Safe and infinite resource scheduling using energy timed automata

We study the existence of infinite and safe schedules for resource-dependent real-time systems, in the setting of multiple continuous resources. Specifically, we explore the multi-variable extension of Energy Timed Automata, where variables are bounded by polyhedra in $R^n$. We ask the question of whether there exist infinite runs satisfying such boundary constraints and show how schedules can be synthesized by characterising these runs as limit sets using quantifier elimination for linear real arithmetic. We show that for linear limit sets, it is possible to characterise such infinite runs.

Additionally, we relate this to an earlier decidability result for single-variable Energy Timed Automata that are flat and segmented, and show constructively that there exist flat and segmented multi-variable Energy Timed Automata that give rise to non-linear limit sets.

Lastly, we solidify our framework and method with a case study. Specifically, a multi-agent extension of an industrial case concerned with oil tanks, originally provided by the HYDAC company.