## 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.

## Abstract

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.

Google Scholar citations.

Frank Kelly's
papers