Liveness Enforcement for a Class of Petri Nets via Resource Allocation

This work focuses on a class of Petri nets (PNs) called Weighted Systems of Simple Sequential Processes with Resources ((WSPR)-P-3). We study how to enforce liveness to (WSPR)-P-3 by appropriately allocating resources. A sufficient condition that guarantees liveness of a net system in this class is first derived. Then, based on such a condition, we propose an algorithm that computes an initial marking of resource places that guarantees the liveness of a (WSPR)-P-3 system where the initial marking of the idle places is given. Note that, we do not guarantee that the resulting solution is optimal, in the sense that a smaller initial marking of resource places that still leads to liveness could exist. However, several numerical examples show that the solution resulting from the proposed approach is optimal.