A generalized method for constructing failure-behavior models of fault-tolerant multiprocessor systems with inter-subsystem redundancy

Abstract

Relevance. The evaluation of reliability characteristics of fault-tolerant multiprocessor systems is an important task, particularly during their analysis and design. GL-models of system failure behavior can be used for this purpose. For systems with inter-subsystem redundancy, such models should take into account the possibility of using the processors of a donor subsystem both when the subsystem remains operational and after it loses operability. Existing approaches do not provide a complete representation of these operating modes. Purpose. To develop a generalized method for constructing GL-models of the failure behavior of fault-tolerant multiprocessor systems with inter-subsystem redundancy. Objective. To formalize the principles of constructing GL-models of a donor subsystem taking into account different modes of processor utilization, to develop an algorithm implementing the proposed method, and to perform experimental verification of the correctness of the constructed models. Methods. The study employs the GL-model formalism, methods for constructing basic and auxiliary GL-models, the formation of extended state vectors, and the analysis of graph connectivity. Scientific novelty. A generalized method for constructing GL-models of fault-tolerant multiprocessor systems with inter-subsystem utilization of reserve processors is proposed. Unlike existing approaches, the proposed method takes into account the possibility of using the processors of a donor subsystem both when it remains operational and after it loses operability, when its operational processors may still be used to support other subsystems. Practical significance. The proposed method can be used for constructing GL-models of complex fault-tolerant multiprocessor systems and for the subsequent evaluation of their reliability characteristics. Results. A method and an algorithm for constructing GL-models of systems with inter-subsystem redundancy have been developed. The proposed approach is based on constructing auxiliary models that describe the sets of reserve and operational processors of a donor subsystem and on forming extended state vectors for constructing GL-models of recipient subsystems. Representative examples are considered for systems with limitations on the number of reserve resources and for systems employing sliding redundancy. Experimental studies confirmed the correctness of the constructed models. It is shown that the complexity of the edge-function expressions of the resulting GL-models is comparable to that of the corresponding basic models with equivalent fault-tolerance parameters. Conclusions. The proposed method provides a formal representation of inter-subsystem redundancy within GL-models and can be integrated with other approaches to constructing failure-behavior models of fault-tolerant multiprocessor systems. The experimental results confirm the correctness of the proposed method and demonstrate the feasibility of its application in the analysis and design of complex fault-tolerant multiprocessor systems.