2. Introduction
First Introduced by Carl Adam Petri in 1962.
A diagrammatic tool to model concurrency and synchronization in
distributed systems.
Used as a visual communication aid to model the system behavior.
Based on strong Mathematical foundation.
3. A Petri Net Specification…
Consist of three types of components:
Places (Circle), Transition (Rectangle) and arcs (arrows):
- Places represent possible states of the system;
Transitions are events or actions which cause the change of state; And
Every arc simply connects a place with a transition or a transition with a place.
5. What is a Petri Net Structure
A directed, weighted, bipartite graph
G=(V, E)
Nodes (V)
• Places (shown as circles)
• Transition (shown as rectangle)
Arcs (E)
• From a place to a transition or from a transition to a place.
• Labelled with a weight (a positive integer, omitted if it is 1)
6. Benefits of Petri Nets
1. Petri Nets have been applied mostly in manufacturing and safety-critical systems.
2. They are most suitable for modeling and analyzing the dynamics of concurrent systems
whose behavior could be described by finite sets of atomic processes and atomic states.
3. Petri nets often make it easier to understand the overall system they represent, because of
their graphical and precise nature of presentation.
4. Petri nets are equally suited for representation of hardware and software systems.
5. Petri nets possess inherent concurrency and parallelism which the asynchronous nature of
Petri nets makes them suitable for representing real
7. Properties
1. Liveness: Checking that all processes that are modeled can be executed.
2. Boundedness: Checking that there is no infinite accumulation of tokens in a place.
3. Place invariants: Identifying a set of places in which the total amount of tokens is constant.
4. Circuits: Flux conservation is achieved when the rate at which tokens are being produced equals
the rate at which tokens are being consumed.
5. T-Invariants: Identifying a set of transitions that have to fire from some initial marking to
return the PN to that marking.
6. Reachability: Deciding whether a certain marking (state) is reachable from another marking.
