A Resource Allocation Approach for Enforcing Liveness on a Class of Petri Nets

Liveness enforcement is of great importance to resource allocation systems (RASs) since liveness is closely related to their performance and security. Petri nets (PNs) are widely used to analyze, model and control RAS. In this paper, we focus on a class of PNs named weighted systems of simple sequential processes with resources ((WSPR)-P-3), which well model a kind of RASs, and we study how to enforce liveness on (WSPR)-P-3 by allocating resources. First, we present a sufficient condition under which a (WSPR)-P-3 system is live, that is, no strongly connected special resource subnet exists in the system. Then, based on this condition, for a (WSPR)-P-3 with only the initial marking of idle places given, we propose an algorithm that computes an initial marking of resource places, which guarantees the liveness of the (WSPR)-P-3 system. Note that, we do not guarantee that the resulting solution is minimal, 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 minimal.