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arXiv · 2406.14376

Multicoloured Hardcore Model: Fast Mixing and Queueing

Sam Olesker-Taylor
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Abstract

We extend the hardcore model to a multicoloured version: a subset of vertices of a graph are coloured such that no vertex is adjacent to one of the same colour; uncoloured vertices do not constrain neighbours. This mathematically models multi-channel resource sharing, such as fibreoptic routing. We analyse certain simple Glauber-type dynamics on such configurations, and find conditions which ensure fast mixing. These dynamics model a queueing system: customers queue for service at vertices, who only serve customers whilst they are coloured in the underlying configuration; uncoloured vertices sit idle. The mixing estimates are applied to control queue lengths in equilibrium.

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Sam Olesker-Taylor. 2024-06-20. Multicoloured Hardcore Model: Fast Mixing and Queueing. https://doi.org/10.4230/lipics.aofa.2024.20

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