Control theory for model-based performance-driven software adaptation

Self-adaptive techniques have been introduced in the last few years to tackle the growing complexity of software systems, where a major complexity factor leans on their dynamic nature subject to sudden and unpredictable changes that can heavily impact on the software architecture quality. Non-functional models, as generated from architectural descriptions of software, have been proven as effective instruments to support designers meeting non-functional requirements since the early architectural phases. However, such models still lack of intrinsic support for adaptable software. Goal of this paper is to extend the modeling capabilities to the case of software adaptation aimed at satisfying performance requirements. In particular, we illustrate how control theory can solve the problem of keeping within pre-defined ranges the indices of a Queueing Network model (such as queue length) through software adaptation actions (such as replacing software services with less resource-demanding ones), while the model is subject to disturbances (such as workload and/or operational profile variations). For this goal we first introduce a library of Modelica components that represent Queueing Network (QN) elements with adaptable parameters (that can be used as knobs for adaptation actions). Then we use such components to build ``adaptable`` QN models that are subject to disturbances. Finally, in the same framework, we introduce controllers that drive the QN adaptation. We demonstrate the soundness of our approach on a simple representative example in two ways: (i) on one end, we provide a formal proof of controller performance guarantees, and (ii) on the other end we show the sensitivity over time of software adaptation actions to different (types and intensities of) disturbances.