Synthesis of a Mathematical Model of a Fault-Tolerant Real-Time Computer System Operating in Non-positional Arithmetic in Residual Classes

In this article, the synthesis of a mathematical model of a fault-tolerant computer system (CS) is carried out. At the same time, a special-purpose CS is considered, designed based on non-positional arithmetic in residual classes (NPARC). The use of the NPARC as the numeral system (NS) of the real-time CS (RTCS) provides ultra-high speed for the implementation of arithmetic operations, and can also provide higher reliability values than in the case of using positional binary NS in the RTCS. However, to date, the important fact of the influence of the NPARC on the fault tolerance of the RTCS has not been considered in detail. This circumstance determines the purpose of the article – to synthesize a mathematical model of a fault-tolerant RTCS operating in the NPARC. In order to carry out the synthesis of a mathematical model of fault-tolerance of RTCS, functioning in the NPARC, the direct and inverse tasks of optimal reservation in the NPARC are formulated and solved in the article. On the basis of the obtained results of solving the task of optimal reservation in the NPARC, mathematical models of fault tolerance of RTCS for various l-byte discharge grids are synthesized. The presented mathematical models are implemented by the method of passive fault tolerance (persistent reservation). It is shown that the use of the NPARC provides no less value of fail-safe feature of RTCS than the practical methods of increasing fault tolerance widely used in the positional binary NS. This is achieved with a smaller additionally introduced amount of structural redundancy, which is especially important for the RTCS of various special aircraft.