Quantitative schedulability analysis of continuous probability tasks in a hierarchical context

We define the concept of degree of schedulability to characterize the schedulability and performance of soft real-time systems. The degree of schedulability of a system is given in terms of the two factors 1) Percentage of Missed Dead- lines (PoMD); and 2) Degradation of the Quality of Service (DoQoS). Our work is set as a model-based framework for hierarchical scheduling systems where we introduce probability based sporadic tasks. The novel aspect is that we consider task arrival patterns that follow user-defined continuous probability distributions. The separately modeled task triggering events represent the system environment. We determine the degree of schedulability of a single scheduling component which can contain both periodic and sporadic tasks using statistical model checking in the form of UPPAAL SMC. Finally, we show the applicability of our framework by analyzing an avionics case study.