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Modelling with Petri Net

Arcs in Petri Nets

The number of arcs (edges) Between two object specifies the number of token to be produced/consumed. Sometimes a number will be written to a single arc.

This can be used to model (dis)assembly process.

  • Current state: The configuration of tokens over the places
  • Reachable state: State reachable from the current state by firing a sequence of enable transitions

  • Deadlock state: State where no transition is enabled

  • Notation: (P1, P2, P3, P4, ...)

  • Example:
    alt text

High Level Petri Nets

Classical Petri nets have some modelling problems:

  • Too large too complex. (you can have sub-nets)
  • Takes too much time to model a given situation
  • Not possible to handle time and data (i.e. Time constraints in traffic light)

Therefore, we have extended it with:

  • Color: You can identify the tokens by the color. Therefore, color denotes the property associated with each token.
  • Time
  • Hierarchy



Extension with Color

Each transition has an formal or informal specification that specify:

  • The number of tokens to be produced
  • The value (property) of these tokens. i.e. the output token equals sum of two inputs
  • Optionally, precondition. The 'if' statement for the output value. alt text

Extension with Time

In order to analyst performance, we must model the Duration And delay.

The value of time tells us the minimum and maximum time that a transition will take to fire after enabled.

This allows us to model performance property of the system.

alt text

Extension with Hierarchy

A hierarchy is a mechanism to structure complex Petri Nets compared to data flow diagram.

A sub-Net is a net component, including sub places, sub transitions and other subnet.

This is the model of abstraction, Can reduce the capacity of the model.