The Thinning Problem

The main problem addressed in this work is how to confine the set of sequential processes of a disjunctive / conjunctive resource allocation system (D/C-RAS) to a subset of their feasible behaviors while optimizing some performance criterion. We provide a canonical characterization of this problem in the form of a Mixed Integer Programming (MIP) formulation, for the case that the optimized performance criterion is the maximization of the system throughput. However, an important additional development of this effort is a complete analytical characterization of the performance control problem of D/C-RAS. This characterization is based on an effective integration of recent results on the liveness-enforcing supervision of D/C-RAS with the theory of Markov Decision Processes, and it concretizes the interaction between the D/C-RAS logical and performance control. Throughout the paper development, a small example highlights the involved concepts and formulations.