Stability of Multi-Path Dual Congestion Control Algorithms

This paper investigates fair, scalable, stable congestion controls which achieve high bandwidth utilization over networks operating multi-path routing. It aims to take advantage of path diversity to achieve efficient bandwidth allocation without causing instability. We develop a multi-path extension to the dual algorithm, which takes into consideration path diversity when evaluating fairness. This algorithm is shown to be globally stable in the absence of propagation delays and a sufficient condition for local stability, for the case when heterogeneous propagation delays are present, is found. The sufficient condition we present is decentralized in the following sense: the gain parameter for each dynamic variable is restricted by the average round-trip time of packets passing through the link or source it represents, but not by the round-trip times of any other packets. This leads to a highly scalable parameter choice scheme. Gain parameters are calculated from local information which is independent of the state of the algorithm, and our delay stability condition is satisfied. The models considered apply to networks consisting of arbitrary interconnections of sources and links with arbitrary heterogeneous propagation delays.