{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/stability-and-instability-of-the-maxweight","title":"Stability and Instability of the MaxWeight Policy","arxiv_id":"1909.10825","date":"2019-09-24","proceeding":null,"authors":["Maury Bramson","Bernardo D'Auria","Neil Walton"],"abstract":"Consider a switched queueing network with general routing among its queues. The MaxWeight policy assigns available service by maximizing the objective function $\\sum_j Q_j \\sigma_j$ among the different feasible service options, where $Q_j$ denotes queue size and $\\sigma_j$ denotes the amount of service to be executed at queue $j$. MaxWeight is a greedy policy that does not depend on knowledge of arrival rates and is straightforward to implement. These properties, as well as its simple formulation, suggest MaxWeight as a serious candidate for implementation in the setting of switched queueing networks; MaxWeight has been extensively studied in the context of communication networks. However, a fluid model variant of MaxWeight was shown by Andrews--Zhang (2003) not to be maximally stable. Here, we prove that MaxWeight itself is not in general maximally stable. We also prove MaxWeight is maximally stable in a much more restrictive setting, and that a weighted version of MaxWeight, where the weighting depends on the traffic intensity, is always stable.","url_abs":"https://arxiv.org/abs/1909.10825v2","url_pdf":"https://arxiv.org/pdf/1909.10825v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"stability-and-instability-of-the-maxweight","repo_url":"https://github.com/brdauria/simulation_of_unstable_MaxWeigth_networks","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}