Second-order properties of families of discrete-event systems

We consider discrete-event systems (DES) whose logical component is characterized by a constraint set and whose temporal mechanism involves synchronization of the clock sequence with a master clock. We are interested in determining sufficient conditions on the constraint sets of a family of such synchronous DES which ensure that the event counting process of one system dominates the convex combination of the event counting processes of a collection of systems. Our point of departure is a result due to Glasserman and Yao (1992), which established a sufficient condition based on characteristic functions. We show that the characteristic function condition is equivalent to a simpler condition on the score spaces themselves, and introduce coevality to obtain weaker sufficient conditions. We prove the near-concavity of the throughput in various parameters for min-linearly constrained DES. These results are then extended to the class of generalized min-linearly constrained DES