Journal of the Operational Research Society

, Volume 49, Issue 3, pp 237–252

Rate control for communication networks: shadow prices, proportional fairness and stability

Theoretical Paper

DOI: 10.1057/palgrave.jors.2600523

Cite this article as:
Kelly, F., Maulloo, A. & Tan, D. J Oper Res Soc (1998) 49: 237. doi:10.1057/palgrave.jors.2600523


This paper analyses the stability and fairness of two classes of rate control algorithm for communication networks. The algorithms provide natural generalisations to large-scale networks of simple additive increase/multiplicative decrease schemes, and are shown to be stable about a system optimum characterised by a proportional fairness criterion. Stability is established by showing that, with an appropriate formulation of the overall optimisation problem, the network's implicit objective function provides a Lyapunov function for the dynamical system defined by the rate control algorithm. The network's optimisation problem may be cast in primal or dual form: this leads naturally to two classes of algorithm, which may be interpreted in terms of either congestion indication feedback signals or explicit rates based on shadow prices. Both classes of algorithm may be generalised to include routing control, and provide natural implementations of proportionally fair pricing.


ATM networkcongestion indicationelastic trafficInternetLyapunov functionproportionally fair pricingqueuesrouting

Copyright information

© Operational Research Society 1998

Authors and Affiliations

  1. 1.University of CambridgeUK