Convergence of REM flow control at a single link

Various TCP congestion control schemes can be interpreted as approximately carrying out a certain basic algorithm to maximize aggregate source utility, different schemes corresponding to different choices of utility functions. The basic algorithm consists of a link algorithm that updates a congestion measure based on its traffic load, and a source algorithm that adapts the source rate to congestion in its path. Though convergent, this algorithm can lead to large equilibrium backlogs. This problem can be eliminated by modifying the basic algorithm to include backlog in the update of the congestion measure. This article proves that the modified algorithm converges when the network can be modeled as a single bottleneck link. Moreover, in equilibrium, the source rates are matched to the link capacity while the buffer is cleared.