Abstract
We describe a queuing model where service is allocated as a function of queue sizes. We consider allocations policies that are insensitive to service requirements and have a maximal stability region. We take a limit where the queuing model becomes congested. We study how service is allocated under this limit. We demonstrate that the only possible limit allocation is one that maximizes a proportionally fair optimization problem.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Walton, N.S. Insensitive, maximum stable allocations converge to proportional fairness. Queueing Syst 68, 51–60 (2011). https://doi.org/10.1007/s11134-011-9223-4
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DOI: https://doi.org/10.1007/s11134-011-9223-4