Modeling and analysis of timed Petri nets using heaps of pieces

The authors show that safe timed Petri nets can be represented by special a utomata over the (max, +) semiring, which compute the height of heaps of pi eces. This extends to the timed case the classical representation a la Mazu rkiewicz of the behavior of safe Petri nets by trace monoids and trace lang uages. For a subclass including all safe free-choice Petri nets, we obtain reduced heap realizations using structural properties of the net (covering by safe state machine components), The authors illustrate the heap-based mo deling by the typical case of safe jobshops, For a periodic schedule, the a uthors obtain a heap-based throughput formula, which is simpler to compute than its traditional timed event graph version, particularly if one is inte rested in the successive evaluation of a large number of possible schedules .