong>Methods.</strong> The mathematical basis of the study is the use of the Weibull distribution for the incoming self-similar flow to describe the characteristics of the SMO, as well as the dynamics description of the self-similar traffic property for different values of the Hurst parameters.</p> <p><strong>Results.</strong> The influence of the traffic self-similarity property on the sensitivity of changes in service quality indicators in queuing systems, depending on the intensity of incoming traffic, the intensity of service requests, and different values of the Hurst parameters, was investigated.</p> <p><strong>Conclusions.</strong> The influence of the traffic self-similarity property on the sensitivity of changes in QS quality of service indicators is most significant with an increase in the intensity of incoming traffic, the intensity of application service, and with values of the Hurst parameter close to 1. This emphasises the importance of taking into account the self-similarity factor when determining the characteristics of similar information and communication systems.</p> Leonid Uryvsky Julia Strelkovska Anastasiia Skolets Copyright (c) 2025 http://creativecommons.org/licenses/by/4.0 2025-12-29 2025-12-29 2 19 26 10.20535/2411-2976.22025.19-26 AI-POWERED WI-FI ACCESS CONTROLLERS: A NEW APPROACH TO WIRELESS NETWORK DESIGN https://infotelesc.kpi.ua/article/view/346532 <p><strong>Background.</strong>&nbsp;Classical Wi-Fi architectures based on conventional access controllers are unable to provide stable, secure, and efficient wireless connectivity under modern conditions of high connection density and dynamic loads.&nbsp;This leads to frequent connection drops, inefficient use of network resources, and complicates proactive threat detection. As a result, organisations face decreased productivity, increased operational costs, and heightened cybersecurity risks.</p> <p><strong>Objective</strong>. The aim of the article is to present an approach to designing Wi-Fi wireless networks using artificial intelligence and genetic algorithms, and to develop a comprehensive model and algorithm for multi-criteria optimisation of the network infrastructure.</p> <p><strong>Methods. </strong>The research uses theoretical analysis of modern AI-based solutions, mathematical modelling of the access point placement optimisation problem, and the application of a genetic algorithm to find Pareto-optimal configurations. An original optimisation procedure is proposed, including stages of population generation, coverage assessment, fitness function calculation, and application of genetic operators.</p> <p><strong>Results. </strong>An innovative mathematical approach for optimising access point placement is proposed, considering not only technical parameters but also architectural features of premises, quality of service (QoS), energy efficiency, and security. A comparative analysis of modern AI solutions from leading vendors (Juniper Mist AI, HPE Aruba Networking Central, Cisco DNA Center) is conducted. A closed-loop optimisation algorithm is developed, combining genetic algorithms for initial design and AI systems for dynamic network adaptation during operation.</p> <p><strong>Conclusions.</strong> The research confirmed the high efficiency of integrating artificial intelligence and genetic algorithms for creating scalable, intelligent network infrastructures capable of real-time autonomous optimisation. The implementation of the proposed solutions significantly improves wireless communication quality, reduces operational costs, and ensures stable network performance under dynamic load conditions.</p> Andrii Bondarchuk Nataliia Korshun Oles Dibrivnyi Svitlana Spivak Copyright (c) 2025 http://creativecommons.org/licenses/by/4.0 2025-12-29 2025-12-29 2 27 35 10.20535/2411-2976.22025.27-35 THE ROLE OF CYBERSECURITY IN FACILITATING DIGITAL ECONOMY: A TREE PARITY MACHINE-BASED APPROACH https://infotelesc.kpi.ua/article/view/346533 <p><strong>Background. </strong>As the digital economy expands, ensuring secure communication and data integrity becomes increasingly vital. Traditional cryptographic algorithms such as RSA and ECC are vulnerable to quantum computing advances, necessitating post-quantum solutions. Tree Parity Machines (TPMs), inspired by neural synchronisation principles, present a promising alternative for secure key exchange, particularly within Internet of Things (IoT) environments.</p> <p><strong>Objective. </strong>This study aims to evaluate the effectiveness of TPMs as a lightweight, energy-efficient, and quantum-resistant method for secure key generation and exchange in cybersecurity applications, with a focus on IoT networks.</p> <p><strong>Methods. </strong>A hybrid methodology combining theoretical analysis and practical simulations was employed. Theoretical modelling explored TPM synchronisation mechanisms, key generation dynamics, and resilience to cyber-attacks such as man-in-the-middle, replay, brute force, and eavesdropping. Practical simulations were conducted in a controlled network environment to assess TPM performance in terms of synchronisation time, key generation rate, computational overhead, and resistance to attacks, compared with traditional cryptographic methods.</p> <p><strong>Results. </strong>Simulation results demonstrated that TPMs outperform RSA/ECC across multiple parameters. TPMs achieved a synchronisation time of 15.2 ms versus 45.6 ms for RSA/ECC, a key generation rate of 500 keys/s compared to 120 keys/s, and reduced energy consumption (1.2 mJ vs. 3.8 mJ). They also exhibited superior resistance to man-in-the-middle attacks (99.9% vs. 90.4%) and required less computational overhead. These findings confirm TPMs’ robustness, scalability, and suitability for resource-constrained IoT environments.</p> <p><strong>Conclusions. </strong>Tree Parity Machines provide an efficient, post-quantum-secure alternative to conventional cryptography, offering enhanced protection against emerging cyber threats. Their lightweight architecture, rapid synchronisation, and minimal energy consumption position them as a key enabler of secure digital infrastructure. Future research should explore TPM integration with blockchain, federated learning, and edge computing to further strengthen cybersecurity frameworks.</p> Lela Mirtskhulava Larysa Globa Nana Gulua Mariam Gugunashvili Svitlana Sulima Copyright (c) 2025 http://creativecommons.org/licenses/by/4.0 2025-12-29 2025-12-29 2 36 47 10.20535/2411-2976.22025.36-47 PHYSICAL LAYER COMMUNICATION SECURITY IN 5G/6G NETWORKS OF INTELLIGENT TRANSPORT SYSTEMS BASED ON PROBABILISTIC CRYPTOGRAPHIC TRANSFORMATIONS https://infotelesc.kpi.ua/article/view/346535 <p><strong>Background. </strong>Ultra-Reliable Low Latency Communication (URLLC) as a service offered by fifth and sixth generation (5G/6G) wireless systems is a technological response to the needs of various mission-critical applications that require reliable data transmission with low latency. These applications also include Intelligent Transportation Systems services, which, among other things, provide connectivity and autonomous vehicle control. The combination of high reliability and low latency requirements in URLLC usage scenarios creates a security problem for URLLC data transmission that cannot be solved using conventional complex cryptographic methods based on a secret key. The article discusses in detail the approach to using physical layer security mechanisms (physical layer security - PLS) as a powerful alternative to classical cryptographic security methods for URLLC, and also proposes the application of the wire-tap channel concept in URLLC with an analysis of the efficiency that can be achieved for physical layer security.</p> <p><strong>Objective.</strong> The aim of the article is to provide an overview of information security solutions in URLLC usage scenarios, as well as to propose a constructive method for information protection for reliable data transmission with low latency without the use of cryptographic mechanisms based on a secret key.</p> <p><strong>Methods.</strong> Theoretical research in the field of the branch channel concept was used to create solutions that allow data protection with information-theoretic stability in URLLC usage scenarios for providing IoT, connected car and autonomous driving services.</p> <p><strong>Results.</strong> The article examines in detail the data security issues in ultra-reliable low latency communication (URLLC) as a service offered by fifth and sixth generation (5G/6G) wireless systems. It is determined that URLLC is a technological response to the needs of various critical applications that require reliable signal transmission with low latency, and among these applications are Intelligent Transportation Systems services, which, among other things, provide connectivity and autonomous vehicle control. It is shown that the combination of high reliability and low latency requirements in URLLC scenarios creates a security problem for URLLC data transmission that cannot be solved using conventional complex cryptographic methods based on a secret key. The feasibility of using physical layer security mechanisms (PLS) as a powerful alternative to classical cryptographic security methods for URLLC is substantiated. The approach to applying the concept of a wire-tap channel in URLLC is considered in detail, as well as the results that can be achieved for physical layer security, and the influence of code parameters for probabilistic cryptographic transformations in accordance with the concept of a wire-tap channel on PLS URLLC. Estimates of the effectiveness of PLS URLLC for finite block length codes are provided.</p> <p><strong>Conclusions. </strong>An effective way to ensure data security for ultra-reliable low-latency physical layer link (PLS URLLC) of fifth-generation 5G wireless systems in the field of connected cars and vehicles of 4-5 levels of automation can be approaches based on the concept of a tapped channel ("wire-tap channel").</p> Viktor Gorytsky Copyright (c) 2025 http://creativecommons.org/licenses/by/4.0 2025-12-29 2025-12-29 2 48 54 10.20535/2411-2976.22025.48-54 METHODS FOR ENHANCING SECURITY IN IP TELEPHONY https://infotelesc.kpi.ua/article/view/346551 <p><strong>Background. </strong>The widespread adoption of IP telephony in corporate and operator networks has led to an increased risk of cyber threats such as fraud, eavesdropping, service interruptions and unauthorised access. Unlike traditional telephony, IP-based systems inherit all the vulnerabilities of IP networks, requiring a systematic, multi-layered approach to security.</p> <p><strong>Objective</strong>. The purpose of the paper is to present and analyse methods for enhancing the security of IP telephony systems. The focus is placed on protecting signalling and media traffic, preventing fraud, ensuring the integrity and confidentiality of communications, and maintaining service availability in the presence of attacks.</p> <p><strong>Methods</strong>. The research involves analysing potential threats for IP telephony systems and various protecting methods such as&nbsp; Encryption for VoIP traffic, Configuration Authentication, Separation of VoIP and Data Traffic, Firewalls and Session Border Controllers (SBCs) which are widely used, Intrusion detection and prevention systems(IDPS), AI and Machine Learning for Real-Time Threat Detection, Blockchain for Security and Authentication which are the future of IP telephony security.</p> <p><strong>Results</strong>. The analysis shows that there is no single universal solution capable of comprehensively protecting IP telephony; instead, effective security is achieved through the combination of multiple complementary mechanisms. For each major threat class, well-established countermeasures and best practices are identified. Current trends in security development for IP telephony systems were analysed.</p> <p><strong>Conclusions</strong>. The conducted review indicates that enhancing security in IP telephony is primarily a question of systematically applying and combining already known methods. The surveyed techniques provide a solid basis for protecting confidentiality, integrity and availability of IP-based voice services. Furthermore, modern technologies like blockchain, artificial intelligence, and machine learning allow experimenting and implementing new methods of IP telephony security enhancement.</p> Serhii Fedorov Rina Novogrudskaya Copyright (c) 2025 http://creativecommons.org/licenses/by/4.0 2025-12-29 2025-12-29 2 55 62 10.20535/2411-2976.22025.55-62 CORRECTION OF FLIGHT SPEED MEASUREMENTS USING RADIO NAVIGATION ANGLE-RANGE MEASURING SYSTEM DATA https://infotelesc.kpi.ua/article/view/346552 <p><strong>Background. </strong>Integration of various navigation devices and systems by data combining is widely used for improving the reliability and accuracy. The classical combining method is that the greatest effect is achieved when combined systems measure the same parameters, and the frequency characteristics of the measurement errors differ significantly. This makes it possible to use the classical compensation and filtering scheme using a Kalman filter.</p> <p><strong>Objective.</strong> This article presents the scheme, algorithm and program for combining flight speed data received from the on-board air data system and data received from the ground-based radio navigation angle-range measuring system. The result of such combining is used to correct the airspeed measurements.</p> <p><strong>Methods.</strong> The peculiarity of the proposed integration procedure is that it consists of several stages. First, the ground speed is recovered by optimal estimation based on the angle-range measurement data. At the second stage, the estimated ground speed is integrated with the airspeed measurements using the compensation and filtering scheme, simultaneously correcting the airspeed measurements.</p> <p><strong>Results.</strong> To verify the proposed integration scheme and algorithm, computer statistical modelling has been performed using a Kalman filter. The obtained results demonstrate the possibility of implementing the proposed scheme and algorithm for correcting the airspeed measurement system with increased accuracy.</p> <p><strong>Conclusions. </strong>The advantages of the proposed design are that the process of ground speed recovery and the process of data combining are performed separately, which makes it possible to control the correction process.</p> Volodymyr Vasyliev Copyright (c) 2025 http://creativecommons.org/licenses/by/4.0 2025-12-29 2025-12-29 2 63 67 10.20535/2411-2976.22025.63-67 SIMULATION MODEL OF RADAR IMAGING TECHNIQUE WITH MODIFIED CW-LFM SAR https://infotelesc.kpi.ua/article/view/346553 <p><strong>Background. </strong>Modern synthetic aperture radar (SAR) systems are crucial for Earth observation, especially in conditions where traditional optical systems fail, such as low visibility or adverse weather. Continuous wave linearly frequency modulated (CW-LFM) signals are promising for their energy efficiency and simplified hardware implementation, but they present significant signal processing challenges, including phase coherence preservation and spectral artifacts removal.</p> <p><strong>Objective.</strong> The study aims to develop and simulate a structural model of a compact SAR system based on CW-LFM signals, with a focus on improving image quality through advanced signal processing algorithms, specifically the use of decorrelation techniques for reference signals.</p> <p><strong>Methods. </strong>The study involves a mathematical formulation of radar imaging processes, development of a simulation model based on the proposed structural scheme, and implementation of signal processing operations such as quadrature detection, discrete Fourier transforms, and digital filtering. A new decorrelation method for reference signals is introduced and evaluated against classical approaches using various image quality metrics.</p> <p><strong>Results.</strong> Simulation results show that the proposed decorrelation technique improves image quality metrics, including SSIM, PSNR, and NCC. The method helps reduce speckle size and enhances image resolution. Artifacts caused by spectrum limitations were effectively suppressed using weighting functions. Quantitative evaluations using both real and artificially generated radar images confirmed the advantage of the proposed method over classical techniques.</p> <p><strong>Conclusions.</strong> The developed simulation model and signal processing improvements demonstrate the feasibility and effectiveness of using decorrelation-enhanced CW-LFM SAR systems for high-resolution radar imaging. The results can support further research and practical implementations in compact airborne and unmanned platforms for civil and defence applications.</p> Volodymyr Pavlikov Semen Zhyla Danyil Kovalchuk Denys Kolesnikov Yaroslav Sydorov Copyright (c) 2025 http://creativecommons.org/licenses/by/4.0 2025-12-29 2025-12-29 2 68 80 10.20535/2411-2976.22025.68-80 THEORY OF GUIDED WAVES IN THE INFINITE SYSTEMS OF COUPLED DIELECTRIC RESONATORS https://infotelesc.kpi.ua/article/view/346554 <p><strong>Background. </strong>One of the promising elements of optical and quantum communication systems is various delay lines built on the high-quality dielectric resonators (DRs). These lines typically comprise a substantial number of elements, making the optimisation of their parameters quite challenging. The theory of DRs serves as a foundation for comprehending, calculating, and optimising the parameters of delay lines and other devices, facilitating a considerable reduction in the computational resources that typically require the use of powerful computers.</p> <p><strong>Objective. </strong>The study aims to derive analytical expressions for the electromagnetic parameters of diverse optical waveguides, composed of numerous types of DRs, to utilise them as transmission lines for optical communication systems. To address this issue, an infinite linear system of equations has been derived based on the perturbation theory applied to Maxwell's equations, which connects the complex amplitudes, wave numbers and the resonator frequencies.</p> <p><strong>Methods. </strong>To derive solutions for the analytical expressions, perturbation theory and the theory of infinite linear equations are employed. The outcome is a set of new general analytical formulae that describe the dispersion curves of lattices made up of an infinite number of various types of DRs.</p> <p><strong>Results. </strong>A theory of wave propagation in systems of interconnected one-, two-, and three-dimensional lattices of DRs extended infinitely in one or more directions has been developed. New analytical expressions for the dispersion characteristic of eigenwaves, delay times, and distributions of complex amplitudes of resonators, without any limitations on their quantity, have been derived. By utilising perturbation theory, a novel analytical model has been developed that describes the eigenwaves of three-dimensional lattices composed of identical ring structures of DRs. General analytical solutions for frequency dependencies and amplitudes for one-, two-, and three-dimensional lattices with varying arrangements of resonators have been identified.</p> <p><strong>Conclusions. </strong>The developed theory serves as the foundation for the analysis and design of many devices operating within the optical wavelength spectrum, constructed upon an infinite variety of distinct types of DRs. The obtained new analytical expressions for calculating optical waveguide parameters, based on coupled oscillations of DRs, enable the development of innovative and more efficient mathematical models for various optical communication devices.</p> Alexander Trubin Copyright (c) 2025 http://creativecommons.org/licenses/by/4.0 2025-12-29 2025-12-29 2 81 96 10.20535/2411-2976.22025.81-96 UNIQUE OPTIMAL TIME MOMENT IN EXPONENTIALLY-CONVEX-REWARD 1-BULLET PROGRESSIVE SILENT DUEL OF ICT INNOVATION LAUNCH https://infotelesc.kpi.ua/article/view/346963 <p><strong>Background.</strong> In the modern digital economy, the timing of the introduction of new information and telecommunication technologies becomes critical: launching too early may lead to unprepared infrastructure or immature market demand, while delaying too long risks losing the market advantage to competitors. These processes can be interpreted through the lens of progressive silent duels. Each market participant must decide when to act — that is, when to introduce, announce, or deploy a technology — without knowing whether the competitor has already done so. In particular, when the reward of acting grows exponentially with time — representing, for instance, cumulative technological maturity or increasing value of full deployment — yet the risk of being second remains severe, the decision problem aligns with an exponentially-convex-reward duel.</p> <p><strong>Objective.</strong> The paper aims to determine the set of optimal time moments for an exponentially-convex-reward 1-bullet silent duel. From a practical standpoint, the objective of this research is to determine the optimal moment for initiating or announcing a new ICT solution in a competitive environment under the following conditions: readiness and payoff grow progressively over time, information about competitors’ actions is unavailable until after both sides have acted, and only one major strategic action is possible within a given competitive cycle. The goal is to identify a stable and universal decision rule, being an optimal strategy of timing, that maximises expected reward under these uncertainty and competition constraints.</p> <p><strong>Methods.</strong> The finite 1-bullet progressive silent duel is considered, in which each of the two duelists shoots with an exponentially-convex reward. The duel is a symmetric matrix game whose optimal value is 0, and the set of optimal strategies is the same for both duelists, regardless of the duel size and how time is quantised. The duel is silenced because the duelist does not learn about the action of the other duelist until the very end of the duel. The duel time quantisation is such that time progresses by the geometrical progression pattern, according to which every following time moment is the partial sum of the respective geometric series. In this duel, the duelist has a single optimal strategy. It is to shoot always at the third time moment, whichever the number of time moments is. Namely, the unique optimal strategy is to shoot at either the duel end moment in the &nbsp;duel, or at the three-quarters of the unit time span in bigger duels.</p> <p><strong>Results.</strong> The theoretical finding is that the unique optimal strategy is to act precisely at the third progressive time moment, which is equivalent to around three quarters of the total planning horizon in larger duels. This result suggests that, irrespective of the granularity of internal planning (how finely time is divided into milestones), and regardless of the scale of competition, there exists a universal “sweet spot” for taking action. In real-world terms, this moment corresponds to a late but not final stage of technological preparation — when the solution has reached sufficient maturity and reliability, when market conditions are becoming favourable but not yet saturated, and when the delay is long enough to exploit exponential improvement effects but short enough to avoid being overtaken by a rival.</p> <p><strong>Conclusions.</strong> The “silent” nature of the duel models the real-world asymmetry of competitive information. For enterprises introducing new ICT systems, the third progressive moment represents a strategically balanced readiness threshold. It minimises the risk of premature launch (insufficient maturity) and the threat of excessive delay (competitor’s precedence), producing a dominant timing equilibrium that is independent of specific market size or implementation granularity.</p> Vadim Romanuke Copyright (c) 2025 http://creativecommons.org/licenses/by/4.0 2025-12-29 2025-12-29 2 97 104 10.20535/2411-2976.22025.97-104