Statistical and exact schedulability analysis of hierarchical scheduling systems

Abstract

Abstract This paper contains two contributions: 1) A development methodology involving two techniques to enhance the resource utilization and 2) a new generic multi-core resource model for hierarchical scheduling systems. As the first contribution, we propose a two-stage development methodology relying on the adjustment of timing attributes in the detailed models during the design stage. We use a lightweight method (statistical model checking) for design exploration, easily assuring high confidence in the correctness of the models. Once a satisfactory design has been found, it can be proved schedulable using the computation costly method (symbolic model checking). In order to analyze a hierarchical scheduling system compositionally, we introduce the notion of a stochastic supplier modeling the supply of resources from each component to its child components in the hierarchy. We specifically investigate two different techniques to widen the set of provably schedulable systems: 1) a new supplier model; 2) restricting the potential task offsets. We also provide a way to estimate the minimum resource supply (budget) that a component is required to provide. In contrast to analytical methods, we prove non-schedulable cases via concrete counterexamples. By having richer and more detailed scheduling models this framework, has the potential to prove the schedulability of more systems. As the second contribution, we introduce a generic resource model for multi-core hierarchical scheduling systems, and show how it can be instantiated for classical resource models: Periodic Resource Models (PRM) and Explicit Deadline Periodic (EDP) resource models. The generic multi-core resource model is presented in the context of a compositional model-based approach for schedulability analysis of hierarchical scheduling systems. The multi-core framework presented in this paper is an extension of the single-core framework used for the analysis in the rest of the paper