Method for constructing GL-models of complex non-basic fault-tolerant multiprocessor systems

Abstract

The paper is devoted to a method for constructing GL-models of the behavior of complex non-basic fault-tolerant multiprocessor systems under a failure flow. Such models can, in particular, be applied to the reliability analysis of these systems using methods based on statistical experiments. The study considers systems whose behavior can be represented by a set of relatively simple conditions, for each of which methods for constructing the corresponding GL-models are available (for example, the occurrence of no more than a specified number of failures within a certain subset of the system’s processors). It is assumed that the operability of the system is maintained only when all these conditions are simultaneously satisfied. In particular, such systems may include so-called hierarchical systems composed of several subsystems, each having a certain level of fault tolerance, as well as systems containing specialized processors of various types. According to the proposed method, models are first constructed for each individual condition, after which they are combined into a unified GL-model by sequentially merging their graphs through specific vertices (these vertices are merged into one, while the remaining vertices and edges are replicated). The sequence of models and the vertices used for merging can be chosen arbitrarily, which allows, if necessary, obtaining a more convenient graph structure for the resulting GL-model. An example illustrating the application of the proposed method is presented. Two variants of model merging – differing in both the sequence of model integration and the vertices used for merging – are examined. Experimental results confirm that, despite differences in the structure of the resulting model graphs, their behavior for identical input vectors coincides and corresponds to the behavior under a failure flow of the fault-tolerant multiprocessor system for which they were constructed. It is also noted that the proposed method imposes no restrictions on the techniques used to build GL-models for individual conditions (models of different types can be combined simultaneously). The conditions do not necessarily correspond to basic systems (i.e., the failure of no more than a specified number of arbitrary processors), and the graphs of the corresponding models may be non-cyclic.