We study the performance of general dynamic matching models. This model is defined by a connected graph, where nodes represent the class of items and the edges the compatibilities between items. Items of different classes arrive one by one to the system according to a given probability distribution. Upon arrival, an item is matched with a compatible item according to the First Come First Served discipline and leave the system immediately, whereas it is enqueued with other items of the same class, if any. We show that such a model may exhibit a non intuitive behavior: increasing the services ability by adding new edges in the matching graph may lead to a larger average population. This is similar to a Braess paradox. We first consider a quasicomplete graph with four nodes and we provide values of the probability distribution of the arrivals such that when we add an edge the mean number of items is larger. Then, we consider an arbitrary matching graph and we show sufficient conditions for the existence or non-existence of this paradox. We conclude that the analog to the Braess paradox in matching models is given when specific independent sets are in saturation, i.e., the system is close to the stability condition.

中文翻译：

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灵活性会损害动态匹配系统的性能

我们研究了一般动态匹配模型的性能。该模型由连通图定义，其中节点表示项目的类别，边表示项目之间的兼容性。不同类别的物品按照给定的概率分布一个一个地到达系统。到达后，根据先到先得规则将一个项目与兼容项目匹配并立即离开系统，而如果有的话，它会与同级别的其他项目一起排队。我们表明，这样的模型可能表现出非直观行为：通过在匹配图中添加新边来增加服务能力可能会导致更大的平均人口。这类似于布雷斯悖论。我们首先考虑一个具有四个节点的拟完全图，我们提供到达概率分布的值，这样当我们添加一条边时，项目的平均数量更大。然后，我们考虑一个任意匹配图，并展示了这个悖论存在或不存在的充分条件。我们得出结论，当特定的独立集合处于饱和时，即系统接近稳定条件时，匹配模型中的 Braess 悖论的类比是给出的。