Establishment of Basic Valid Petri Net Model <br>Below some basic valid Petri Net models are defined. These basic models possess the properties of being bounded, live, and reversible. A complex manufacturing system can be achieved by extending these basic models according to Petri Net valid extension theorem. A simple serial system is depicted in Figure 3a. Once the initial fire condition m,,=( 1, 0 )I, is satisfied, the system can run recurrently. Figure 3b is the generalized model of serial system. For parallel system, as depicted in Figure 3c, the initial fire condition is rnk( I, 1 ,..., 1, 0, O,.. .,O )T, where placep, through p. initially contain tokens and places h+tl through p.+,,, do not. Figure 3d is a valid Petri Net model for series- parallel system. The validity of these models are easy to prove (Yuan 1998).
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