Queueing Systems

, Volume 55, Issue 1, pp 1–8 | Cite as

Equilibria of a class of transport equations arising in congestion control

  • Francois Baccelli
  • Ki Baek Kim
  • David R. McDonald


This paper studies a class of transport equations arising from stochastic models in congestion control. This class contains two cases of loss models as particular cases: the rate-independent case where the packet loss rate is independent of the throughput of the flow and the rate-dependent case where it depends on it. This class of equations covers both the case of persistent and of non-persistent flows. For the first time, we give a direct proof of the fact that there is a unique density solving the associated differential equation. This density and its mean value are provided as closed form expressions.


Density Stationary solutions ODE Uniqueness PDE Congestion control 


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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  • Francois Baccelli
    • 1
  • Ki Baek Kim
    • 2
  • David R. McDonald
    • 3
  1. 1.INRIA-ENS, Département d’InformatiqueEcole Normale SupérieureParis cedex 05France
  2. 2.INRIA-ENS, Département d’InformatiqueEcole Normale SupérieureParis cedex 05France
  3. 3.Department of Mathematics and StatisticsUniversity of Ottawa, 585 King Edward AvenueOttawaCanada

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