# A stochastic matching model on hypergraphs

## TL;DR

This paper introduces a stochastic matching model on hypergraphs, extending previous graph-based models to hypergraph structures, and analyzes its stability across different hypergraph geometries for applications like supply chains and healthcare.

## Contribution

It extends existing graph matching models to hypergraphs and studies the stability of the resulting stochastic system in various hypergraph configurations.

## Key findings

- Model successfully extends to hypergraphs
- Stability conditions identified for different hypergraph geometries
- Applicable to diverse real-world systems like healthcare and supply chains

## Abstract

Motivated by applications to a wide range of assemble-to-order systems, operations scheduling, healthcare systems and collaborative economy applications, we introduce a stochastic matching model on hypergraphs, extending the model in [15] 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 by groups of two or more. We study the stability of this stochastic system, for various hypergraph geometries.