Discontinuities and non-monotonicities in Mono-T-Semiflow timed continuous Petri nets

In this work steady-state throughput changes due to firing rate variations in timed continuous Petri nets with infinite server semantics are considered. Two peculiar behaviors may appear: discontinuities and non-monotonicities. None of them are possible in Mono-T-Semiflow (MTS) nets when a certain structural condition, defined on the basis of the steady-state marking, is fulfilled. This work investigates the relation between discontinuities and non-monotonicities when the mentioned condition is not satisfied. First, using a graph-based perspective, such condition is classified using structural objects of the net. Then, the system throughput under firing rate variations is studied taking advantage of this classification. The equivalence between monotonicities and the structural condition is derived, whilst a counterexample shows that for discontinuities the implication goes in one way.