Interrupt Timed Automata (ITA) are an expressive timed model, introduced to take into account interruptions according to levels. Due to this feature, this formalism is incomparable with Timed Automata. However several decidability results related to reachability and model checking have been obtaine d. We add auxiliary clocks to ITA, thereby extending its expressive power while preserving decidability of reachability. Moreover, we define a parametrized version of ITA, with polynomials of parameters appearing in guards and updates. While parametric reasoning is particularly relevant for timed models, it very often leads to undecidability results. We prove that various reachability problems, including robust reachability, are decidable for this model, and we give complexity upper bounds for a fixed or variable number of clocks, levels and parameters.

We provide a subclass of parametric timed automata (PTA) that we can actually and efficiently analyze, and we argue that it retains most of the practical usefulness of PTA for the modeling of real-time systems. The currently most useful known subclass of PTA, L/U automata, has a strong syntactical restriction for practical purposes, and we show that the associated theoretical results are mixed. We therefore advocate for a different restriction scheme: since in classical timed automata, real-valued clocks are always compared to integers for all practical purposes, we also search for parameter values as bounded integers. We show that the problem of the existence of parameter values such that some TCTL property is satisfied is PSPACE-complete. In such a setting, we can of course synthesize all the values of parameters and we give symbolic algorithms, for reachability and unavoidability properties, to do it efficiently, i.e., without an explicit enumeration. This also has the practical advantage of giving the result as symbolic constraints between the parameters. We finally report on a few experimental results to illustrate the practical usefulness of our approach.