Largeness Avoidance in Availability Modeling using Hierarchical and Fixed-point Iterative Techniques

Accurate modeling of availability is a practical problem in today’s complex high-availability systems. But as the system gets more complex, the state-space required for accurate modeling tends to grow very fast. In order to mitigate the largeness in model generation / solution, the system model could be divided into subsystem models, and solution for sub-models can be combined to yield overall model solution. Such hierarchical composition techniques reduce the state-space tremendously. But simple hierarchical techniques provide exact results only when sub-model solutions are independent. In many scenarios, some components or procedures are shared across subsystems, which violate independence in sub-model solution. Hence approximation techniques like nearly independent systems are required to model systems where submodel solutions are dependent. This paper demonstrates approximation techniques for availability modeling for a fluid pressure control system using the concepts of nearly independent subsystems and fixed-point iteration.