In: IEEE Trans. Autom. Control, Vol. 44, No. 4, pages 683-697. 1999.
Abstract: We 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 á 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). We illustrate the heap-based modeling by the typical case of safe jobshops. For a periodic schedule, we 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.
Keywords: Timed Petri nets; automata with multiplicities; heaps of pieces; (max,+) semiring; scheduling.
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