Abstract
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.
Highlights
In the engineering of non-functional requirements of software intensive systems, quantitative evaluation of stochastic models supports early assessment of design choices and provides model-driven guidance for development and operation
Practices of Model Driven Engineering (MDE) [23], [75] and automated model transformation have been widely investigated to reconciliate these contrasting needs [3], [49], [71] by deriving formal stochastic models from semi-formal artifacts of the Unified Modeling Language (UML). These artfacts are often extended by the profile for Modeling and Analysis of Real-Time Embedded systems (MARTE) [67], [8] the profile for Dependability Analysis and Modeling (DAM) [7], or the Systems Modeling Language (SysML) [68], with behavioral characteristics captured by various combinations of use case, sequence, and activity diagrams, and statecharts
To perform timed Failure Logic Analysis (FLA) of the considered class of systems, transient evaluation of the system behavior is needed to characterize the time spent in each step of the failure process and the probability that it is completed within a given time
Summary
In the engineering of non-functional requirements of software intensive systems, quantitative evaluation of stochastic models supports early assessment of design choices and provides model-driven guidance for development and operation. The applicability of non-Markovian solution methods turns out to be fragile, unless the formalism for the expression of the high-level model is explicitly designed to obtain structure and parameters that make the underlying stochastic process amenable to efficient solution techniques Pursuing the latter approach, a numerical method is presented in [26], [27] to perform availability analysis of a system specified as a dynamic fault tree, exploiting the model structure to compute stochastic bounds on the distribution of the time to failure and evaluate different maintenance policies for the system components. We extend the approach of [38], [11] into a comprehensive methodology for quantitative modeling and analysis of non-Markovian systems specified as an extension of statecharts1 In this formalism, parallel regions including steps with GEN duration are synchronized through operators supporting hierarchical composition of the underlying SemiMarkov Processes (SMPs). We describe them here through a metamodel and a running example (Section 2.1) and we characterize their underlying stochastic process (Section 2.2)
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