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arXiv · 2504.18801

Semi-log-convexity of ${\rm M}/{\rm M}/\infty$ queues on $\mathbb{Z}_+$

Huige Chen·Huaiqian Li
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Abstract

We solve the problem left in the recent paper by N. Gozlan et al [Potential Analysis 58, 2023, 123--158], establishing the semi-log-convexity of semigroups associated with ${\rm M}/{\rm M}/\infty$ queuing processes on the set of non-negative integers. Our approach is global in nature and yields the sharp constant.

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Huige Chen, Huaiqian Li. 2025-04-26. Semi-log-convexity of ${\rm M}/{\rm M}/\infty$ queues on $\mathbb{Z}_+$. https://doi.org/10.1016/j.spl.2025.110432

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