# PetriNets - 3 Net Models of Distributed Systems and...

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3 Net Models of Distributed Systems and Work f ows 3.1 INFORMAL INTRODUCTION TO PETRI NETS In 1962 Carl Adam Petri introduced a family of graphs, called Place-Transition (P/T), nets, to model dynamic systems [25]. P/T nets are bipartite graphs populated with tokens that f ow throughthe graph. A bipartite graph is one with two classes of nodes; arcs always connect a node in one class with one or more nodes in the other class. In the case of P/T nets the two classes of nodes are places and transitions ; arcs connect one place with one or more transitions or a transition with one or more places. To model the dynamic behavior of systems, the places of a P/T net contain tokens; F ring of transitions removes tokens from some places, called input places, and adds them to other places, called output places. The distribution of tokens in the places of a P/T net at a given time is called the marking of the net and re f ects the state of the system being modeled. P/T nets are very powerful abstractions and can express both concurrency and choice. P/T nets are used to model various activities in a distributed system; a transi- tion may model the occurrence of an event, the execution of a computational task, the transmission of a packet, a logic statement, and so on. The input places of a transition model the preconditions of an event, the input data for the computational task, the presence of data in an input buffer, the preconditions of a logic statement. The output places of a transition model the postconditions associated with an event, the results of the computational task, the presence of data in an output buffer, or the conclusions of a logic statement. P/T nets, or Petri nets (PNs), as they are commonly called, provide a very useful abstraction for system analysis and for system speci F cation, as shown in Figure 3.1. 137

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138 NET MODELS OF DISTRIBUTED SYSTEMS AND WORKFLOWS M; Petri Net Model of System S Modeling Translation MP; Model Properties SP; System Properties System Analysis Static Analysis of the Net Model Dynamic Analysis of the Net Model Remapping (a) Translation MP; Model Properties Dynamic Analysis of the Net Static Analysis of the Net (b) S; Real-life System M; Petri Net Description of a Software System S S; Software System Fig. 3.1 Applications of Petri nets. (a) PNs are often used to model complex systems that are dif f cult or impossible to analyze by other means. In such cases one may construct a PN model of the system, , then carry out a static and/or dynamic analysis of the net model and from this analysis infer the properties of the original system .I f is a software system one may attempt to translate it directly into a PN rather than build a model of the system. (b) A software system could be speci f ed using the PN language. The net description of the system can be analyzed and, if the results of the analysis are satisfactory, then the system can be built from the PN description.
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PetriNets - 3 Net Models of Distributed Systems and...

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