Stability analysis of a second-order delay-difference proportionally-fair rate allocation algorithm

A delay-difference second-order proportionally-fair rate allocation algorithm has been proposed. As, conventional proportionally-fair rate allocation algorithms deploy some form of scaled gradient ascent iterative algorithms for converging to the user optimal rates, using fast second-order algorithms such as Jacobi or approximate Newton methods can be considered as natural and good candidates for increasing the convergence speed of the rate allocation algorithm. Stability analysis related to scaled gradient ascent algorithms in the presence of propagation delays has been performed by some researchers such as R. Johari et al. in Cambridge. In the current paper, the stability conditions of a second-order Jacobi method in the presence of propagation delays with the simplifying premise of equality between all of the users' propagation delays is derived mathematically. Simulation results show that even in the general case of different propagation delays, while maintaining stability, the proposed method, outperforms the conventional ones in convergence speed.