Convexity properties of loss and overflow functions

Krishnan Kumaran; M.R.H. Mandjes; Alexander Stolyar

doi:10.1016/S0167-6377(02)00191-8

Convexity properties of loss and overflow functions

Krishnan Kumaran, M.R.H. Mandjes, Alexander Stolyar

Stochastic Operations Research

Research output: Contribution to journal › Article › Academic › peer-review

12 Citations (Scopus)

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.

Original language	English
Article number	10.1016/S0167-6377(02)00191-8
Pages (from-to)	95-100
Number of pages	6
Journal	Operations research letters
Volume	31
Issue number	2
DOIs	https://doi.org/10.1016/S0167-6377(02)00191-8
Publication status	Published - Mar 2003

Keywords

METIS-212731
IR-70723
Queueing Theory
Trade-off between network resources
Large deviations
EWI-17776

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AU - Kumaran, Krishnan

AU - Mandjes, M.R.H.

AU - Stolyar, Alexander

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N2 - 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.

AB - 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.

KW - METIS-212731

KW - IR-70723

KW - Queueing Theory

KW - Trade-off between network resources

KW - Large deviations

KW - EWI-17776

U2 - 10.1016/S0167-6377(02)00191-8

DO - 10.1016/S0167-6377(02)00191-8

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SP - 95

EP - 100

JO - Operations research letters

JF - Operations research letters

SN - 0167-6377

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