On performance monotonicity and basic servers semantics of continuous Petri nets

Continuous Petri nets were introduced as an approximation to deal with the state explosion problem which can appear in discrete event models. When time is introduced, the flow through a fluidified transition can be defined in many ways. The most used in literature are infinite and finite servers semantics. Both can be seen as derived from stochastic Petri nets. The practical problems addressed in this contribution are: (1) a sufficient condition for the performance monotonicity, and (2) a study of the transition semantics, always related to continuous Petri nets. We prove that under some conditions, the subclass of mono-T-semiflow is monotone and also for the same class of nets we prove a property for which infinite servers semantics offers a better approximation than finite servers semantics for the discrete model