A method for constructing GL-models of behavior under failure flow for complex non-basic fault-tolerant multiprocessor systems

Abstract

The paper proposes a method for constructing GL-models of the behavior of complex non-basic fault-tolerant multiprocessor systems under a failure flow. The aim of the study is to develop a universal approach that enables the formation of an integrated GL-model for systems characterized by multiple independent or weakly coupled operability conditions. Such models can be used, in particular, to evaluate the reliability parameters of the systems under consideration using statistical simulation methods. The study focuses on systems whose operability is determined by the simultaneous fulfillment of several relatively simple conditions, for each of which established methods for constructing GL-models are available (for example, a condition limiting the number of failures within a certain subset of processors). These include, in particular, hierarchical systems composed of multiple subsystems with their own levels of fault tolerance, as well as systems containing specialized processors of different types. The proposed method involves the preliminary construction of auxiliary GL-models for each operability condition; followed by their integration into a unified model through the sequential merging of their graphs via selected vertices (the merged vertices form a single vertex, while the remaining vertices and edges are copied). The order of model merging and the choice of corresponding vertices can be defined arbitrarily, providing flexibility in the structure of the resulting GL-model. Examples of the method’s application are presented, illustrating various options for determining the sequence of merging auxiliary models and selecting the connecting vertices of their graphs, as well as the use of different methods for constructing these models. The scientific novelty of the work lies in the generalization and formalization of the sequential GL-model merging procedure, which makes it possible to combine models of arbitrary structure and type into a unified model of a complex system without compromising the correctness of its behavior. Experimental results confirm that, despite structural differences in the graphs of the obtained models, their behavior on identical input vectors coincides completely and accurately reflects the operation of the fault-tolerant multiprocessor system under a failure flow. It is also shown that the method imposes no restrictions on the construction techniques of GL-models for individual conditions: models of different types can be combined, the conditions do not necessarily correspond to basic systems, and the model graphs may be other than a cycle graph. Furthermore, the paper provides complexity estimates for GL-models constructed by the proposed method, including the number of vertices and edges in their graphs and the overall complexity of edge functions, depending on the characteristics of the corresponding auxiliary models. The practical value of the method is that it enables automated construction of comprehensive models for systems with complex operability conditions and supports efficient reliability evaluation of real multiprocessor systems.