evaluation net (E-Net)

Timed Petri nets are a special form of Petri nets 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) and thus enable their use in simulation. In the context of time-based Petri nets, they are also referred to as higher- level nets.

The examination of real systems has shown that with the original Petri nets neither the times for the processing of processes can be represented nor data-dependent decisions are possible. These limitations are removed by abandoning the mathematical treatability by the introduction of the so-called evaluation nets (E-nets) and thus the possibility for modeling and simulation of complex systems is created.

An evaluation net model consists of two main parts:

• the evaluation net 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 network is always composed of the following basic elements:

• the tokens, which represent the moving model objects with their specific properties ( token attributes),
• the places, in each case at most one mark can be located
• and the transitions, which represent the processes by which the tokens - the model objects - undergo changes in their properties and with respect 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 switching transitions.

A place is used to locate 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" by a directed edge with that transition to which this input 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 describing the change of the marker attributes when switching the transition
• and a process time describing the time needed to execute the model activity.

With the so-called conflict transitions a decision procedure is added additionally. 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 the conflict transitions, the transport of the tokens is influenced in its direction according to the determination found by evaluation of the decision rule.