The Concept of Unschedulability Core for Optimizing Real-Time Systems with Fixed-Priority Scheduling

In the design optimization of real-time systems scheduled with fixed priority, schedulability analysis is used to define the feasibility region within which tasks meet their deadlines, so that optimization algorithms can find the best solution within the region. However, the complexity of schedulability analysis techniques often makes it difficult to leverage existing optimization frameworks and scale to large designs. In this paper, we propose the concept of unschedulability core, a compact representation of the schedulability conditions, and develop efficient algorithms for its calculation. We present a new optimization framework that leverages such a concept. We show that this concept is applicable to a range of optimization problems, for example, when the decision variables include the task priority assignment and the selection of mechanisms protecting shared buffers. Experimental results on two case studies demonstrate that the new optimization procedure maintains the optimality of the solutions, but is a few orders of magnitude faster than other exact algorithms (branch-and-bound, integer linear programming).