We shall in this course model and analyze dynamic systems with the aid of Petri Nets.
According to Webster a system is "a complex unity formed of many often diverse parts subject to a common plan or serving a common purpose".
Examples of systems are:We may further state about systems that:
- a university
- a lecture event
- a collection of streets and traffic
- a vending machine
- they are associated with a specific goal or activity
- they are comprised of components (sub-systems) which interact
- some component activities occur concurrently or independently
- some component activities are linked in some way
- the interaction mainly defines system behavior
- they have some location, either physical or logical
A system consisting of a number of activities can be modeled by listing the pre- and post-conditions of the activities. The truth values of all conditions make up the state of the system. When an activity who's all pre-conditions are satisfied takes place the state of the system changes and new activities may be enabled and so on.A lecture event, seen from the professors point of view, consists of the activities: PREPARE (lecture), ENTER (lecture room), DELIVER (lecture), and LEAVE (lecture room). The pre-conditions for PREPARE are: UNPREPARED and IDLE (to prepare), and the post-conditions are: PREPARED and IDLE (for whatever).
It should be clear that from such a verbal description is not easy to get an overall understanding of the system. A system may be described graphically for easy communication between people. In this course we will make use of Petri Nets, originally proposed by Carl Adam Petri in his dissertation in 1962, for such descriptions. We could separate between PN Graphs (the graphical representation) and PN Structures (the mathematical representation) but as they are equivalent we may use Petri Nets for both.