The concept of Maximal Unschedulable Deadline Assignment for optimization in fixed-priority scheduled real-time systems

This paper considers the problem of design optimization for real-time systems scheduled with fixed priority, where task priority assignment is part of the decision variables, and the timing constraints and/or objective function linearly depend on the exact value of task response times (such as end-to-end deadline constraints). The complexity of response time analysis techniques makes it difficult to leverage existing optimization frameworks and scale to large designs. Instead, we propose an efficient optimization framework that is three orders of magnitude (1000 times) faster than Integer Linear Programming (ILP) while providing solutions with the same quality. The framework centers around three novel ideas: (1) an efficient algorithm that finds a schedulable task priority assignment for minimizing the average worst-case response time; (2) the concept of Maximal Unschedulable Deadline Assignment (MUDA) that abstracts the schedulability conditions, i.e., a set of maximal virtual deadline assignments such that the system is unschedulable; and (3) a new optimization procedure that leverages the concept of MUDA and the efficient algorithm to compute it.