On the duality between firing rate and initial marking variations in TCPN

Abstract

A performance measure which is often used when evaluating systems modeled by Petri nets is the throughput of a transition in steady-state, i.e., the number of firings per unit time in permanent regime if it exists. When fluid Petri nets are considered, such measure corresponds to the continuous flow of the transitions. Its value depends on the firing rates associated to transitions and also on the initial marking of the net. In this work two properties of the steady-state throughput, monotonicity and continuity, are studied under firing rate and initial marking variations. It is shown that in certain cases there exists a kind of duality between both type of changes, that is, some property eventually holds no matter if firing rate or initial marking is varied. These results are obtained in a structural framework using the P-flows, T-flows, and configurations of the net model.