发表机构
Inria and DI ENS, École Normale Supérieure PSL University（法国国家信息与自动化研究所与巴黎高等师范学院PSL大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究超图随机匹配中代理弃权（不执行）对稳定性的影响，发现稳定性敏感依赖于弃权机制，并提出新的稳定机制及MaxWeight型策略，给出稳定性判据。
AI 中文摘要
在许多现实生活中的匹配问题中，等待的代理可能在匹配之前放弃，例如患者在接受器官之前死亡，乘客/司机取消乘车请求，或原材料/中间产品在生产线上变质。这提出了在随机匹配模型中纳入弃权（不执行）的需求。在这项工作中，我们考虑具有批量到达和一般权重匹配的超图上的匹配模型。由于我们的模型允许分数权重，我们可能无法谈论单个项目，因此同一类别的项目之间的弃权（不执行）不要求是独立的。为了简单起见，我们假设项目在离散时间到达。我们表明，稳定性取决于弃权（不执行）的确切性质，这与无弃权（不执行）情况形成鲜明对比，在无弃权（不执行）情况下，稳定性仅通过到达率依赖于到达过程。据我们所知，这是随机匹配中第一个这样的敏感性结果。我们发现了一种新的稳定机制，该机制既不存在于无弃权（不执行）情况，也不存在于图情况，这解释了为什么在随机匹配中纳入弃权（不执行）并非直截了当。结合无弃权（不执行）情况下在线分配框架中提示的平衡机制，它给出了稳定性的充分必要条件。最后，虽然验证稳定性是一个难题，但我们给出了一族由 $\varepsilon > 0$ 参数化的 MaxWeight 型策略，对于所有足够小的 $\varepsilon$，这些策略是最大程度稳定的。不幸的是，没有有效的 $\varepsilon$ 界限，但我们展示了如何在实现过程中调整其值。
英文摘要
In many real-life matching problems, waiting agents might abandon before being matched, such as patients deceasing before receiving organs, passengers/drivers cancelling ride requests, or raw materials/intermediary products degrading in production lines. This poses the need for incorporating reneging in stochastic matching models. In this work, we consider matching models on hypergraphs with batch arrivals and general-weight matchings. Since our model allows fractional weights, we may not be able to talk about individual items, and thus reneging is not required to be independent between items of the same class. For the simplicity sake's, we assume items arrive at discrete time. We show that stability depends on the exact nature of reneging, in stark contrast with the non-reneging case where it depends on the arrivals only through the arrival rates. To our best knowledge, this is the first such sensitivity result in stochastic matching. We uncover a new stabilising mechanism which exists neither in the non-reneging case nor in the graph case, which explains why incorporating reneging in stochastic matching is not straightforward. Together with balancing mechanism as hinted in the online assignment framework for the non-reneging case, it gives a criterion necessary and sufficient for stability. Finally, whilst verifying stability is a hard problem, we give a family of MaxWeight-type policies parameterised by $\varepsilon > 0$, which are maximally stabilising for all $\varepsilon$ sufficiently small. Unfortunately there is no effective bound for $\varepsilon$, but we show how to adjust its value during implementation.
Comments43 pages
