Перегляд за Автор "Nikolsky, Serhii"
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Документ Mathematical model of computer system reliability in residual classes(Національний технічний університет "Харківський політехнічний інститут", 2022) Krasnobayev, Victor; Koshman, Serhii; Nikolsky, Serhii; Kovalchuk, DmytroThe subject of the article is the construction of a mathematical model of the reliability of a computer system (CS) that operates in a system of residual classes (RNS). This mathematical model is based on the use of structural sliding reservation. The purpose of the article is to increase the reliability of the CS, which operates in the system of residual classes, as well as to calculate and compare the reliability, in terms of the probability of failure-free operation, of the CS in the RNS and the ternary computing system, which operates in the positional binary number system (PBNS). Tasks: to analyze the influence of the number system used on the reliability of the CS; to investigate the properties of the RNS and determine their influence on the structure of the CS in the RNS; build a mathematical model of reliability and, on its basis, perform the calculation and comparative analysis of the reliability of the CS in the RNS and the tripled CS in the PBNS. Research methods: methods of analysis and synthesis of computer systems, number theory, coding theory in RNS, reliability theory. The following results are obtained. The paper shows that the provision of a given level of reliability in the design of the CS using the RNS is due to the presence of various types of redundancy at the same time: structural, informational, temporal, functional and load. In RNS, these types of redundancy can be effectively used to improve the reliability of the CS. The CS in the RNS represents a computational structure that is identical in structure and principle of operation to the sliding structural redundancy model in the PBNS in the case of a loaded (hot) mode of operation of the redundant elements. Proceeding from this, the paper presents a mathematical model of the reliability of the CS in the RNS. In this paper, the calculation and comparative analysis of the reliability of a tripled computing structure in a PBNS with an ideal majority element and a CS in an RNS with an ideal reliability automaton are carried out. Conclusions. As shown by the results of calculations and comparative analysis in some time intervals of operation, the probability of non-failure operation of the CS in the RNS is higher than the probability of non-failure operation of the aircraft in the PBNS with a tripled majority structure. This implies the effective use of the RNS to improve the reliability of the CS.Документ Method for diagnosing data errors of a computer system functioning in the system of residual classes(Національний технічний університет "Харківський політехнічний інститут", 2021) Koshman, Serhii; Krasnobayev, Victor; Nikolsky, SerhiiThe subject of the article is the development of a method for diagnosing data errors of a computer system functioning in the residue number system (RNS). This method is based on the tabular principle of data diagnostics operation implementation. The purpose of the article is to reduce the time of performing the operation of diagnosing the data of a computer system that functions in the RNS in the dynamics of the computational process. Tasks: to analyze the possible application of RNS as a number system in computer data processing systems; to investigate existing methods of data diagnostics and identify possible shortcomings in data diagnostics in the dynamics of the computational process with the introduction of minimal information redundancy; to develop a method for diagnosing the data presented in the RNS, which is based on the tabular principle of the implementation of the diagnostic operation. Research methods: methods of analysis and synthesis of computer systems, number theory, coding theory in RNS. The following results were obtained. The work shows that the data diagnostics is carried out after the control operation has been performed. To carry out the operation of diagnosing data in the RNS, when one-time errors occur, methods for determining an alternative set (AS) of numbers are used. In this case, the main disadvantage of the considered methods is the considerable time required to determine the AS. To reduce the time for determining the AC numbers in the work, the method for diagnosing data in the RNS has been improved. Improvement of the method involves the compilation of a table (the first stage) of correspondence to each correct number of a possible set of incorrect numbers when one-time errors occur in the data. Based on the analysis of the contents of the table of the first stage, a table (of the second stage) is drawn up of the correspondence of each incorrect number to the possible values of the correct numbers. Conclusions. The use of the improved method increases the efficiency of diagnostics of the data presented in the RNS by reducing the time for determining the AC numbers. This is achieved by quickly fetching pre-calculated AC table values.Документ The structure of the computer system in the residual classes(Національний технічний університет "Харківський політехнічний інститут", 2023) Koshman, Serhii; Krasnobayev, Victor; Nikolsky, Serhii; Kovalchuk, DmytroThe subject of the article is the formulation and solution of the inverse problem of optimal redundancy in the system of residual classes (RNS) based on the use of the dynamic programming method. The solution of this problem makes it possible to improve the reliability of the operation of computer systems and components (CSC) in the RNS. The purpose of the article is to increase the reliability of the functioning of CSC, which are built on the basis of the use of RNS, without reducing the speed of calculations, as well as to calculate and compare the reliability, in terms of the probability of failure-free operation, of CSC in RNS and a tripled computing system that operates in a positional binary number system (PNS). Tasks: to analyze the influence of the number system used on the reliability of the CSC, taking into account the primary and secondary redundancy; to synthesize a computing system in RNS for a l-byte bit grid based on the use of the passive fault tolerance method (constant structural redundancy); formulate and solve the inverse problem of optimal redundancy in RNS based on the use of the dynamic programming method; to check the correctness of the results obtained, calculate the conditional amount of computer system equipment in the residual classes; evaluate the efficiency of using RNS to improve reliability when building a redundant CSC in relation to a redundant CSC in the PNS. Research methods: methods of analysis and synthesis of computer systems, number theory, coding theory in RNS, reliability theory. The following results are obtained. The paper shows that the use of PNS as a number system does not allow a radical increase in the performance and reliability of CSC. In this regard, the article developed the concept of using RNS as a number system for constructing a CSC. Based on this, the inverse problem of optimal redundancy in RNS is formulated and solved. Conclusions. As shown by the results of calculations and comparative analysis, the use of RNS provides a higher reliability of the CSC than the majority three-channel computing system in the PNS. The obtained research results can be used for the synthesis of fault-tolerant computer structures in RNS.