29.2 A BRIEF OUTLINE OF PETRI NET THEORY

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There are four basic elements in a petri net; places, transitions, arcs, and tokens. If we are to think in terms of a factory, tokens are equivalent to work parts. Arcs are the paths the work will follow through the factory. Places are buffers where parts are stored temporarily, and transitions are equivalent to machines where the parts are used to make new parts.

The basic operation is that tokens are introduced to the network, and then transitions are fired in different orders, and thus tokens are created and destroyed at the transitions. The example below follows the petri net for a few cycles. The first figure shows the Petri Net with the initial markings.

The reader should note that there are a few interesting properties found in Petri nets.

Transitions are fired when all of their inputs are satisfied, and the user specifies that transition.

Most analysis of petri nets uses random firings of the transitions to obtain statistical performance.

Other basic references to the petri net theory are available in Peterson [1981] and Reisig [1985].