Convexity properties of loss and overflow functions

Convexity properties of loss and overflow functions

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Article ID: iaor2004417
Country: Netherlands
Volume: 31
Issue: 2
Start Page Number: 95
End Page Number: 100
Publication Date: Mar 2003
Journal: Operations Research Letters
Authors: , ,
Abstract:

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 by Kumaran and Mandjes, 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.

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