Quantitative analysis of continuous weighted marked graphs

This paper deals with the computation of the asymptotic firing rate vector and the stationary marking of continuous weighted marked graphs under infinite servers semantics. The continuous weighted marked graphs are a particular class of continuous Petri net where each place has exactly one input and one output transition. First, we give an explicit formula to compute the asymptotic firing rate vector of transitions using the structure of the given net. Then, under the assumption that there exists only one critical circuit in the strongly connected continuous neutral weighted marked graphs, an original approach to compute the vector of stationary marking is presented. Finally, an application to a flexible manufacturing system is given.