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

F. P. Kelly, A.K. Maulloo and D.K.H. Tan (Statistical Laboratory, University of Cambridge)

Journal of the Operational Research Society 49 (1998), 237-252.


This paper analyses the stability and fairness of two classes of rate control algorithm for communication networks. The algorithms provide natural generalizations to large-scale networks of simple additive increase/multiplicative decrease schemes, and are shown to be stable about a system optimum characterized by a proportional fairness criterion. Stability is established by showing that, with an appropriate formulation of the overall optimization problem, the network's implicit objective function provides a Lyapunov function for the dynamical system defined by the rate control algorithm. The network's optimization 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 generalized to include routing control, and provide natural implementations of proportionally fair pricing.

Keywords: ATM network, congestion indication, elastic traffic, Internet, Lyapunov function, proportionally fair pricing, queues, routing, tatonnement.

Available as pdf.

Further references on proportional fairness, and a review paper.

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