Proportionally fair pricing: dynamics, stability and pathology
J.E. Carroll, P.A. Kirkby · IEE Proceedings - Communications · 2000
A potential key to the future control on the Internet of high quality-of-service traffic is dynamic pricing of bandwidth allocations, with ‘proportional fairness’ as one attractive possibility. For the first time to the authors' knowledge, ‘small-changes’ and complex frequency-domain techniques (as used in classical control theory) are used to study dynamics of the relationships between bid-prices, proportionally fair bandwidth allocations and resource prices; instability, stability and convergence rates; integration from one (approximate) solution to another (accurate) solution allowing assessment of stability of major changes of traffic on the network; how coalitions of customers might distort the market by changing their bids but not getting any change in their allocation of bandwidth. Both standard proportional fairness and price-limited proportional fairness are discussed; the latter having floor prices for the resources. These prevent large unwanted allocations of bandwidth that may be needed at a later time; provide a smooth transition between low and high demands and greatly speed up dynamic allocations at low utilisation.