On the modelling of the dynamical behaviour of weighted T-systems

The dynamic behaviour of the Petri nets which are simple event graphs may be totally evaluated with a set of deterministic equations in the algebra (min, +). In this paper we are interested in the evaluation of the dynamic comportement of the Petri nets which are weighted graphs. We propose, in this case, a new algebraic structure (min, div) which provides an original technique of representation, in particular for important classes of application of this graph for which it is possible to linearise the mathematical model which describes their behaviour.