Petri Nets

Petri Nets (PN's) is a formal and graphical appealing language which is appropriate for modeling systems with concurrency. PN's has been under development since the beginning of the 60'ies, when Carl Adam Petri defined the language. It was the first time a general theory for discrete parallel systems was formulated. Description of a PN model. The language is a generalization of automata theory such that the concept of concurrently occurring events can be expressed. PN model is oriented to the description of both states of a system and actions producing evolution through the states. In this sense, it differs from other formal models of concurrent systems which usually are state-based or action-based. PN's treat states and actions on equal footing. In fact, the structure of a PN can be seen as a bipartite graph whose two different kind of nodes, places and transitions, correspond with states and actions of the system. Certain similarity with queueing models can be observed at this point. Storage rooms and service stations of queueing networks represent also states and actions, respectively. In queueing models the state of the system is represented by means of a given distribution of customers at storage rooms (queues). In an analogous way, a marking or distribution of tokens (marks) over the places of the PN defines the state of the system. Therefore, as for queueing networks, the representation of a state is distributed (see Figure 1.a). The behavior of a queueing network is governed by the departures of customers from stations, after finishing service, and the movement towards other storage rooms. The token game is the analogue in PN models. Tokens are stored at places and the firing of a transition produces a change of the distribution of tokens or new marking (see Figure 1.b). Adequacy of the paradigm. The first main property of PN models for the description of concurrent systems is its simplicity. A very few and simple mathematical entities are necessary for the formal definition of nets. This fact constitute a great advantage, mainly in the modeling of concurrent systems which are enough complicated per se. In spite of the simplicity of the model, its generality must be remarked. The three basic schemes in the modeling of concurrent systems can be included in the PN structure: sequencing, choice, and concurrency. Moreover, other typical and well-known elements in the modeling of distributed systems, as rendezvous , shared resources, …