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evaluation net (E-Net)

Timed Petri nets are a special form of Petri n ets and are called E-nets, or evaluation nets. In contrast to conventional Petri nets, they take time-related aspects into account when switching transitions (transitions), thus enabling their use in simulation

. In the context of timed Petri nets, they are also referred to as higher-level nets. The examination of real systems has shown that original Petri nets can neither be used to represent the times for the processing of processes

nor can data-dependent decisions be made.These limitations, while abandoning mathematical treatability, are removed by the introduction of the so-calledevaluation

nets (E-nets), thus making it possible to model and simulate complex systems.An evaluation net model consists of two main parts

:

  • the evaluation network itself, which describes the functional properties of the system to be modeled, and
  • a descriptive part for the formal description of the procedural properties of transitions.
An evaluation net is always constructed from the following basic elements:

  • the tokens, which represent the moving model objects with their specific properties (token attributes),
  • the locations, in each of which at most one marker can be located.
  • and the transitions, which represent the processes through which the tokens - the model objects - undergo changes in their properties and in relation to their directions in the network.
A mark consists of a - possibly empty - set of parameters, the so-called object and mark attributes. It is used to realize objects of a system whose properties are described by the marker attributes. These marker attributes are modified accordingly when the transitions are switched.

A location is used to localize markers and as a connecting element between transitions. A place can contain at most one mark; thus, evaluation networks are safe by definition. A place is always connected in "forward-direction" via a directed edge with that transition, to which this entry-place is.

A transition is described by:

  • the corresponding graphic symbol to represent the logic of the marker transport when switching the transition
  • a process part that describes the change of the marker attributes when switching the transition
  • and a process time that describes the time required to execute the model activity.
In the case of the so-called conflict transitions, a decision procedure is added. This realizes - if necessary in dependence on the mark attributes - a direction value, by which the mark transport is influenced in its direction.

A transition becomes active, if its type-specific as well as with the conflict transitions its procedural switching condition (decision rule) is fulfilled.

When this condition occurs, the process time assigned to the transition is determined and started. After the process time has elapsed, the transition switches. In this process, the tokens are moved from the pre-positions to the post-positions according to the switching rule of the respective transition type and the token attributes are changed according to the rules defined in the process part. In case of conflict transitions, the transport of the tokens is influenced in its direction according to the determination found by evaluating the decision rule.

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Englisch: evaluation net - E-Net
Updated at: 03.11.2013
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Translations: DE