Convexity properties of loss and overflow functions

We show that the fluid loss ratio in a fluid queue with finite buffer and constant link capacity is always a jointly convex function of and . This generalizes prior work [6] which shows convexity of the 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. 2000 Mathematics Subject Classification: 60K25 (primary).