Real-Time Systems || Timed Petri Nets

✍ Scribed by Cheng, Albert M. K.

• Publisher: John Wiley & Sons, Inc.
• Year: 2002
• Weight: 171 KB
• Category: Article
• ISBN-13: 9780471224624
• DOI: 10.1002/0471224626.ch8

✦ Synopsis

TIMED PETRI NETS

Petri nets were developed as an operational formalism for specifying untimed concurrent systems. They can show concurrent activities by depicting control and data flows in different parts of the modeled system. As an operational formalism, a Petri net gives a dynamic representation of the state of a system through the use of moving tokens. The original, classical, untimed Petri nets have been used successfully to model a variety of industrial systems. More recently, time extensions of Petri nets have been developed to model and analyze time-dependent or real-time systems. The fact that Petri nets can show the different active components of the modeled system at different stages of execution or at different instants of time makes this formalism especially attractive for modeling embedded systems that interact with the external environment.

8.1 UNTIMED PETRI NETS

A Petri net, or place-transition net, consists of four basic components: places, transitions, directed arcs, and tokens. A place is a state the specified system (or part of it) may be in. The arcs connect transitions to places and places to transitions. If an arc goes from a place to a transition, the place is an input for that transition and the arc is an input arc to that transition. If an arc goes from a transition to a place, the place is an output for that transition and the arc is an output arc from that transition. More than one arc may exist from a place to a transition, indicating the input place's multiplicity. A place may be empty, or may contain one or more tokens. The state of a Petri net is defined by the number of tokens in each place, known as the marking and represented by a marking vector M. M[i] is the number of tokens in place i.