Second-order properties of families of discrete event systems

This paper deals with the comparison of the event occurrence processes of one family of discrete event systems (DES) with those of another. The DES we consider include certain timed Petri-nets and generalized semi-Markov schemes, though we study them in a general framework that ignores the underlying state transition mechanism. First, we obtain two results on comparing a single DES with a family of others. As a consequence of these two results we prove the “near” concavity of the throughput of min-linearly constrained DES in various system parameters. This not only covers various known concavity results for tandems, cycles, and fork-join networks of stations with general blocking and starvation, but also establishes new ones for certain classes of networks which involve splitting and merging of traffic streams. Finally, we motivate some preliminary work on establishing comparisons between families of discrete event systems with a novel proof of the optimality of the round-robin policy in routing jobs to homogeneous queues in parallel