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Loynes construction for the extended bipartite matching

Pascal Moyal 1 Ana Bušic 2, 3 Jean Mairesse 4
2 DYOGENE - Dynamics of Geometric Networks
DI-ENS - Département d'informatique de l'École normale supérieure, CNRS - Centre National de la Recherche Scientifique : UMR 8548, Inria de Paris
Abstract : We propose an explicit construction of the stationary state of Extended Bipartite Matching (EBM) models, as defined in (Busic et. al., 2013). We use a Loynes-type backwards scheme similar in flavor to that in (Moyal et al., 2017), allowing to show the existence and uniqueness of a bi-infinite perfect matching under various conditions, for a large class of matching policies and of bipartite matching structures. The key algebraic element of our construction is the sub-additivity of a suitable stochastic recursive representation of the model, satisfied under most usual matching policies. By doing so, we also derive stability conditions for the system under general stationary ergodic assumptions, subsuming the classical markovian settings.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-01968565
Contributor : Ana Busic <>
Submitted on : Wednesday, January 2, 2019 - 7:40:28 PM
Last modification on : Friday, January 8, 2021 - 5:34:03 PM

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  • HAL Id : hal-01968565, version 1
  • ARXIV : 1803.02788

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Pascal Moyal, Ana Bušic, Jean Mairesse. Loynes construction for the extended bipartite matching. 2018. ⟨hal-01968565⟩

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