The “bound reaching problem” on the fluidization of timed Petri nets

Fluidization is a classical technique to overcome the state explosion problem, which consists in relaxing its behaviour, dealing with hybrid or continuous systems. In the Petri nets framework, continuous net systems are the result of removing the integrality constraint in the firing of transitions. This relaxation may highly reduce the complexity of analysis techniques but may not approximate some properties of the original system, such as its throughput. This paper deals with the basic operation of fluidization of discrete timed Petri nets. More precisely, the “bound reaching problem” is identified, which points out the differences between discrete and continuous behaviour in a case in which the probability of a transition to be enabled is low in the discrete case. An approach denoted p-semantics is proposed to tackle this problem and compared with other methods.