126.96.36.199 Petri Networks (PNET)
Petri Nets (PNET) are a modeling method based on a special network theory (developed by C.A. Petri). By means of PNET, event-driven (also not technical) systems with discrete parts and discrete local state transitions are with regard to its causal structure and dynamic (e. g. manufacturing system including control software, service system, communication system, real-time computer system). Particularly the concurrent, parallel processes and its corresponding synchronizations can be exactly specified by means of a unique representation of its causal relations. A special characteristic of the PNET is its dynamic notation of the timewise actual filling of places (marking by tokens).
The strong points of PNET are:
- The appropriateness for the behavior modeling of high complex, high distributed (sub-) systems with many but simply functioning parts-in particular when including an environment which is also event-oriented,
- easy corrections and upgrades because of the simple notation and the concept of the fusion of several networks,
- possibility for hierarchical refinement of individual components by taking into consideration certain consistency rules,
- precise specification with simple semantics,
- unique representation of the causal relations, in particular in the case of concurrent processes (conflicts, deadlocks, etc. are detected and can be solved by means of simple network changes),
- explicit representation of the dynamic by means of tokens,
- possibility to model both asynchronous and synchronous communication,
- the mathematical foundation of the PNET (network theory) makes a correct assessment of the network models possible for important operational characteristics (deadlocks, livelocks, reachability, invariants, etc.).
Peculiarities to be taken into consideration when modeling with PNET:
- In very large PNETs, it is important to decompose into subnets at an early stage in order to make the specification easier to understand.
When modeling with PNET, the availability of a library containing network representations of frequently used function types with exactly defined characteristics is a great help (e. g. for access, synchronization, lock, conflict solution mechanisms, etc.).
- Learning the notation including the semantics is easy. Modeling complex systems with PNET requires training.
The method is applied in SD1.5 - User-Level System Structure and SD3.3 - Definition of Requirements for the Functionality in order to model the courses of functions.
Support by a tool, data flow diagrams can be transformed into to Petri Nets that can be analyzed. The user changes processes into transitions by means of graphical identification, and via an additional labeling of the arrows in the data flow diagram; he can insert places between the transitions. The data flow diagram thus prepared is transferred to a PNET-based tool for further processing (analysis, simulation). This way, a dynamic consistency assessment is possible for data flow diagrams.
- The tool support for PNET is definitely required in connection with modeling and analysis of large (sub-) systems in order to utilize the advantages of the method. A whole number of such tools is available.
According to /Graubmann, 85/ and /Grabowski, 90/, automata represented by Specification and Description Language (SDL) can be transformed into Petri Nets and may then be analyzed with regard to deadlocks and other dynamic characteristics. Petri Nets resulting from an automatic transformation with Specification and Description Language (SDL) can also be embedded into existing subnets within the scope of a total design.
Apart from the most simple PNET form-the condition/transition nets-there are several other versions. A simple upgrade are the place/transition nets where each place may have several similar tokens which can be transported even in various numbers while a transition is switched. Even very complex systems can be easily specified with this PNET. Time-related PNETs allow the definition of time delays for the switching and thus a detailed specification of a system. The most powerful form of PNET are the predicate/transition nets. In this connection, there are various so-called individual tokens that may fill a place in a mixed way. When switching, they are transported by the arrows in different combinations. This and additional switching conditions are described by predicates. In case of real-time systems this refers to the local storage and the controlled exchange of data that are specified on a high abstraction level. The causal process model of the PNET is effectively completed by these possibilities.
Other publications on Petri-Nets
||generally oriented introduction into Petri Nets with several examples
||representation of the principles required for the transformation of SDL diagrams into Petri Nets
||tool-oriented representation of the validation of SDL diagrams via transformation into Petri Nets
||introduction into the design with Petri Nets
||mathematically oriented introduction into the basics of Petri Nets with proofs; standard and reference documentation
Last Updated 29.May.2002
Updated by Webmaster
Last Revised 29.May.2002
Revised by Webmaster