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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.14376 |
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| _version_ | 1866914876170960896 |
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| author | Olesker-Taylor, Sam |
| author_facet | Olesker-Taylor, Sam |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14376 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multicoloured Hardcore Model: Fast Mixing and Queueing Olesker-Taylor, Sam Probability Discrete Mathematics 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. |
| title | Multicoloured Hardcore Model: Fast Mixing and Queueing |
| topic | Probability Discrete Mathematics |
| url | https://arxiv.org/abs/2406.14376 |