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Документ Відкритий доступ Generalization of the method for constructing GL-models of complex fault-tolerant multiprocessor systems with additional failure conditions(Odesа Polytechnic National University, 2025) Romankevich, Vitaliy A.; Yermolenko, Ihor A.; Morozov, Kostiantyn V.; Romankevich, Alexei M.; Melnyk, Oleksandr O.The article is devoted to methods for constructing GL-models of fault-tolerant multiprocessor systems. GL-models can be used as behavioral models of such systems under failure flows to evaluate their reliability metrics through statistical experiments. The study considers two types of systems: consecutive two-dimensional systems and mixed-type systems. A consecutive two-dimensional system is defined as one in which components are arranged in the form of a rectangular matrix, and the system fails when a rectangular block of a certain size appears, consisting entirely of failed components. A mixed-type system fails if at least one of the following conditions is met: a specified number of arbitrary components have failed; a specified number of consecutive components have failed; or a rectangular block of a certain size, consisting entirely of failed components, appears within the component matrix. Currently, there are no formalized methods for constructing GL-models for the aforementioned types of systems. The objective of this work is to develop a universal method for constructing GL-models for both consecutive two-dimensional systems and mixedtype systems. It is shown that, to construct a GL-model for such a system, it is sufficient to determine the maximum number of failed components under which the system remains operational. Based on this threshold, a basic system model is constructed without considering additional failure conditions. Then, all combinations of component failures that lead to system failure are identified. The basic model is subsequently weakened at the vectors corresponding to these critical failure combinations. This paper presents, for the first time, an algorithm for constructing GL-models for consecutive two-dimensional systems and mixed-type systems. In addition, it introduces methods for calculating the maximum allowable number of component failures under which the system remains functional, as well as estimating the total number of failure combinations that result in system failure. Experimental results confirm that the proposed models adequately represent the real behavior of such systems under failure flows. Examples are provided to illustrate the GL-model construction process for both of the aforementioned system types.Документ Відкритий доступ On the computational complexity of cascade GL-models for fault-tolerant multiprocessor systems(Odesa Polytechnic National University, Institute of Computer Systems, 2025) Romankevich, Vitaliy A.; Morozov, Kostiantyn V.; Romankevich, Alexei M.; Nikishyn, Yehor O.The article addresses the problem of evaluating the computational complexity of basic cascade GL-models used for modeling the behavior of fault-tolerant multiprocessor systems in the flow of failures. The purpose of this work is to reduce the complexity of such models by optimal selection of their parameters. It has been demonstrated that a single system usually corresponds to an entire family of cascade GL-models, differing in cascade depth and parameters, with each having its own computational complexity. To simplify the process of modeling the system behavior under a flow of failures, it is advisable to choose the cascade GL-model configuration with the lowest complexity. However, additional constraints on the model, such as cascade depth limitations, must also be considered. This work applies an empirical-analytical research method. An analysis of computational complexity for cascade GLmodels was conducted using specially developed software, which automated model construction for various combinations of parameters. Subsequently, a comparative analysis of the complexity of their edge function expressions was performed to identify dependencies on parameter values. Experimental studies were carried out for fault-tolerant multiprocessor systems with varying numbers of processors and different maximum allowable failure multiplicities (but not exceeding half of the total number of processors in the system). It was shown that cascade GL-models typically have significantly lower computational complexity compared to standard basic GL-models, especially for systems with a small maximum number of allowed failures. However, in cases where the allowed number of failures equals or exceeds half of the processor count, standard models may become less complex. Based on the conducted analysis, practical recommendations for selecting the parameters of cascade GL-models were formulated for the first time. In particular, the lowest complexity is achieved when the fault tolerance coefficient of the auxiliary model is minimized at each cascade level; however, this leads to a maximal cascade depth. If cascade depth is limited, the lowest complexity is achieved by evenly or nearly evenly distributing the fault-tolerance coefficients among auxiliary models. If an even distribution is impossible, it is advisable to place higher-value coefficients at deeper cascade levels. Experimental results demonstrate that the application of the proposed recommendations can significantly reduce the overall complexity of edge function expressions in the cascade GL-model compared to the basic GL-model, with the effectiveness of the approach increasing as the system size grows.