Convexity properties of loss and overflow functions

Krishnan Kumaran, Michel Mandjes, Alexander Stolyar

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)95-100
Number of pages6
JournalOperations Research Letters
Issue number2
StatePublished - Mar 2003
Externally publishedYes


  • Large deviations
  • Queueing theory
  • Trade-off between network resources

ASJC Scopus subject areas

  • Software
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Applied Mathematics


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