# Article

 Article title CALCULATION OF FUNCTION OF REALIZABILITY OF PROBLEM SOLUTION ON DISTRIBUTED COMPUTATION SYSTEMS IN CASE OF FAILURES AND RESTORATIONS Authors K.V. Pavsky, V.A. Pavsky Section SECTION III. DISTRIBUTED COMPUTING AND SYSTEMS Month, Year 12, 2016 @en Index UDC 004.272:[519.87:519.248] DOI 10.18522/2311-3103-2016-12-8491 Abstract Modern distributed computer systems (CS) are of large scale and intended to solve problems of varying complexity. The number of nodes in such systems can reach hundreds of thousands of units. Experience shows that times between different types of failure in computer systems can be measured in hours. Such systems have increased requirements for reliability and robustness. De-velopment of effective tools for analyzing the functioning of such systems becomes urgent. Quality of CS functioning is evaluated using the set of indices of: reliability, robustness, realizability of solving problems, etc. Indices of realizability of solving problems characterize the process of solving problems on not absolutely reliable computer systems. Realizability function is the conditional probability that a complex problem represented by a parallel program will be solved in a given time on a CS functioning with a given number of working elementary machines (EM) and using for solution all the working EMs. The paper proposes a stochastic model of the functioning of computer systems at solving complex problems. The formulas of function for calculating the realizability of solving tasks in distributed computer systems are proposed. The derivation of equation for calculating the efficiency indices is based on the assumption that the time of problem solution on CS is a function of time of problem solution on one elementary machine, and the function has a finite number of discontinuities. The discontinuities have the probabilistic character and correspond to the CS failures which require reconfiguration of the CS (structure readjustability with regard to working machine only). Calculation of the obtained expression is executed by using approximation calculation. The example for calculation of the probability of solving problem in a given time on a computer system is presented. Download PDF Keywords Distributed computer systems; failures; renewal; stochastic model; realizability function of solving problems. References 1. TOP500 Supercomputers Official Site. TOP500 Lists. Available at: http://www.top500.org. 2. Dongarra J.J., A.J. van der Steen. 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