A Practical Approach for Maximally Permissive Liveness-Enforcing Supervision of Complex Resource Allocation Systems

Past works towards the effective deployment of the maximally permissive liveness-enforcing supervisor (LES) for sequential resource allocation systems (RAS) have been stalled by: (i) the NP-Hardness of the computation of this policy for the majority of the considered RAS classes and (ii) the inability of the adopted more compact representations of the underlying RAS dynamics to provide an effective representation of the target policy for all RAS instantiations. This paper proposes a novel approach to the aforementioned problem, that can be perceived as a two-stage process: The first stage computes the maximally permissive LES by employing an automaton-based representation of the RAS behavior and techniques borrowed from the Ramadge & Wonham (R&W) Supervisory Control framework. The second stage seeks the development of a more compact representation for the dichotomy into admissible and inadmissible—or “safe” and “unsafe”—subspaces of the RAS state space, that is effected by the LES developed in the first stage. This compact representation is obtained by: (i) taking advantage of certain properties of the underlying subspaces and (ii) the employment of pertinent data structures. The resulting approach is also “complete,” i.e., it will return an effectively implementable LES for any given RAS instantiation. Numerical experimentation demonstrates the efficacy of the approach and establishes its ability to support the deployment of maximally permissive LES for RAS with very large structure and state spaces.