On the method of building of non-basic GL-models which are formed on combination of edge functions of basic models

Abstract

This work is dedicated to the problem of building GL-models of behavior of non-basic fault-tolerant multiprocessor systems in the failure flow. Such models can be used to calculate the reliability parameters of the latter. The system, depending on the fulfillment of certain conditions, is resistant to failures of various multiplicities. These conditions depend only on the states of the system's processors and can be represented by special Boolean expressions. A method of constructing GL-models of such systems based on combining expressions of the edge functions of auxiliary basic models is proposed. At the same time, the specific feature of the models that were built by the proposed method is that they are based on cyclic graphs. This simplifies the process of evaluating their connectivity and also simplifies the analysis of the model's operation. In addition, this allows using other methods of modifying GLmodels if necessary. The method involves using auxiliary models that have the same number of edges. In order to equalize the number of edges, auxiliary models can be extended with additional edges with edge functions of a special type. It is shown that this extension does not change the behavior of the models. In particular, the procedure of orthogonalization of the Boolean expressions is described, which should be carried out if the conditions can be satisfied simultaneously. It is shown that the expressions of the edge functions of the obtained GL-models, which can be quite complex, can sometimes be significantly simplified. Numerous experiments have been conducted to confirm the adequacy of the models (built by the proposed method) to the behavior of the corresponding systems in the failure flow. The example is given to demonstrate the application of the proposed method. The resulting model is analyzed and shown to correspond to the behavior of the system for which it was built.