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

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 $\mathrm{M}/\mathrm{M}/\infty$ queuing processes on the set of non-negative integers. Our approach is global in nature and yields the sharp constant.

7 pages

References in corpus (1)

• Sharp Li--Yau Inequalities for Dunkl Harmonic Oscillators