Delft University of Technology
Faculty Mechanical, Maritime and Materials Engineering Transport Technology / Logistic Engineering
H.C.J. Veelenturf Continue Petri-netten.
Literature survey, 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 state.
Nevertheless nets have their limitations and therefore various extensions have been made, such as -for example- timed 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 feasible situation.
An efficient algorithm is available for the computation of both firing speeds and functionning interval. Two cases can be considered while using this algorithm:
1. Transportation times are ignored. 2. Transportation times are modelled.
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.
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 same process.
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. Reports on Logistic Engineering (in Dutch)
