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Motivated by a wide range of assemble-to-order systems and systems of thecollaborative economy applications, we introduce a stochastic matching model onhypergraphs and multigraphs, extending the model introduced by Mairesse andMoyal 2016. In this thesis, the stochastic matching model$(\mathbb{S},\Phi,\mu)$ on general graph structures are defined as follows:given a compatibility general graph structure$\mathbb{S}=(\mathcal{V},\mathcal{S})$ which of a set of nodes denoted by$\mathcal{V}$ that represent the classes of items and by a set of edges denotedby $\mathcal{S}$ that allows matching between different classes of items. Itemsarrive at the system at a random time, by a sequence (assumed to be $i.i.d.$)that consists of different classes of $\mathcal{V}$, and request to be matcheddue to their compatibility according to $\mathbb{S}$. The compatibility bygroups of two or more (hypergraphical cases) and by groups of two withpossibilities of matching between the items of the same classes (multigraphicalcases). The unmatched items are stored in the system and wait for a futurecompatible item and as soon as they are matched they leave it together. Uponarrival, an item may find several possible matches, the items that leave thesystem depend on a matching policy $\Phi$ to be specified. We study thestability of the stochastic matching model on hypergraphs, for differenthypergraphical topologies. Then, the stability of the stochastic matching modelon multigraphs using the maximal subgraph and minimal blow-up to distinguishthe zone of stability.

Stochastic matching model on the general graphical structures