A product form for the general stochastic matching model

TL;DR

This paper proves that the stability condition for a general stochastic matching model with FCFS policy is both necessary and sufficient, providing a product-form stationary distribution through a novel reversibility approach.

Contribution

It establishes the sufficiency of the stability condition for the general model and derives a product-form stationary distribution using a new reversibility property.

Findings

Stability condition is both necessary and sufficient for the model.

Derived a product-form stationary distribution for the system.

Introduced an original reversibility property related to the matching model.

Abstract

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.