Converting existing analysis to the EDP resource model

In (hard) real-time embedded systems, it is necessary to guarantee that tasks always meet their deadlines i.e. results should neither be too early nor too late. In the context of fixed-priority systems, this is usually done by performing schedulability analysis in which the (best-case and) worst-case response-time of each task is computed and compared with its (best-case) worst-case deadline to determine schedulability. Resource reservation has been proposed as a means to provide temporal isolation between applications. Building upon this notion, hierarchical scheduling frameworks for different resource models have been proffered in the literature with complementary schedulability conditions. Unfortunately, these novel ideas do not directly allow for the reuse of existing results, but rather favor derivations from first principles. In this document, we investigate a means to reuse existing results from non-hierarchical scheduling theory by modeling the unavailability of a resource in a two-level hierarchical framework using two fictive tasks with highest priorities. We show that this novel method using our unavailability model not only allows for unifying the analysis but can also be easily applied in determining linear response-time upper bounds. For the latter, we also consider approaches for obtaining tighter bounds for harmonic tasks