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arXiv · 2305.00187

On the sub-additivity of stochastic matching

Pascal Moyal·Ana Busic·Jean Mairesse
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Abstract

We consider a stochastic matching model with a general compatibility graph, as introduced in \cite{MaiMoy16}. We prove that most common matching policies (including FCFM, priorities and random) satisfy a particular sub-additive property, which we exploit to show in many cases, the coupling-from-the-past to the steady state, using a backwards scheme {\em \`a la} Loynes. We then use these results to explicitly construct perfect bi-infinite matchings, and to build a perfect simulation algorithm in the case where the buffer of the system is finite.

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Pascal Moyal, Ana Busic, Jean Mairesse. 2023-04-29. On the sub-additivity of stochastic matching. https://arxiv.org/abs/2305.00187

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