Convexity properties of loss and overflow functions

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

Research output: Contribution to journalArticleAcademicpeer-review

14 Citations (Scopus)


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
Article number10.1016/S0167-6377(02)00191-8
Pages (from-to)95-100
Number of pages6
JournalOperations research letters
Issue number2
Publication statusPublished - Mar 2003


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


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