/faculteit technologie management PN-1 Petri nets refresher Prof.dr.ir. Wil van der Aalst Eindhoven University of Technology, Faculty of Technology Management, Department of Information and Technology, P.O.Box 513, NL-5600 MB, Eindhoven, The Netherlands.

/faculteit technologie management PN-2 Process modeling Emphasis on dynamic behavior rather than structuring the state space Transition system is too low level We start with the classical Petri net Then we extend it with: –Color –Time –Hierarchy

/faculteit technologie management PN-3 Classical Petri net Simple process model –Just three elements: places, transitions and arcs. –Graphical and mathematical description. –Formal semantics and allows for analysis. History: –Carl Adam Petri (1962, PhD thesis) –In sixties and seventies focus mainly on theory. –Since eighties also focus on tools and applications (cf. CPN work by Kurt Jensen). –“Hidden” in many diagramming techniques and systems.

/faculteit technologie management PN-4 Elements

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/faculteit technologie management PN-7 Rules Connections are directed. No connections between two places or two transitions. Places may hold zero or more tokens. First, we consider the case of at most one arc between two nodes.

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/faculteit technologie management PN-9 Rules Connections are directed. No connections between two places or two transitions. Places may hold zero or more tokens. First, we consider the case of at most one arc between two nodes.

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/faculteit technologie management PN-11 Enabled A transition is enabled if each of its input places contains at least one token. enabled Not enabled

/faculteit technologie management PN-12 Firing An enabled transition can fire (i.e., it occurs). When it fires it consumes a token from each input place and produces a token for each output place. fired

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/faculteit technologie management PN-14 Play “Token Game” In the new state, make_picture is enabled. It will fire, etc.

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/faculteit technologie management PN-19 Remarks Firing is atomic. Multiple transitions may be enabled, but only one fires at a time, i.e., we assume interleaving semantics (cf. diamond rule). The number of tokens may vary if there are transitions for which the number of input places is not equal to the number of output places. The network is static. The state is represented by the distribution of tokens over places (also referred to as marking).

/faculteit technologie management PN-20 Non-determinism Two transitions are enabled but only one can fire

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/faculteit technologie management PN-22 Example: Single traffic light

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/faculteit technologie management PN-24 Two traffic lights OR

/faculteit technologie management PN-25 Problem

/faculteit technologie management PN-26 Solution How to make them alternate?

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/faculteit technologie management PN-28 Elements

/faculteit technologie management PN-29 Playing the “Token Game” on the Internet Applet to build your own Petri nets and execute them: pn_applet/pn_applet.htm FLASH animations:

/faculteit technologie management PN-30 Exercise: Train system (1) Consider a circular railroad system with 4 (one- way) tracks (1,2,3,4) and 2 trains (A,B). No two trains should be at the same track at the same time and we do not care about the identities of the two trains.

/faculteit technologie management PN-31 Exercise: Train system (2) Consider a railroad system with 4 tracks (1,2,3,4) and 2 trains (A,B). No two trains should be at the same track at the same time and we want to distinguish the two trains.

/faculteit technologie management PN-32 Exercise: Train system (3) Consider a railroad system with 4 tracks (1,2,3,4) and 2 trains (A,B). No two trains should be at the same track at the same time. Moreover the next track should also be free to allow for a safe distance. (We do not care about train identities.)

/faculteit technologie management PN-33 Exercise: Train system (4) Consider a railroad system with 4 tracks (1,2,3,4) and 2 trains. Tracks are free, busy or claimed. Trains need to claim the next track before entering.