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Published byJacob Heidrich Modified over 5 years ago
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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.
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Elements
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Modeling problem
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Modeling problem (1): Zero testing
Transition t should fire if place p is empty. ? t p
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Initially there are N tokens
Solution Only works if place is N-bounded t Initially there are N tokens N input and output arcs p’ p
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Modeling problem (2): Priority
Transition t1 has priority over t2 t1 ? t2 Hint: similar to Zero testing!
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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.
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High level Petri nets Extending classical Petri nets with color, time and hierarchy (informal introduction)
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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
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Inability to test for zero tokens in a place
? t p “Tricks” only work if p is bounded
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Models tend to become (too) large
Size linear in the number of products.
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Models tend to become (too) large (2)
Size linear in the number of tracks.
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Models cannot reflect temporal aspects
Duration of each phase is highly relevant.
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No support for structuring large models
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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.
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Running example: Making punch cards
free desk employees waiting patients served patients patient/ employees
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Extension with color (1)
Tokens have a color (i.e., a data value)
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Extension with color (2)
Places are typed (also referred to as color set). record Brand:string * RegistrationNo:string * Year:int * Color:string * Owner:string
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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.
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Running example: Tokens are colored
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Running example: Places are typed
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Running example: Initial state
start is enabled
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Running example: Transition start fired
New value is created by simply merging the two records. stop is enabled
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Running example: Transition stop fired
New values are created by simply spliting the record into two parts.
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