We show that the fluid loss ratio in a fluid queue with finite buffer $b$ and constant link capacity $c$ is always a jointly convex function of $b$ and $c$. This generalizes prior work [6] which shows convexity of the $(b,c)$ trade-off for large number of i.i.d. multiplexed sources, using the large deviations rate function as approximation for fluid loss. Our approach also leads to a simpler proof of the prior result, and provides a stronger basis for optimal measurement-based control of resource allocation in shared resource systems.

CWI. Probability, Networks and Algorithms [PNA]

Kumaran, K., Mandjes, M., & Stolyar, A. (2002). Convexity properties of loss and overflow functions. CWI. Probability, Networks and Algorithms [PNA]. CWI.