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Modeling and analysis of timed Petri nets using heaps of pieces

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2 Author(s)
Gaubert, S. ; Inst. Nat. de Recherche en Inf. et Autom., Le Chesnay, France ; Mairesse, J.

The authors show that safe timed Petri nets can be represented by special automata over the (max, +) semiring, which compute the height of heaps of pieces. This extends to the timed case the classical representation a la Mazurkiewicz of the behavior of safe Petri nets by trace monoids and trace languages. 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 modeling by the typical case of safe jobshops. For a periodic schedule, the authors obtain a heap-based throughput formula, which is simpler to compute than its traditional timed event graph version, particularly if one is interested in the successive evaluation of a large number of possible schedules

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Automatic Control, IEEE Transactions on  (Volume:44 ,  Issue: 4 )