Precise Robustness Analysis of Time Petri Nets with Inhibitor Arcs

Quantifying the robustness of a real-time system consists in measuring the maximum extension of the timing delays such that the system still satisfies its specification. In this work, we introduce a more precise notion of robustness, measuring the allowed variability of the timing delays in their neighbourhood. We consider here the formalism of time Petri nets extended with inhibitor arcs. We use the inverse method, initially defined for timed automata. Its output, in the form of a parametric linear constraint relating all timing delays, allows the designer to identify the delays allowing the least variability. We also exhibit a condition and a construction for rendering robust a non-robust system.