Fixed Point Iteration in Availability Modeling

This paper presents a fixed point iteration technique for modeling system availability of large fault tolerant systems. The systems modeled are composed of several subsystems having redundant components. Real systems have a large number of subsystems and very general types of interaction between components within a subsystem and between subsystems. Exact solution techniques applied to real systems often result in the generation of a Markov chain with a million or more states which is too large to be solved. Simplifying approximations are often used. However, these approximations often do not account for general types of stochastic dependence between components and between subsystems. The accuracy of such approximations is insufficient in the analysis of many high availability systems.

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