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**1. Introduction**

**Timed Petri Nets** 

http://dx.doi.org/10.5772/50117

José Reinaldo Silva and Pedro M. G. del Foyo

Additional information is available at the end of the chapter

that includes its dual part, is used

cited.

In the early 60's a young researcher in Darmstadt looked for a good representation for communicating systems processes that were mathematically sound and had, at the same time, a visual intuitive flavor. This event marked the beginning of a schematic approach that become very important to the modeling of distributed systems in several and distinct areas of knowledge, from Engineering to biologic systems. Carl Adam Petri presented in 1962 his PHD which included the first definition of what is called today a Petri Net. Since its creation Petri Nets evolved from a sound representation to discrete dynamic systems into a general schemata, capable to represent knowledge about processes and (discrete and distributed) systems according to their internal relations and not to their work domain. Among other advantages, that feature opens the possibility to reuse some experiences acquired in the design

**Chapter 16**

In the conventional approach, the key issue for modeling is the partial ordering among constituent events and the properties that arise from the arrangement of state and transitions once some basic interpretation rules are preserved. Such representation can respond from several systems of practical use where the foundation for analysis is based in reachability and other property analysis. However, there are some cases where such approach is not enough to represent processes completely, for instance, when the assumption that all transitions can fire instantaneously is no longer a good approximation. In such cases a time delay can be associated to firing transitions. This is absolutely equivalent (in a broader sense) to say that firing pre-conditions must hold for a time delay before the firing is completed. The first

Thus, what we have in conclusion is that even in a hypothesis that we should consider only firing pre-conditions1 [31][19] a time delay is associated with a transition location and consequently to its firing. Several applications in manufacturing, business, workflow and <sup>1</sup> In many text books and review articles the enabling condition is presented using only firing pre-conditions as a requirement. This can be justified since the use of this week firing condition is sufficient if a complete net, that is,

> ©2012 Silva and del Foyo, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly

©2012 Silva and del Foyo, licensee InTech. This is a paper distributed under the terms of the Creative CommonsAttribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

of known and well tested systems while treating new challenges.

approach is called T-time Petri Net and the second P-time Petri Nets.

