Robustness Analysis for Scheduling Problems Using the Inverse Method

Given a Parametric Timed Automaton (PTA) A and a reference valuation for timings, the Inverse Method (IM) synthesizes a constraint around the reference valuation where A behaves in the same time-abstract manner. This provides us with a quantitative measure of robustness of the behavior of A around the reference valuation. We show in this paper how IM can be applied in a specific way to treat the robustness of scheduling systems. We also explain how to use the method in order to synthesize large zones of the timing parameter space where the system is guaranteed to be schedulable. We illustrate the method on several examples of the literature as well as a case study originating from an industrial design project.