A stochastic matching model on hypergraphs

Motivated by applications to a wide range of areas, including assemble-to-order systems, operations scheduling, healthcare systems, and the collaborative economy, we study a stochastic matching model on hypergraphs, extending the model of Mairesse and Moyal (J. Appl. Prob.53, 2016) to the case of hypergraphical (rather than graphical) matching structures. We address a discrete-event system under a random input of single items, simply using the system as an interface to be matched in groups of two or more. We primarily study the stability of this model, for various hypergraph geometries.

A product form for the general stochastic matching model

We consider a stochastic matching model with a general compatibility graph, as introduced by Mairesse and Moyal (2016). We show that the natural necessary condition of stability of the system is also sufficient for the natural ‘first-come, first-matched’ matching policy. To do so, we derive the stationary distribution under a remarkable product form, by using an original dynamic reversibility property related to that of Adan, Bušić, Mairesse, and Weiss (2018) for the bipartite matching model.