.ExtendedPetriNets

Information

The standard Modelica library contains a sub-library PetriNet for modeling of discrete phenomena with Petri net formalism. It is designed for, and implements, black deterministic priority Petri nets, which are well suited e.g., for control system specification but can have rather limited expressiveness in other problem domains. Such may be in reliability engineering or in investigation of socio-technical aspects of complex technical systems.

Therefore, the Petri net library already available is extended to form a new library ExtendedPetriNet with

1. transitions allowing for deterministic or stochastic time delays before their firing (using builit-in random number generators BIRNG or custom made ones), and
2. places capable of containing more than one token,

Several modeling and simulation examples are given to demonstrate the usability of the enhancements - among them - queuing models and models to determine system availability, see the adjoned *.pdf document Petri_Net_Extensions.

For the time being, the extended library is currently structured in a manner that all extensions are clearly seperated from the original Petri net library. Three sub-packages have been added:

1. Extensions
2. Modules
3. ExamplesExtendedPetriNets.

Author:

Stefan Fabricius
Swiss Federal Institute of Technology (ETH)
Laboratory for Safety Analysis
Weinbergstrasse 11
8001 Zurich
Switzerland
email: fabricius@lsa.iet.mavt.ethz.ch

Release History and Notes:

• April 11th, 2002, Version 1.0
  

Copyright (C) 2002, with the author.

The ExtendedPetriNet library is free software; it can be redistributed and/or modified under the terms of the Modelica license, see the license conditions in the documentation to Modelica.

The library comes with absolutely no warranty. It has been carefully tested, yet, the absence of faults or bugs cannot be guaranteed.

Comments or bug reports are most welcome.

The PetriNets library allows to model discrete components by a special kind of Petri nets with at most one token on a place, as well as by state transition diagrams (which are special kinds of Petri nets). Petri nets and state transition diagrams are "higher level" constructs for the description of switching elements, parallel activities or syncronization. For several kinds of applications it is much easier and clearer to use these components instead of modeling the discrete behaviour directly with the basic language constructs of Modelica ("if" or "when" statements). A typical Petri net is shown in the following figure:

A Petri net is defined in the following way:

1. It consists of a set of places and of a set of transitions. The places are split into start places which are "active" at the start of the simulation and of "normal" places which are "non-active" at the beginning.
2. Places are connected by transitions, whereby no places and no transitions are directly connected (i.e., a place is connected to a transition which in turn is connected to another place). Any number of start places can be present.
3. An "active" place is characterized by a "token" placed on the place. In the ModelicaAdditions.PetriNets libray a place is "active" when the public variable "state" of the place is true.
4. There are several transition elements in the library. Whenever the states of all inputs to the transition elements are active and when the condition of the transition is true then the following actions are performed:
   • all input states are marked as "inactive", i.e., the token is removed.
   • all output states are marked as "active", i.e., they are marked by new tokens.
   The conditionPort connector of a transition element is used to signal via a Boolean signal whether the condition of a transition is true or false. Alternatively, the condition can be provided as an equation to set the public variable condition of the corresponding transition element.
5. There are several place components in this library (such as Place01, Place10, Place11) which have different number of input and output transition connectors. This is due to the current limitations of the annotations of Modelica, which do not allow to define the graphical location of the elements of a vector of (transition) connectors with unknown length.
6. If two or more transitions of a place would fire at the same time instant, priorities are used in order that exactly one of them fires. The highest priority has a transition connector of a place with the lowest index (e.g. outTransition1 has a higher priority as outTransition2).

The method used in this library to realize Petri nets in Modelica is described in detail in:

Mosterman P.J., Otter M. and Elmqvist H. (1998):

Modeling Petri-Nets as Local Constraint Equations for Hybrid Systems using Modelica. 1998 Summer Computer Simulation Conference (SCSC'98), Reno, U.S.A., 19.-20. Juli (download from here).

This package is not part of the Modelica standard library, because it is planned to realize a package with only one place and one transition component, once vector connectors with unknown length have better support in Modelica.

Main Author:

Martin Otter
Deutsches Zentrum für Luft und Raumfahrt e.V. (DLR)
Institut für Robotik und Mechatronik
Postfach 1116
D-82230 Wessling
Germany
email: Martin.Otter@dlr.de

Release Notes:

• June 12, 2000 by Martin Otter:
  Realized.

Copyright (C) 2000, DLR.

The ModelicaAdditions.PetriNets package is free software; it can be redistributed and/or modified under the terms of the Modelica license, see the license conditions and the accompanying disclaimer in the documentation of package Modelica in file "Modelica/package.mo".

Contents

Name	Description
Interfaces
Examples
Place01	Place with one output transition
Place10	Place with one input transition
Place11	Place with one input and one output transition
Place21	Place with two input and one output transition
Place12	Place with one input and two output transitions
Place22	Place with two input and two output transitions
Transition	Transition with one input and one output connection
Parallel	Transition with one input and two output connections
Synchronize	Transition with two input and one output connections
Modules
ExamplesExtendedPetriNets
Extensions