Petri Net
A Petri net, also called a place-transition net, is a mathematical representation of concurrent systems--systems in which an activity of one component of the system can occur simultaneously with other component activities. Modeling of a system based on a Petri net can reveal information about the structure and behavior of that system.
Examples of concurrent systems are the dynamic structure of an atom, high-speed computers, air traffic control systems, chemical reactions, and economic systems. In a computer system, for example, peripheral devices, such as printers and tape drives may operate concurrently under the master control of the computer. In an economic system, manufacturers may be producing some products while retailers are selling other products, and customers are using still other products, all at the same time. In such concurrent systems, each component can be described independently of the other components, although interaction of the components is necessary for the functioning of the system as a whole. Each component also has its state of being, which can change with time.
This concurrent nature of activity makes modeling a challenge. The transfer of information or materials from one of the system components to another means that all component activities need to be synchronized while the transfer is occurring, although not necessarily before or after the time of transfer. Thus, one component may wait for the other. Other activities may occur in a random fashion. Describing such actions can be complex.
Petri nets were conceived by Carl Adam Petri in the 1960s to describe the complex activities of concurrent systems. Part of Petri's doctoral dissertation concerned the communication between components of computer systems. From his work came the basic concepts on which Petri net have developed.
In mathematical terms, a Petri net is a so-called four-tuple, consisting of a number of places (P, also the state of being of a component), an equal number of transitions (T, the change from one component state to another), an input function (IN) that defines the movement from one place to a transition (the beginning of a change of state of being), and an output function (OUT) that defines the movement from a transition to a place (the completion of a change in state). In a Petri net model, a place is denoted by a circle and a transition is denoted by a line.
Different arrangements of circles and lines are used to model various component activities, such as:
- sequential execution, where one transition requires the completion of a first transition
- conflict, where two component transitions are trying to occur but only one is acceptable
- concurrency, where component activities are occurring at the same time in a independent way
- synchronization, where component activities are occurring at the same time in a related way
- merging, where several transitions lead to the same place
- priorities, a sorting-out of transition event order so as to permit the overall system functioning to continue.
The power of Petri nets as an analytical modeling system has increased since the development of high-level Petri nets. Also known as Colored Petri nets, these permit very large models to be constructed, which can have separate but interconnected sub-models. Currently, an XML-based language called Petri net Markup Language is being developed to provide an information interchange format between Petri nets.
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