Compositional high level Petri nets with timing constraints - a comparison

We aim at comparing various timed extensions of a fully compositional class of high-level Petri nets, called M-nets. On one hand, as a classical approach, a class of timed M-nets is considered, where intervals of duration are attached to each transition. More precisely, we study this class enriched by the recently introduced hierarchical operation of timed refinement. On the other hand, M-nets enriched by the causal time concept (H. Klaudel et al., 1999); Franck Pommereau, 2002) are considered, they are called causal time M-nets and allow us to introduce timing constraints without extending the original untimed model of M-nets. Causal time M-nets are shown to form the more powerful class. It covers timed and even hierarchical timed M-nets. Moreover, as shown by some significant examples, it permits the modelling of systems involving overlapping timing constraints. Some special cases are quoted where hierarchical timed M-nets may become favorite.