A General Stochastic Matching Model On Multigraphs

We extend the general stochastic matching model on graphs introduced in Mairesse and Moyal (2016), to matching models on multigraphs, that is, graphs with self-loops. The evolution of the model can be described by a discrete time Markov chain whose positive recurrence is investigated. Necessary and sufficient stability conditions are provided, together with the explicit form of the stationary probability in the case where the matching policy is 'First Come, First Matched'.