A Decomposition-Based Modeling Framework for Complex Systems

Stochastic model-based approaches are widely used for performability evaluation of complex software/hardware systems. Many techniques have been developed to mitigate the complexity of the associated models, but most of them are domain-specific, and they support the analysis of a limited class of systems. This paper provides a contribution in the definition of a general modeling framework that adopts three different types of decomposition techniques to deal with model complexity. First, a functional decomposition is applied at the system-level, thus identifying a set of subsystems, called entities, each one performing a function with respect to the validation objectives. The entities can interact with each other through some dependency relations that state how the behavior of each entity can affect the other(s). Then a temporal decomposition is used to divide the system's lifetime in a sequence of phases such that two consecutive phases have at least one different dependency relation. Last, a model-level decomposition produces a set of separate sub-models that can be solved in isolation, passing some intermediate results between them, if and when required. This modeling framework has been applied to analyze a General Packet Radio Service (GPRS) mobile telephone system. The purpose of this case-study is to demonstrate the applicability of the framework, in terms of its computational complexity, and the accuracy of the obtained results. The proposed approach provides results sufficiently accurate, though it induces some acceptable approximation. Moreover, it significantly reduces the computational complexity with respect to solving the whole non-decomposed model, and shows only a slight increase in complexity with respect to the ad-hoc solution technique specifically developed for the GPRS case-study.