petri - Introduction to Petri Nets By Kendra Cooper...

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Introduction to Petri Nets By Kendra Cooper Contents Introduction Original Petri Nets Weighted Petri Nets Other Types of Petri Nets Properties of a Petri Net Problems Introduction Petri nets were developed in the early 1960s by C.A. Petri in his Ph.D. dissertation o C.A. Petri. Kommunikation mit Automaten . PhD thesis, Institut für instrumentelle Mathematik, Bonn, 1962. They are useful for modeling concurrent, distributed, asynchronous behaviour in a system What is a Petri net? Petri Net is a 5 tuple PN = (P,T,F,W,M 0 ), where P = {p1, p2, … pm} is a finite set of places T = {t1, t2, …, tn} is a finite set of transitions F (P X T) (T X P) is a set of arcs W: F {1,2,3,…} is a weighting function M 0 :P {0,1,2,…} is the initial marking // defines number of tokens per place P T = and P T Example p1 p2 t1
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This Petri net has: 2 places: p1, p2 1 transition: t1 p1 has one token: M(p1) = 1 p2 has 0 tokens: M(p2) = 0 Firing a Transition When a transition t fires Each pi that has an edge from pi to t removes a token from pi Each pj that has an edge from t to pj adds a token to pj Example Petri net before t1 fires: Petri net after t1 fires: A transition must be enabled before it fires There is a token in each pi that has an edge to the transition An enabled transition may or may not fire. Example Petri Net before t1 fires: p1 p2 t1 p1 p2 t1
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Petri Net after t1 fires: Original Petri Nets Only 1 token can be removed/added from a place when a transition fires (i.e., the weight is always 1) Weighted Petri Nets Generalized the original Petri net to allow multiple tokens to be added/removed when a transition fires. The edges are labeled with the weight (i.e., number of tokens) If there is no label, then the default value is 1 Example 1 (abstract example) Petri Net before transition t1 fires Petri Net after transition t1 fires p1 p2 t1 p3 p1 p2 t1 p3 p1 p2 t1 p3 2 4 p1 p2 t1 p3 2 4
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petri - Introduction to Petri Nets By Kendra Cooper...

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