A Global Stability Result in Utility-Based Congestion Control

In this paper, we introduce a new utility-based congestion control algorithm, M-REM (modified-REM), and show its convergence. The algorithm is a slight modification of the so-called REM (random exponential marking) gradient projection algorithm, in which all buffers in the network are cleared when equilibrium source rates are reached. By defining the "price" of a particular link as a weighted sum of the Lagrange multiplier and buffer length associated with that link, we show that M-REM is globally asymptotically stable, while preserving the decentralized nature of REM.