The method of constructing a GL-model for a consecutive k-out-of-n system

Abstract

The paper is devoted to the method of constructing GL-models of the behavior of multiprocessor systems in a failure flow, in particular, consecutive k-out-of-n systems are considered, whose main characteristic is the failure of the system when a certain number of processors connected consecutively fail. The GL-models under construction are based on the basic models with a minimum number of lost edges. It has been determined that to build a GL-model of systems of this type, it is sufficient to calculate the maximum possible number of failed processors at which the system remains operational. A GL-model of a system that can handle this number of failures is built without considering the consecutive failures. The next step is to determine all possible consecutive failures that cause the system to fail, and the model is modified to reflect the system failure when consecutive failures occur. The paper describes a method for calculating the maximum allowable number of failures at which the system remains operational. An example of building GL-models for consecutive k-out-of-n systems is given.