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

This preview shows pages 1–4. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 12/12/2009 for the course SE 3306 taught by Professor Nhut during the Spring '09 term at University of Texas at Dallas, Richardson.

### Page1 / 8

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online