Ergodicity and Throughput Bounds of Petri Nets with Unique Consistent Firing Count Vector

This paper addresses ergodicity and throughput bounds characterizations for a subclass of timed and stochas-tic Petri nets, interleaving qualitative and quantitative theories. The considered nets represent an extension of the well known subclass of marked graphs, deened as having a unique consistent ring count vector, independently of the stochastic interpretation of the net model. In particular, persistent and mono-T-semiiow nets subclasses are considered. Upper and lower throughput bounds are computed using linear programming problems deened on the incidence matrix of the underlying net. The bounds proposed here depend on the initial marking and the mean values of the delays but not on the probability distributions (thus including both the deterministic and the stochastic cases). From a diierent perspective, the considered subclasses of stochastic nets can be viewed as special classes of synchronized queueing networks, thus the proposed bounds can be applied to these networks.