Compositional Analysis of Hierarchical UML Statecharts

Quantitative evaluation of stochastic models supports early verification of design choices and assessment of non-functional requirements. Model Driven Engineering (MDE) leverages automated derivation of formal stochastic models from semi-formal artifacts of the Unified Modeling Language (UML) to facilitate deployment of quantitative evaluation methods without disrupting industrial practices. As a major limitation, when generally distributed (GEN) temporal parameters are considered to enhance the model expressivity, the structure and complexity of the underlying stochastic process cannot be easily controlled, possibly impairing the model analyzability. We present a hierarchical modeling formalism based on UML statecharts with GEN durations, designed to guarantee ease of modeling and efficient evaluation of steady-state or transient behaviour until absorption. To this end, fairly lax restrictions are applied to the model syntax to enable separate analysis of the Semi-Markov Process (SMP) underlying each model component. Scalability of solution is assessed by analyzing a suite of synthetic models referred to the context of timed Failure Logic Analysis (FLA) of component-based systems, specifically designed to point out each factor of computational complexity. Notably, the analysis derives both the probability that the system is in each step before failure and the Cumulative Distribution Function (CDF) of the duration of the overall failure process. A challenging case study that significantly and jointly stresses the main factors of computational complexity is finally addressed, performing steady-state analysis of a non-Markovian variant of a server virtualized system from the literature on software rejuvenation.