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Petri Nets Refresher: Understanding Classical Petri Nets and Extensions

Refresh your knowledge on classical Petri nets and their extensions with an emphasis on dynamic behavior, color, time, and hierarchy. Learn about process modeling and the principles of firing and transition in Petri nets. Dive into Petri nets history and key elements and rules for modeling. Explore Petri nets applications and solve exercise scenarios related to train systems.

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Petri Nets Refresher: Understanding Classical Petri Nets and Extensions

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  1. Petri netsrefresher 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.

  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

  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.

  4. Elements

  5. 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.

  6. Elements

  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.

  8. Enabled • A transition is enabled if each of its input places contains at least one token. enabled Not enabled Not enabled

  9. 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

  10. Play “Token Game” • In the new state, make_picture is enabled. It will fire, etc.

  11. 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).

  12. Non-determinism Two transitions are enabled but only one can fire

  13. Example: Single traffic light

  14. Two traffic lights OR

  15. Problem

  16. Solution How to make them alternate?

  17. Elements

  18. Playing the “Token Game” on the Internet • Applet to build your own Petri nets and execute them: http://is.tm.tue.nl/staff/wvdaalst/workflowcourse/pn_applet/pn_applet.htm • FLASH animations: www.workflowcourse.com

  19. 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.

  20. 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.

  21. 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.)

  22. 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.

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