A product form for the general stochastic matching model

We consider a stochastic matching model with a general compatibility graph, as introduced in \cite{MaiMoy16}. We show that the natural necessary condition of stability of the system is also sufficient for the natural matching policy ‘First Come, First Matched’ (FCFM). For doing so, we derive the stationary distribution under a remarkable product form, by using an original dynamic reversibility property related to that of \cite{ABMW17} for the bipartite matching model.