Performability analysis of guarded-operation duration: A translation approach for reward model solutions

Performability measures are often defined for analyzing the worth of fault-tolerant systems whose performance is gracefully degradable. Accordingly, performability evaluation is inherently well suited for application of reward model solution techniques. On the other hand, the complexity of performability evaluation for solving engineering problems may prevent us from utilizing those techniques directly, suggesting the need for approaches that would enable us to exploit reward model solution techniques through problem transformation. In this paper, we present a performability modeling effort that analyzes the guarded-operation duration for onboard software upgrading. More specifically, we define a "performability index" Y that quantifies the extent to which the guarded operation with a duration φ reduces the expected total performance degradation. In order to solve for Y, we progressively translate its formulation until it becomes an aggregate of constituent measures conducive to efficient reward model solutions. Based on the reward-mapping-enabled intermediate model, we specify reward structures in the composite base model which is built on three stochastic activity network reward models. We describe the model-translation approach and show its feasibility for design-oriented performability modeling.