Convexity properties of loss and overflow functions

Authors:
Krishnan Kumaran;Michel Mandjes;Alexander Stolyar
Affiliations:
Bell Labs/Lucent Technologies, 600 Mountain Ave., Murray Hill, NJ 07974, USA;CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands and Faculty of Mathematical Sciences, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands;Bell Labs/Lucent Technologies, 600 Mountain Ave., Murray Hill, NJ 07974, USA
Venue:
Operations Research Letters
Year:
2003

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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.