Multi-dimensional Petri Nets

Petri nets have become a mature modelling and analysis tool applicable in many application domains. Since the introduction of the Petri net concept in 1962 (Petri 14]), Petri nets have been investigated and applied by many researchers. Many extensions of the classical Petri net have been proposed. To model attributes, `colour' has been added. Time concepts have been added to describe the temporal behaviour of a system. In object-oriented Petri nets, tokens have a life-cycle and an identiication. The multi-dimensional Petri net model presented in this paper deals with these extensions in a unifying way. In this model an arbitrary number of dimension may be identiied, e.g. a `spatial dimension', a `time dimension', a `colour dimension', etc. This paper also discusses the relations between the multi-dimensional Petri net model and other Petri net based models. Multi-dimensional Petri nets can be analysed using traditional techniques. Moreover, it is possible to project a multi-dimensional Petri net onto a limited number of dimensions. By analysing the projected multi-dimensional Petri net we can deduce properties of the original multi-dimensional Petri net. Therefore , multi-dimensional Petri nets are also interesting from an analysis point of view.