Introduction to Petri Nets

Places that are used to represent a system’s state through occupancy by tokens.  They are input and output points for transitions.  By tradition, circles or ovals are used in Petri diagrams to represent places.   A place may be occupied by one or many tokens at any point in time.  All nets must have a Start place and an End place.

Transitions are used to change a system’s state by consuming tokens from its input places and distributing new tokens to its output places.  In Petri diagrams they are represented by squares or rectangles.  Transitions contain triggers that become enabled when all of the transition’s input places become occupied with tokens.  When the trigger becomes enabled the transition can then fire.  The firing event depends on the type of trigger employed.  Automatic, manual and timed are the most common.

Arcs connect places and transitions.  They are directional and in diagrams are represented by arrows.  Inward arcs go from a place to a transition and an outward arc goes from a transition to a place.  Arcs may also contain a guard, which is a condition that must be passed before a token can be placed on it or consumed from it.  Arcs include a “weight” property that can be used to determine the number of tokens consumed or produced in a transition or to weight the token values.

Tokens infer process states from the places they occupy.  On diagrams they are usually symbolized by a solid circle or by a dot inside of a place’s symbol.  In higher-level Petri models (sometimes called Colored P-Nets) tokens are allow to possess properties.