1. /faculteit technologie management PN-1 مهندسی مجدد فرآیندهای تجاری بخش دوم: مدلسازی فرآیندها به کمک Petri nets

2. /faculteit technologie management PN-2 Elements

3. /faculteit technologie management PN-3 Modeling problem

4. /faculteit technologie management PN-4 Modeling problem (1): Zero testing Transition t should fire if place p is empty. t ? p

5. /faculteit technologie management PN-5 Solution Only works if place is N-bounded t N input and output arcs Initially there are N tokens p p’

6. /faculteit technologie management PN-6 Modeling problem (2): Priority Transition t1 has priority over t2 t1 t2 ? Hint: similar to Zero testing!

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8. /faculteit technologie management PN-8 A bit of theory Extensions have been proposed to tackle these problems, e.g., inhibitor arcs. These extensions extend the modeling power (Turing completeness*). Without such an extension not Turing complete. Still certain questions are difficult/expensive to answer or even undecidable (e.g., equivalence of two nets). * Turing completeness corresponds to the ability to execute any computation.

9. /faculteit technologie management PN-9 High level Petri nets Extending classical Petri nets with color, time and hierarchy (informal introduction)

10. /faculteit technologie management PN-10 Limitations of classical Petri nets Inability to test for zero tokens in a place. Models tend to become large. Models cannot reflect temporal aspects No support for structuring large models, cf. top- down and bottom-up design

11. /faculteit technologie management PN-11 Inability to test for zero tokens in a place t ? p “Tricks” only work if p is bounded

12. /faculteit technologie management PN-12 Models tend to become (too) large Size linear in the number of products.

13. /faculteit technologie management PN-13 Models tend to become (too) large (2) Size linear in the number of tracks.

14. /faculteit technologie management PN-14 Models cannot reflect temporal aspects Duration of each phase is highly relevant.

15. /faculteit technologie management PN-15 No support for structuring large models

16. /faculteit technologie management PN-16 High-level Petri nets To tackle the problems identified. Petri nets extended with: –Color (i.e., data) –Time –Hierarchy For the time being be do not choose a concrete language but focus on the main concepts. Later we focus on a concrete language: CPN. These concepts are supported by many variants of CPN including ExSpect, CPN AMI, etc.

17. /faculteit technologie management PN-17 Running example: Making punch cards waiting patients served patients free desk employees patient/ employees

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21. /faculteit technologie management PN-21 Extension with color (1) Tokens have a color (i.e., a data value)

22. /faculteit technologie management PN-22 Extension with color (2) Places are typed (also referred to as color set). record Brand:string * RegistrationNo:string * Year:int * Color:string * Owner:string

23. /faculteit technologie management PN-23 Extension with color (3) The relation between production and consumption needs to be specified, i.e., the value of a produced token needs to be related to the values of consumed tokens. The value of the token produced for place sum is the sum of the values of the consumed tokens.

24. /faculteit technologie management PN-24 Running example: Tokens are colored

25. /faculteit technologie management PN-25 Running example: Places are typed

26. /faculteit technologie management PN-26 Running example: Initial state start is enabled

27. /faculteit technologie management PN-27 Running example: Transition start fired stop is enabled New value is created by simply merging the two records.

28. /faculteit technologie management PN-28 Running example: Transition stop fired New values are created by simply spliting the record into two parts.

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32. /faculteit technologie management PN-32 The number of tokens produced is no longer fixed (1) Note that the network structure is no longer a complete specification!

33. /faculteit technologie management PN-33 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.

34. /faculteit technologie management PN-34 Example Model as a colored Petri net.

35. /faculteit technologie management PN-35 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

36. /faculteit technologie management PN-36 Types color Product = string; color Number = int; color StockItem = record prod:Product * num:Number; color Stock = list StockItem; StockItem Stock

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