Policy mixtures: a novel approach for enhancing the operational flexibility of resource allocation systems with alternate routings

Liveness-enforcing supervisors (LESs) guarantee deadlock-free operations in resource allocation systems (RASs). Given the growing emphasis on higher resource utilization and operational flexibility, it is greatly desirable to obtain the optimal LES that can provide the maximum behavioral latitude. In general, however, computation of the maximally permissive LES is computationally intractable and, accordingly, the class of algebraic LESs has been proposed in the literature as a viable suboptimal alternative for various RAS classes. The objective of this work is to further enhance the permissiveness of algebraic LESs by taking advantage of the routing flexibility inherent in contemporary RASs. Specifically, we consider a class of algebraic LES that allows supervisor parameterizations based on the system routing flexibility, and propose a method to effectively mix the algebraic LESs obtained from the policy instantiation through a set of different parameter values. The resulting policy mixture, to be called dynamic algebraic LES, provides increased permissiveness as it allows flexible online switching among different resource reservation schemes, corresponding to different process routings. The proposed method for constructing the dynamic algebraic LES is presented in the context of the class of conjunctive/disjunctive RASs, which subsumes the major RAS classes currently studied in the literature.