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.

中文翻译：

---

一般随机匹配模型的乘积形式

我们考虑由 Mairesse 和 Moyal (2016) 介绍的具有一般兼容性图的随机匹配模型。我们证明了系统稳定的自然必要条件对于自然的“先到先匹配”匹配策略也是充分的。为此，我们通过使用与 Adan、Bušić、Mairesse 和 Weiss (2018) 的二分匹配模型相关的原始动态可逆性属性，推导出显着乘积形式下的平稳分布。