/faculteit technologie management PN-1 Petri nets refresher Prof.dr.ir. Wil van der Aalst Eindhoven University of Technology, Faculty of Technology Management,

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Presentation transcript:

/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 High level Petri nets Extending classical Petri nets with color, time and hierarchy (informal introduction)

/faculteit technologie management PN-3

/faculteit technologie management PN-4

/faculteit technologie management PN-5

/faculteit technologie management PN-6 The number of tokens produced is no longer fixed (1) Note that the network structure is no longer a complete specification!

/faculteit technologie management PN-7 The number of tokens produced is no longer fixed (2) The number of tokens produced for each output place is between 0 and 3 and the sum should be 3.

/faculteit technologie management PN-8 Example Model as a colored Petri net.

/faculteit technologie management PN-9 The entire stock is represented by the value of a single token, i.e., a list of records. Product and quantity are in the value of the token

/faculteit technologie management PN-10 Types color Product = string; color Number = int; color StockItem = record prod:Product * num:Number; color Stock = list StockItem; StockItem Stock

/faculteit technologie management PN-11

/faculteit technologie management PN-12

/faculteit technologie management PN-13

/faculteit technologie management PN-14

/faculteit technologie management PN-15 Extension with time (1) Each token has a timestamp. The timestamp specifies the earliest time when it can be consumed.

/faculteit technologie management PN-16 Extension with time (2) The enabling time of a transition is the maximum of the tokens to be consumed. If there are multiple tokens in a place, the earliest ones are consumed first. A transition with the smallest firing time will fire first. Transitions are eager, i.e., they fire as soon as they can. Produced token may have a delay. The timestamp of a produced token is the firing time plus its delay.

/faculteit technologie management PN-17 Running example: Enabling time Transition start is enabled at time 2 = max{0,min{2,4,4}}.

/faculteit technologie management PN-18 Running example: Delays Tokens for place busy get a delay of = firing time plus 3 time units

/faculteit technologie management PN-19 Running example: Transition start fired Transition start fired a time 2. Continue to play (timed) token game…

/faculteit technologie management PN-20

/faculteit technologie management PN-21

/faculteit technologie management PN-22 Exercise: Final state?

/faculteit technologie management PN-23 Exercise: Final state?