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 | Real-Time Systems Scheduling Analysis and Verification. Albert M. K. Cheng Copyright 2002 John Wiley Sons Inc. ISBN 0-471-18406-3 CHAPTER 8 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. 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. 212 UNTIMED PETRI NETS 213 Graphically circles denote places bars represent transitions arrows denote arcs and heavy dots .
