Report 92.3.LT.3002, Transport Technology, Logistic Engineering.
Several methods are available for modelling and analyzing discrete event
systems. Since C.A. Petri published his dissertation "Kommunikation
mit Automaten", a new method has been developed: Petri-nets.
Petri-nets are composed of places and transitions, which are connected to
eachother by arcs. Places may contain tokens, which flow through
the net. The distribution of tokens over the places is called marking or
Nevertheless Petri-nets have their limitations and therefore
various extensions have been made, such as -for example- timed Petri-nets
and colored Petri-nets. None of these extensions proved to be useful for
the modelling of systems with a large number of identical items, which all
pass the same process. The large number of items leads to an exponential
increase of reachable states of the system. This results in long
computation times. As a solution to this problem a new extension has been
developped: continuous Petri-nets.
The main difference between ordinary Petri-nets and continuous Petri-nets
lies in the definition of the state of the system. In ordinary Petri-nets the
state of the system is defined as the distribution of tokens over the places.
In continuous Petri-nets this definition is replaced by: the distribution of
firing speeds over the transitions. The firing speeds remain constant during a
certain time interval. This results in a limited number of states, thus a
An efficient algorithm is available for the computation of both firing speeds
and functionning interval. Two cases can be considered while using this
Current literature concerning the use of Petri-nets in industrial situations
shows only a few publications about continuous Petri-nets. A recent development
is the use of continuous Petri-nets to approximate timed Petri-nets.
- Transportation times are ignored.
- Transportation times are modelled.
It can be concluded that:
- Continuous Petri-nets provide a good method to restrict the number of
states in a situation with a large number of items, which all pass the
- An efficient algorithm is available to work with continuous Petri-nets.
- The use of continuous Petri-nets is extended to the approximation of timed
Petri-nets. The use of color forms also a potential extension of the
application field of continuous Petri-nets. The continuous Petri-net theory
doesn't exclude the use of color; however, at this moment, no literature
on this topic available.
- There is almost no literature about continuous Petri-nets.
- There is no software for use with continuous Petri-nets.
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