Infinite horizon optimal impulsive control with applications to Internet congestion control

Konstantin Avrachenkov*, Oussama Habachi, Alexey Piunovskiy, Yi Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


We investigate infinite-horizon deterministic optimal control problems with both gradual and impulsive controls, where any finitely many impulses are allowed simultaneously. Both discounted and long-run time-average criteria are considered. We establish very general and at the same time natural conditions, under which the dynamic programming approach results in an optimal feedback policy. The established theoretical results are applied to the Internet congestion control, and by solving analytically and nontrivially the underlying optimal control problems, we obtain a simple threshold-based active queue management scheme, which takes into account the main parameters of the transmission control protocols, and improves the fairness among the connections in a given network.

Original languageEnglish
Pages (from-to)703-716
Number of pages14
JournalInternational Journal of Control
Issue number4
Publication statusPublished - 3 Apr 2015

Bibliographical note

Funding Information:
This work was partially funded by INRIA Alcatel-Lucent Joint Lab, ADR ‘Semantic Networking’.

Publisher Copyright:
© 2015 Taylor & Francis.


  • infinite time horizon
  • Internet congestion control
  • long-run average and discounted criteria
  • optimal impulsive control
  • α-fairness

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications


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