Convexity properties of loss and overflow functions


Kumaran, Krishnan and Mandjes, Michel and Stolyar, Alexander (2003) Convexity properties of loss and overflow functions. Operations Research Letters, 31 (2). pp. 95-100. ISSN 0167-6377

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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 (Queueing Systems 38 (2001) 471), 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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Copyright:© 2003 Elsevier
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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