Equilibria of a class of transport equations arising in congestion control

Authors:
Francois Baccelli;Ki Baek Kim;David R. Mcdonald
Affiliations:
INRIA-ENS, Département d'Informatique, Ecole Normale Supérieure, Paris cedex 05, France;INRIA-ENS, Département d'Informatique, Ecole Normale Supérieure, Paris cedex 05, France;Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Avenue, Ottawa, Canada K1N6N5
Venue:
Queueing Systems: Theory and Applications
Year:
2007

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Abstract

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.